library(tidyverse)
## Warning: package 'ggplot2' was built under R version 4.0.4
library(openintro)
library(ggplot2)
library(plotrix)

Week 9 Lab: Looking at atheism survey and exploring what’s at play when making inference about population proportions using categorical data. Correct link for article: https://www.webpages.uidaho.edu/~stevel/251/Global_INDEX_of_Religiosity_and_Atheism_PR__6.pdf

# Insert code for Exercise 1 here

Exercise 1

Correct link for article: https://www.webpages.uidaho.edu/~stevel/251/Global_INDEX_of_Religiosity_and_Atheism_PR__6.pdf

In the first paragraph, several key findings are reported. Do these percentages appear to be sample statistics (derived from the data sample) or population parameters?

Answer* Most of the percentages appear to be sample statistics that are derived from the sample data as opposed to percentages from population percentages. The % findings outlined in the paragraph seem to be sample statistics. Had these been population percentages, they would have been conclusions drawn from the sample statistics and would relate to the entire population, or the population parameter.

Worth noting, I also looked for Greek letters (sigma, mu) in search of parameters; I looked for English letters to indicate statistics (x-bar; p-hat).

Paragraph 1: “Zurich, 27 July 2012 — We have no opinion polling data prior to the 20th century, but according to the latest global poll released by WIN-Gallup International, a world-wide network of leading opinion pollsters, atheists are a small minority in the early years of 21st century. Only 13% say they are atheists. They are mostly concentrated in East Asia where 47% of the Chinese and 31% of the Japanese say they are atheists; and Western Europe, 14% of whose population says the same. Elsewhere sizeable majorities claim to be religious; the global average is 59%. Another sizeable group claims to be “not-religious” but stops short of defining itself as “atheist”. Their global average is 23%." …

Exercise 2

The title of the report is “Global Index of Religiosity and Atheism”. To generalize the report’s findings to the global human population, what must we assume about the sampling method? Does that seem like a reasonable assumption?

Answer “Global” indicates this is an index of religiosity and atheism of the world population. To generalize findings, we must assume the sampling method used was random and representative across the entire world. In looking at the sample size and mode of field work (see snippet below), and thinking about it from a “reasonable assumption” perspective, it does not seem reasonable. If a sample of 1,000 was taken from each country, it seems there could be a problem with the sampling since there are population differences between large countries and small countries. The global index could be skewed if the countries aren’t represented proportionally in the sampling.

Sample Size and Mode of Field Work: A total of 51,927 persons were interviewed globally. In each country a national probability sample of around 1000 men and women was interviewed either face to face (35 countries; n=33,890), via telephone (11 countries; n=7,661) or online (11 countries; n=10,376).

#Go to Table 6 (pages 15 and 16), which reports the sample size and response percentages for all 57 countries. 
#While this is a useful format to summarize the data, we will base our analysis on the original data set of individual responses to the survey. #Load this data set into R with the following command.

download.file("http://www.openintro.org/stat/data/atheism.RData", destfile = "atheism.RData")
load("atheism.RData")
view(atheism)

Exercise 3

What does each row of Table 6 correspond to? What does each row of atheism correspond to?

Answer Table 6 shows the following:
1. Countries included in the polling (shows countries of the world that were included in the sample) 2. Sample size of each country (gives us indication of proportions) 3. Responses as a percentage for each country

Each row of the data set “atheism” corresponds to the following: 1. nationality (individual responses from each country) 2. response (as an atheist or non-atheist value as opposed to response percentages as seen in the table) 3. year (the year the response was gathered)

glimpse(atheism)
## Rows: 88,032
## Columns: 3
## $ nationality <fct> Afghanistan, Afghanistan, Afghanistan, Afghanistan, Afg...
## $ response    <fct> non-atheist, non-atheist, non-atheist, non-atheist, non...
## $ year        <int> 2012, 2012, 2012, 2012, 2012, 2012, 2012, 2012, 2012, 2...

Exercise 4

To investigate the link between these two ways of organizing this data, take a look at the estimated proportion of atheists in the United States. Towards the bottom of Table 6, we see that this is 5%. We should be able to come to the same number using the atheism data.

Using the command below, create a new dataframe called us12 that contains only the rows in atheism associated with resApondents to the 2012 survey from the United States. Next, calculate the proportion of atheist responses. Does it agree with the percentage in Table 6? If not, why?

Answer Calculated proportion of atheist responses = 0.0499002, which is approximately 5%. (see code chunks below) Percentage in table 6: 5% atheist responses of 1002 responses Yes, the calculated proportion of atheist responses agrees with the percentage in Table 6.

us12 <- subset(atheism, nationality == "United States" & year == "2012")
summary(us12)
##         nationality          response        year     
##  United States:1002   atheist    : 50   Min.   :2012  
##  Afghanistan  :   0   non-atheist:952   1st Qu.:2012  
##  Argentina    :   0                     Median :2012  
##  Armenia      :   0                     Mean   :2012  
##  Australia    :   0                     3rd Qu.:2012  
##  Austria      :   0                     Max.   :2012  
##  (Other)      :   0
#calculate proportion of atheist responses
#get number of us atheists
us_atheist <- nrow (us12[us12$response =="atheist",])
us_atheist
## [1] 50
#calculate proportion of atheist responses
#get number of us rows

us_rows <- nrow(us12)
us_rows
## [1] 1002
#calculate proportion of atheist responses
us_atheist/us_rows
## [1] 0.0499002

Exercise 5

Inference on proportions As was hinted at in Exercise 1, Table 6 provides statistics, that is, calculations made from the sample of 51,927 people. What we’d like, though, is insight into the population parameters. You answer the question, “What proportion of people in your sample reported being atheists?” with a statistic; while the question “What proportion of people on earth would report being atheists” is answered with an estimate of the parameter.

The inferential tools for estimating population proportion are analogous to those used for means in the last chapter: the confidence interval and the hypothesis test.

Write out the conditions for inference to construct a 95% confidence interval for the proportion of atheists in the United States in 2012. Are you confident all conditions are met?

Answer In the last chapter lab, we checked if the conditions necessary for inference were satisfied by obtaining sample sizes to check the conditions. We computed group size by using the by command as follows: by(nc\(weight, nc\)habit, length)

If the random (picked radomly across the country) sample size is less than 10% of the US population, the observations are independent - and this condition necessary for inference is satisfied as observations must be independent. In the us12 data set, there are 1,002 observations. This number of observations is significantly below 10% of the US population, so the observations are, in fact, independent.

In the US in 2012, the success/fail condition is satisfied:
Calc 1 - Population of 1,002 * 0.0499 = 50 Calc 2 - Population of 1,002 * 0.9500 = 952 Both calculations are greater than 10. The condition is met if there are at least 10 expected successes and 10 expected failures in the sample.

Expected number of successes is at least 10: np ≥ 10 Expected number of failures is at least 10: n(1-p) ≥ 10 where n is the sample size & p is the probability of success on a given trial.

I am confident all conditions are met.

#calculate proportion of non_atheist responses
#get number of us non-atheists
us_non_atheist <- nrow (us12[us12$response =="non-atheist",])
us_non_atheist
## [1] 952
#calculate proportion of non_atheist responses
us_non_atheist/us_rows
## [1] 0.9500998
#Success/fail condition satisfied:  Is the calculation greater than 10?

us_rows *(us_atheist/us_rows)
## [1] 50
#Success/fail condition satisfied:  Is the calculation greater than 10?

us_rows *(us_non_atheist/us_rows)
## [1] 952
#If the conditions for inference are reasonable, calculate the standard error and construct the interval using the inference function 
inference(us12$response, est = "proportion", type = "ci", method = "theoretical", 
          success = "atheist")
## Warning: package 'BHH2' was built under R version 4.0.4
## Single proportion -- success: atheist 
## Summary statistics:

## p_hat = 0.0499 ;  n = 1002 
## Check conditions: number of successes = 50 ; number of failures = 952 
## Standard error = 0.0069 
## 95 % Confidence interval = ( 0.0364 , 0.0634 )

Note that since the goal is to construct an interval estimate for a proportion, it’s necessary to specify what constitutes a “success”, which here is a response of “atheist”.

Although formal confidence intervals and hypothesis tests don’t show up in the report, suggestions of inference appear at the bottom of page 7: “In general, the error margin for surveys of this kind is ± 3-5% at 95% confidence”.

Exercise 6

Based on the R output, what is the margin of error, statistic expressing the amount of random sampling error in the results, for the estimate of the proportion of atheists in US in 2012?

Answer Copied/pasted summary statistics from ‘R Console’ output above: Summary statistics: p_hat = 0.0499 ; n = 1002 Check conditions: number of successes = 50 ; number of failures = 952 Standard error = 0.0069 95 % Confidence interval = ( 0.0364 , 0.0634 )

Calculated moE = 0.0135 (see code chunk below)

#find margin of error 
lower_boundary <- 0.0364
upper_boundary <- 0.0634
diff <- upper_boundary-lower_boundary
moE <- diff/2
moE
## [1] 0.0135

Exercise 7

Using the inference function, calculate confidence intervals for the proportion of atheists in 2012 in two other countries of your choice, and report the associated margins of error. Be sure to note whether the conditions for inference are met. It may be helpful to create new data sets for each of the two countries first, and then use these data sets in the inference function to construct the confidence intervals.

Answer If the random (picked radomly across the country) sample size is less than 10% of the countries (India and Poland) populations, the observations are independent - and this condition necessary for inference is satisfied as observations must be independent. In the india12 data set, there are 1,092 observations. This number of observations is significantly below 10% of India’s population, so the observations are, in fact, independent. In the poland12 data set, there are 525 observations. This number of observations is also significantly below 10% of Poland’s population, so the observations are also independent.

In India in 2012, the success/fail condition is satisfied:
Calc 1 - Population of 1,092 * 0.03021978 = 33 Calc 2 - Population of 1,092 * 0.9697802 = 1059 Both calculations are greater than 10. The condition is met if there are at least 10 expected successes and 10 expected failures in the sample.

Expected number of successes is at least 10: np ≥ 10 Expected number of failures is at least 10: n(1-p) ≥ 10 where n is the sample size & p is the probability of success on a given trial.

I am confident the conditions for inference are met.

In Poland in 2012, the success/fail condition is satisfied:
Calc 1 - Population of 525 * 0.04952381 = 26 Calc 2 - Population of 525 * 0.9504762. = 499 Both calculations are greater than 10. The condition is met if there are at least 10 expected successes and 10 expected failures in the sample.

Expected number of successes is at least 10: np ≥ 10 Expected number of failures is at least 10: n(1-p) ≥ 10 where n is the sample size & p is the probability of success on a given trial.

I am confident the conditions for inference are met.

moE for India = 0.01015

moE for Poland = 0.01855

#Create data sets for two additional countries
#India
india12 <- subset(atheism, nationality == "India" & year == "2012")
india12
##       nationality    response year
## 21654       India non-atheist 2012
## 21655       India non-atheist 2012
## 21656       India non-atheist 2012
## 21657       India non-atheist 2012
## 21658       India non-atheist 2012
## 21659       India non-atheist 2012
## 21660       India non-atheist 2012
## 21661       India non-atheist 2012
## 21662       India non-atheist 2012
## 21663       India     atheist 2012
## 21664       India non-atheist 2012
## 21665       India non-atheist 2012
## 21666       India non-atheist 2012
## 21667       India non-atheist 2012
## 21668       India non-atheist 2012
## 21669       India non-atheist 2012
## 21670       India non-atheist 2012
## 21671       India non-atheist 2012
## 21672       India non-atheist 2012
## 21673       India non-atheist 2012
## 21674       India non-atheist 2012
## 21675       India non-atheist 2012
## 21676       India non-atheist 2012
## 21677       India non-atheist 2012
## 21678       India non-atheist 2012
## 21679       India non-atheist 2012
## 21680       India non-atheist 2012
## 21681       India non-atheist 2012
## 21682       India non-atheist 2012
## 21683       India non-atheist 2012
## 21684       India non-atheist 2012
## 21685       India non-atheist 2012
## 21686       India non-atheist 2012
## 21687       India non-atheist 2012
## 21688       India non-atheist 2012
## 21689       India non-atheist 2012
## 21690       India non-atheist 2012
## 21691       India non-atheist 2012
## 21692       India non-atheist 2012
## 21693       India non-atheist 2012
## 21694       India non-atheist 2012
## 21695       India non-atheist 2012
## 21696       India non-atheist 2012
## 21697       India non-atheist 2012
## 21698       India non-atheist 2012
## 21699       India non-atheist 2012
## 21700       India non-atheist 2012
## 21701       India non-atheist 2012
## 21702       India non-atheist 2012
## 21703       India non-atheist 2012
## 21704       India non-atheist 2012
## 21705       India non-atheist 2012
## 21706       India non-atheist 2012
## 21707       India non-atheist 2012
## 21708       India non-atheist 2012
## 21709       India non-atheist 2012
## 21710       India non-atheist 2012
## 21711       India non-atheist 2012
## 21712       India non-atheist 2012
## 21713       India non-atheist 2012
## 21714       India non-atheist 2012
## 21715       India     atheist 2012
## 21716       India non-atheist 2012
## 21717       India non-atheist 2012
## 21718       India non-atheist 2012
## 21719       India non-atheist 2012
## 21720       India non-atheist 2012
## 21721       India     atheist 2012
## 21722       India     atheist 2012
## 21723       India non-atheist 2012
## 21724       India non-atheist 2012
## 21725       India non-atheist 2012
## 21726       India non-atheist 2012
## 21727       India non-atheist 2012
## 21728       India non-atheist 2012
## 21729       India non-atheist 2012
## 21730       India non-atheist 2012
## 21731       India non-atheist 2012
## 21732       India non-atheist 2012
## 21733       India non-atheist 2012
## 21734       India non-atheist 2012
## 21735       India non-atheist 2012
## 21736       India non-atheist 2012
## 21737       India non-atheist 2012
## 21738       India non-atheist 2012
## 21739       India non-atheist 2012
## 21740       India non-atheist 2012
## 21741       India non-atheist 2012
## 21742       India non-atheist 2012
## 21743       India non-atheist 2012
## 21744       India non-atheist 2012
## 21745       India non-atheist 2012
## 21746       India non-atheist 2012
## 21747       India non-atheist 2012
## 21748       India non-atheist 2012
## 21749       India non-atheist 2012
## 21750       India non-atheist 2012
## 21751       India non-atheist 2012
## 21752       India non-atheist 2012
## 21753       India non-atheist 2012
## 21754       India     atheist 2012
## 21755       India non-atheist 2012
## 21756       India non-atheist 2012
## 21757       India non-atheist 2012
## 21758       India non-atheist 2012
## 21759       India non-atheist 2012
## 21760       India non-atheist 2012
## 21761       India non-atheist 2012
## 21762       India non-atheist 2012
## 21763       India non-atheist 2012
## 21764       India non-atheist 2012
## 21765       India non-atheist 2012
## 21766       India non-atheist 2012
## 21767       India non-atheist 2012
## 21768       India non-atheist 2012
## 21769       India non-atheist 2012
## 21770       India non-atheist 2012
## 21771       India non-atheist 2012
## 21772       India non-atheist 2012
## 21773       India non-atheist 2012
## 21774       India non-atheist 2012
## 21775       India non-atheist 2012
## 21776       India non-atheist 2012
## 21777       India non-atheist 2012
## 21778       India non-atheist 2012
## 21779       India non-atheist 2012
## 21780       India non-atheist 2012
## 21781       India     atheist 2012
## 21782       India non-atheist 2012
## 21783       India non-atheist 2012
## 21784       India non-atheist 2012
## 21785       India non-atheist 2012
## 21786       India non-atheist 2012
## 21787       India non-atheist 2012
## 21788       India non-atheist 2012
## 21789       India non-atheist 2012
## 21790       India non-atheist 2012
## 21791       India non-atheist 2012
## 21792       India non-atheist 2012
## 21793       India non-atheist 2012
## 21794       India non-atheist 2012
## 21795       India non-atheist 2012
## 21796       India non-atheist 2012
## 21797       India non-atheist 2012
## 21798       India     atheist 2012
## 21799       India non-atheist 2012
## 21800       India non-atheist 2012
## 21801       India non-atheist 2012
## 21802       India non-atheist 2012
## 21803       India non-atheist 2012
## 21804       India non-atheist 2012
## 21805       India non-atheist 2012
## 21806       India non-atheist 2012
## 21807       India non-atheist 2012
## 21808       India non-atheist 2012
## 21809       India non-atheist 2012
## 21810       India non-atheist 2012
## 21811       India non-atheist 2012
## 21812       India non-atheist 2012
## 21813       India non-atheist 2012
## 21814       India non-atheist 2012
## 21815       India non-atheist 2012
## 21816       India non-atheist 2012
## 21817       India non-atheist 2012
## 21818       India non-atheist 2012
## 21819       India non-atheist 2012
## 21820       India     atheist 2012
## 21821       India non-atheist 2012
## 21822       India non-atheist 2012
## 21823       India non-atheist 2012
## 21824       India non-atheist 2012
## 21825       India non-atheist 2012
## 21826       India non-atheist 2012
## 21827       India non-atheist 2012
## 21828       India non-atheist 2012
## 21829       India non-atheist 2012
## 21830       India non-atheist 2012
## 21831       India non-atheist 2012
## 21832       India non-atheist 2012
## 21833       India non-atheist 2012
## 21834       India non-atheist 2012
## 21835       India non-atheist 2012
## 21836       India non-atheist 2012
## 21837       India non-atheist 2012
## 21838       India non-atheist 2012
## 21839       India non-atheist 2012
## 21840       India non-atheist 2012
## 21841       India non-atheist 2012
## 21842       India non-atheist 2012
## 21843       India non-atheist 2012
## 21844       India non-atheist 2012
## 21845       India non-atheist 2012
## 21846       India non-atheist 2012
## 21847       India non-atheist 2012
## 21848       India non-atheist 2012
## 21849       India non-atheist 2012
## 21850       India non-atheist 2012
## 21851       India non-atheist 2012
## 21852       India non-atheist 2012
## 21853       India non-atheist 2012
## 21854       India non-atheist 2012
## 21855       India non-atheist 2012
## 21856       India non-atheist 2012
## 21857       India non-atheist 2012
## 21858       India non-atheist 2012
## 21859       India non-atheist 2012
## 21860       India non-atheist 2012
## 21861       India non-atheist 2012
## 21862       India non-atheist 2012
## 21863       India non-atheist 2012
## 21864       India non-atheist 2012
## 21865       India     atheist 2012
## 21866       India non-atheist 2012
## 21867       India non-atheist 2012
## 21868       India non-atheist 2012
## 21869       India non-atheist 2012
## 21870       India non-atheist 2012
## 21871       India non-atheist 2012
## 21872       India non-atheist 2012
## 21873       India non-atheist 2012
## 21874       India non-atheist 2012
## 21875       India non-atheist 2012
## 21876       India non-atheist 2012
## 21877       India non-atheist 2012
## 21878       India non-atheist 2012
## 21879       India non-atheist 2012
## 21880       India non-atheist 2012
## 21881       India non-atheist 2012
## 21882       India non-atheist 2012
## 21883       India non-atheist 2012
## 21884       India non-atheist 2012
## 21885       India non-atheist 2012
## 21886       India non-atheist 2012
## 21887       India non-atheist 2012
## 21888       India non-atheist 2012
## 21889       India non-atheist 2012
## 21890       India non-atheist 2012
## 21891       India non-atheist 2012
## 21892       India non-atheist 2012
## 21893       India non-atheist 2012
## 21894       India non-atheist 2012
## 21895       India non-atheist 2012
## 21896       India     atheist 2012
## 21897       India non-atheist 2012
## 21898       India non-atheist 2012
## 21899       India non-atheist 2012
## 21900       India non-atheist 2012
## 21901       India non-atheist 2012
## 21902       India non-atheist 2012
## 21903       India non-atheist 2012
## 21904       India non-atheist 2012
## 21905       India non-atheist 2012
## 21906       India non-atheist 2012
## 21907       India non-atheist 2012
## 21908       India non-atheist 2012
## 21909       India non-atheist 2012
## 21910       India non-atheist 2012
## 21911       India non-atheist 2012
## 21912       India non-atheist 2012
## 21913       India non-atheist 2012
## 21914       India non-atheist 2012
## 21915       India non-atheist 2012
## 21916       India non-atheist 2012
## 21917       India non-atheist 2012
## 21918       India non-atheist 2012
## 21919       India non-atheist 2012
## 21920       India non-atheist 2012
## 21921       India non-atheist 2012
## 21922       India non-atheist 2012
## 21923       India non-atheist 2012
## 21924       India non-atheist 2012
## 21925       India non-atheist 2012
## 21926       India non-atheist 2012
## 21927       India non-atheist 2012
## 21928       India non-atheist 2012
## 21929       India non-atheist 2012
## 21930       India non-atheist 2012
## 21931       India non-atheist 2012
## 21932       India non-atheist 2012
## 21933       India non-atheist 2012
## 21934       India non-atheist 2012
## 21935       India non-atheist 2012
## 21936       India non-atheist 2012
## 21937       India non-atheist 2012
## 21938       India non-atheist 2012
## 21939       India non-atheist 2012
## 21940       India non-atheist 2012
## 21941       India non-atheist 2012
## 21942       India non-atheist 2012
## 21943       India non-atheist 2012
## 21944       India non-atheist 2012
## 21945       India non-atheist 2012
## 21946       India non-atheist 2012
## 21947       India non-atheist 2012
## 21948       India non-atheist 2012
## 21949       India non-atheist 2012
## 21950       India non-atheist 2012
## 21951       India     atheist 2012
## 21952       India non-atheist 2012
## 21953       India non-atheist 2012
## 21954       India non-atheist 2012
## 21955       India non-atheist 2012
## 21956       India non-atheist 2012
## 21957       India non-atheist 2012
## 21958       India non-atheist 2012
## 21959       India non-atheist 2012
## 21960       India     atheist 2012
## 21961       India non-atheist 2012
## 21962       India non-atheist 2012
## 21963       India non-atheist 2012
## 21964       India non-atheist 2012
## 21965       India non-atheist 2012
## 21966       India non-atheist 2012
## 21967       India non-atheist 2012
## 21968       India non-atheist 2012
## 21969       India non-atheist 2012
## 21970       India non-atheist 2012
## 21971       India     atheist 2012
## 21972       India non-atheist 2012
## 21973       India non-atheist 2012
## 21974       India non-atheist 2012
## 21975       India non-atheist 2012
## 21976       India non-atheist 2012
## 21977       India non-atheist 2012
## 21978       India non-atheist 2012
## 21979       India non-atheist 2012
## 21980       India non-atheist 2012
## 21981       India non-atheist 2012
## 21982       India non-atheist 2012
## 21983       India non-atheist 2012
## 21984       India non-atheist 2012
## 21985       India non-atheist 2012
## 21986       India non-atheist 2012
## 21987       India non-atheist 2012
## 21988       India non-atheist 2012
## 21989       India non-atheist 2012
## 21990       India non-atheist 2012
## 21991       India non-atheist 2012
## 21992       India non-atheist 2012
## 21993       India non-atheist 2012
## 21994       India non-atheist 2012
## 21995       India non-atheist 2012
## 21996       India non-atheist 2012
## 21997       India non-atheist 2012
## 21998       India non-atheist 2012
## 21999       India     atheist 2012
## 22000       India non-atheist 2012
## 22001       India non-atheist 2012
## 22002       India non-atheist 2012
## 22003       India non-atheist 2012
## 22004       India non-atheist 2012
## 22005       India non-atheist 2012
## 22006       India non-atheist 2012
## 22007       India non-atheist 2012
## 22008       India non-atheist 2012
## 22009       India non-atheist 2012
## 22010       India non-atheist 2012
## 22011       India non-atheist 2012
## 22012       India non-atheist 2012
## 22013       India non-atheist 2012
## 22014       India non-atheist 2012
## 22015       India non-atheist 2012
## 22016       India non-atheist 2012
## 22017       India non-atheist 2012
## 22018       India non-atheist 2012
## 22019       India non-atheist 2012
## 22020       India non-atheist 2012
## 22021       India non-atheist 2012
## 22022       India non-atheist 2012
## 22023       India non-atheist 2012
## 22024       India non-atheist 2012
## 22025       India non-atheist 2012
## 22026       India non-atheist 2012
## 22027       India non-atheist 2012
## 22028       India non-atheist 2012
## 22029       India non-atheist 2012
## 22030       India non-atheist 2012
## 22031       India non-atheist 2012
## 22032       India non-atheist 2012
## 22033       India non-atheist 2012
## 22034       India non-atheist 2012
## 22035       India non-atheist 2012
## 22036       India non-atheist 2012
## 22037       India non-atheist 2012
## 22038       India non-atheist 2012
## 22039       India non-atheist 2012
## 22040       India non-atheist 2012
## 22041       India non-atheist 2012
## 22042       India non-atheist 2012
## 22043       India non-atheist 2012
## 22044       India non-atheist 2012
## 22045       India non-atheist 2012
## 22046       India non-atheist 2012
## 22047       India non-atheist 2012
## 22048       India non-atheist 2012
## 22049       India non-atheist 2012
## 22050       India non-atheist 2012
## 22051       India     atheist 2012
## 22052       India     atheist 2012
## 22053       India non-atheist 2012
## 22054       India non-atheist 2012
## 22055       India non-atheist 2012
## 22056       India non-atheist 2012
## 22057       India non-atheist 2012
## 22058       India non-atheist 2012
## 22059       India non-atheist 2012
## 22060       India non-atheist 2012
## 22061       India non-atheist 2012
## 22062       India non-atheist 2012
## 22063       India non-atheist 2012
## 22064       India non-atheist 2012
## 22065       India non-atheist 2012
## 22066       India non-atheist 2012
## 22067       India non-atheist 2012
## 22068       India non-atheist 2012
## 22069       India non-atheist 2012
## 22070       India non-atheist 2012
## 22071       India non-atheist 2012
## 22072       India non-atheist 2012
## 22073       India non-atheist 2012
## 22074       India non-atheist 2012
## 22075       India non-atheist 2012
## 22076       India non-atheist 2012
## 22077       India non-atheist 2012
## 22078       India non-atheist 2012
## 22079       India non-atheist 2012
## 22080       India non-atheist 2012
## 22081       India non-atheist 2012
## 22082       India non-atheist 2012
## 22083       India non-atheist 2012
## 22084       India non-atheist 2012
## 22085       India non-atheist 2012
## 22086       India non-atheist 2012
## 22087       India non-atheist 2012
## 22088       India non-atheist 2012
## 22089       India non-atheist 2012
## 22090       India non-atheist 2012
## 22091       India non-atheist 2012
## 22092       India non-atheist 2012
## 22093       India non-atheist 2012
## 22094       India non-atheist 2012
## 22095       India non-atheist 2012
## 22096       India non-atheist 2012
## 22097       India non-atheist 2012
## 22098       India non-atheist 2012
## 22099       India non-atheist 2012
## 22100       India non-atheist 2012
## 22101       India non-atheist 2012
## 22102       India non-atheist 2012
## 22103       India non-atheist 2012
## 22104       India non-atheist 2012
## 22105       India non-atheist 2012
## 22106       India non-atheist 2012
## 22107       India     atheist 2012
## 22108       India non-atheist 2012
## 22109       India non-atheist 2012
## 22110       India non-atheist 2012
## 22111       India non-atheist 2012
## 22112       India non-atheist 2012
## 22113       India non-atheist 2012
## 22114       India non-atheist 2012
## 22115       India non-atheist 2012
## 22116       India non-atheist 2012
## 22117       India non-atheist 2012
## 22118       India non-atheist 2012
## 22119       India non-atheist 2012
## 22120       India non-atheist 2012
## 22121       India non-atheist 2012
## 22122       India non-atheist 2012
## 22123       India non-atheist 2012
## 22124       India non-atheist 2012
## 22125       India non-atheist 2012
## 22126       India non-atheist 2012
## 22127       India non-atheist 2012
## 22128       India non-atheist 2012
## 22129       India non-atheist 2012
## 22130       India non-atheist 2012
## 22131       India     atheist 2012
## 22132       India non-atheist 2012
## 22133       India non-atheist 2012
## 22134       India non-atheist 2012
## 22135       India non-atheist 2012
## 22136       India non-atheist 2012
## 22137       India non-atheist 2012
## 22138       India non-atheist 2012
## 22139       India non-atheist 2012
## 22140       India non-atheist 2012
## 22141       India non-atheist 2012
## 22142       India non-atheist 2012
## 22143       India non-atheist 2012
## 22144       India non-atheist 2012
## 22145       India non-atheist 2012
## 22146       India non-atheist 2012
## 22147       India non-atheist 2012
## 22148       India non-atheist 2012
## 22149       India non-atheist 2012
## 22150       India non-atheist 2012
## 22151       India non-atheist 2012
## 22152       India non-atheist 2012
## 22153       India non-atheist 2012
## 22154       India non-atheist 2012
## 22155       India non-atheist 2012
## 22156       India non-atheist 2012
## 22157       India non-atheist 2012
## 22158       India non-atheist 2012
## 22159       India non-atheist 2012
## 22160       India non-atheist 2012
## 22161       India non-atheist 2012
## 22162       India non-atheist 2012
## 22163       India non-atheist 2012
## 22164       India non-atheist 2012
## 22165       India non-atheist 2012
## 22166       India non-atheist 2012
## 22167       India non-atheist 2012
## 22168       India non-atheist 2012
## 22169       India non-atheist 2012
## 22170       India non-atheist 2012
## 22171       India non-atheist 2012
## 22172       India non-atheist 2012
## 22173       India non-atheist 2012
## 22174       India non-atheist 2012
## 22175       India non-atheist 2012
## 22176       India non-atheist 2012
## 22177       India non-atheist 2012
## 22178       India non-atheist 2012
## 22179       India non-atheist 2012
## 22180       India non-atheist 2012
## 22181       India non-atheist 2012
## 22182       India non-atheist 2012
## 22183       India non-atheist 2012
## 22184       India non-atheist 2012
## 22185       India non-atheist 2012
## 22186       India non-atheist 2012
## 22187       India non-atheist 2012
## 22188       India non-atheist 2012
## 22189       India non-atheist 2012
## 22190       India non-atheist 2012
## 22191       India non-atheist 2012
## 22192       India non-atheist 2012
## 22193       India non-atheist 2012
## 22194       India non-atheist 2012
## 22195       India non-atheist 2012
## 22196       India non-atheist 2012
## 22197       India non-atheist 2012
## 22198       India non-atheist 2012
## 22199       India non-atheist 2012
## 22200       India non-atheist 2012
## 22201       India non-atheist 2012
## 22202       India non-atheist 2012
## 22203       India non-atheist 2012
## 22204       India non-atheist 2012
## 22205       India non-atheist 2012
## 22206       India non-atheist 2012
## 22207       India non-atheist 2012
## 22208       India non-atheist 2012
## 22209       India non-atheist 2012
## 22210       India non-atheist 2012
## 22211       India non-atheist 2012
## 22212       India non-atheist 2012
## 22213       India non-atheist 2012
## 22214       India non-atheist 2012
## 22215       India non-atheist 2012
## 22216       India non-atheist 2012
## 22217       India non-atheist 2012
## 22218       India     atheist 2012
## 22219       India non-atheist 2012
## 22220       India non-atheist 2012
## 22221       India non-atheist 2012
## 22222       India non-atheist 2012
## 22223       India non-atheist 2012
## 22224       India non-atheist 2012
## 22225       India non-atheist 2012
## 22226       India non-atheist 2012
## 22227       India non-atheist 2012
## 22228       India non-atheist 2012
## 22229       India non-atheist 2012
## 22230       India non-atheist 2012
## 22231       India non-atheist 2012
## 22232       India non-atheist 2012
## 22233       India non-atheist 2012
## 22234       India non-atheist 2012
## 22235       India non-atheist 2012
## 22236       India non-atheist 2012
## 22237       India non-atheist 2012
## 22238       India non-atheist 2012
## 22239       India non-atheist 2012
## 22240       India non-atheist 2012
## 22241       India non-atheist 2012
## 22242       India     atheist 2012
## 22243       India     atheist 2012
## 22244       India non-atheist 2012
## 22245       India non-atheist 2012
## 22246       India non-atheist 2012
## 22247       India non-atheist 2012
## 22248       India non-atheist 2012
## 22249       India non-atheist 2012
## 22250       India non-atheist 2012
## 22251       India non-atheist 2012
## 22252       India non-atheist 2012
## 22253       India non-atheist 2012
## 22254       India non-atheist 2012
## 22255       India non-atheist 2012
## 22256       India non-atheist 2012
## 22257       India non-atheist 2012
## 22258       India non-atheist 2012
## 22259       India non-atheist 2012
## 22260       India non-atheist 2012
## 22261       India non-atheist 2012
## 22262       India non-atheist 2012
## 22263       India non-atheist 2012
## 22264       India non-atheist 2012
## 22265       India non-atheist 2012
## 22266       India non-atheist 2012
## 22267       India non-atheist 2012
## 22268       India non-atheist 2012
## 22269       India non-atheist 2012
## 22270       India non-atheist 2012
## 22271       India non-atheist 2012
## 22272       India non-atheist 2012
## 22273       India non-atheist 2012
## 22274       India non-atheist 2012
## 22275       India non-atheist 2012
## 22276       India non-atheist 2012
## 22277       India     atheist 2012
## 22278       India non-atheist 2012
## 22279       India non-atheist 2012
## 22280       India non-atheist 2012
## 22281       India non-atheist 2012
## 22282       India non-atheist 2012
## 22283       India non-atheist 2012
## 22284       India non-atheist 2012
## 22285       India non-atheist 2012
## 22286       India non-atheist 2012
## 22287       India non-atheist 2012
## 22288       India non-atheist 2012
## 22289       India non-atheist 2012
## 22290       India non-atheist 2012
## 22291       India non-atheist 2012
## 22292       India non-atheist 2012
## 22293       India non-atheist 2012
## 22294       India non-atheist 2012
## 22295       India non-atheist 2012
## 22296       India non-atheist 2012
## 22297       India non-atheist 2012
## 22298       India non-atheist 2012
## 22299       India non-atheist 2012
## 22300       India non-atheist 2012
## 22301       India non-atheist 2012
## 22302       India non-atheist 2012
## 22303       India non-atheist 2012
## 22304       India non-atheist 2012
## 22305       India non-atheist 2012
## 22306       India non-atheist 2012
## 22307       India non-atheist 2012
## 22308       India non-atheist 2012
## 22309       India non-atheist 2012
## 22310       India non-atheist 2012
## 22311       India non-atheist 2012
## 22312       India non-atheist 2012
## 22313       India non-atheist 2012
## 22314       India non-atheist 2012
## 22315       India non-atheist 2012
## 22316       India non-atheist 2012
## 22317       India non-atheist 2012
## 22318       India non-atheist 2012
## 22319       India non-atheist 2012
## 22320       India non-atheist 2012
## 22321       India non-atheist 2012
## 22322       India non-atheist 2012
## 22323       India non-atheist 2012
## 22324       India non-atheist 2012
## 22325       India non-atheist 2012
## 22326       India non-atheist 2012
## 22327       India non-atheist 2012
## 22328       India non-atheist 2012
## 22329       India non-atheist 2012
## 22330       India non-atheist 2012
## 22331       India non-atheist 2012
## 22332       India non-atheist 2012
## 22333       India non-atheist 2012
## 22334       India non-atheist 2012
## 22335       India non-atheist 2012
## 22336       India non-atheist 2012
## 22337       India non-atheist 2012
## 22338       India     atheist 2012
## 22339       India non-atheist 2012
## 22340       India non-atheist 2012
## 22341       India non-atheist 2012
## 22342       India non-atheist 2012
## 22343       India non-atheist 2012
## 22344       India non-atheist 2012
## 22345       India non-atheist 2012
## 22346       India non-atheist 2012
## 22347       India non-atheist 2012
## 22348       India non-atheist 2012
## 22349       India non-atheist 2012
## 22350       India     atheist 2012
## 22351       India non-atheist 2012
## 22352       India non-atheist 2012
## 22353       India non-atheist 2012
## 22354       India non-atheist 2012
## 22355       India non-atheist 2012
## 22356       India non-atheist 2012
## 22357       India non-atheist 2012
## 22358       India non-atheist 2012
## 22359       India non-atheist 2012
## 22360       India non-atheist 2012
## 22361       India non-atheist 2012
## 22362       India non-atheist 2012
## 22363       India non-atheist 2012
## 22364       India non-atheist 2012
## 22365       India non-atheist 2012
## 22366       India non-atheist 2012
## 22367       India non-atheist 2012
## 22368       India non-atheist 2012
## 22369       India non-atheist 2012
## 22370       India non-atheist 2012
## 22371       India non-atheist 2012
## 22372       India non-atheist 2012
## 22373       India non-atheist 2012
## 22374       India non-atheist 2012
## 22375       India non-atheist 2012
## 22376       India non-atheist 2012
## 22377       India non-atheist 2012
## 22378       India non-atheist 2012
## 22379       India non-atheist 2012
## 22380       India non-atheist 2012
## 22381       India non-atheist 2012
## 22382       India non-atheist 2012
## 22383       India non-atheist 2012
## 22384       India non-atheist 2012
## 22385       India non-atheist 2012
## 22386       India non-atheist 2012
## 22387       India non-atheist 2012
## 22388       India non-atheist 2012
## 22389       India     atheist 2012
## 22390       India non-atheist 2012
## 22391       India non-atheist 2012
## 22392       India non-atheist 2012
## 22393       India non-atheist 2012
## 22394       India non-atheist 2012
## 22395       India non-atheist 2012
## 22396       India non-atheist 2012
## 22397       India non-atheist 2012
## 22398       India non-atheist 2012
## 22399       India non-atheist 2012
## 22400       India non-atheist 2012
## 22401       India non-atheist 2012
## 22402       India non-atheist 2012
## 22403       India non-atheist 2012
## 22404       India     atheist 2012
## 22405       India non-atheist 2012
## 22406       India non-atheist 2012
## 22407       India non-atheist 2012
## 22408       India non-atheist 2012
## 22409       India non-atheist 2012
## 22410       India non-atheist 2012
## 22411       India non-atheist 2012
## 22412       India non-atheist 2012
## 22413       India non-atheist 2012
## 22414       India non-atheist 2012
## 22415       India non-atheist 2012
## 22416       India non-atheist 2012
## 22417       India non-atheist 2012
## 22418       India non-atheist 2012
## 22419       India non-atheist 2012
## 22420       India non-atheist 2012
## 22421       India non-atheist 2012
## 22422       India non-atheist 2012
## 22423       India non-atheist 2012
## 22424       India non-atheist 2012
## 22425       India non-atheist 2012
## 22426       India non-atheist 2012
## 22427       India non-atheist 2012
## 22428       India non-atheist 2012
## 22429       India non-atheist 2012
## 22430       India non-atheist 2012
## 22431       India     atheist 2012
## 22432       India non-atheist 2012
## 22433       India non-atheist 2012
## 22434       India non-atheist 2012
## 22435       India non-atheist 2012
## 22436       India non-atheist 2012
## 22437       India non-atheist 2012
## 22438       India non-atheist 2012
## 22439       India non-atheist 2012
## 22440       India non-atheist 2012
## 22441       India non-atheist 2012
## 22442       India non-atheist 2012
## 22443       India     atheist 2012
## 22444       India non-atheist 2012
## 22445       India non-atheist 2012
## 22446       India non-atheist 2012
## 22447       India non-atheist 2012
## 22448       India non-atheist 2012
## 22449       India non-atheist 2012
## 22450       India non-atheist 2012
## 22451       India non-atheist 2012
## 22452       India non-atheist 2012
## 22453       India non-atheist 2012
## 22454       India non-atheist 2012
## 22455       India non-atheist 2012
## 22456       India non-atheist 2012
## 22457       India non-atheist 2012
## 22458       India non-atheist 2012
## 22459       India non-atheist 2012
## 22460       India non-atheist 2012
## 22461       India non-atheist 2012
## 22462       India non-atheist 2012
## 22463       India non-atheist 2012
## 22464       India non-atheist 2012
## 22465       India non-atheist 2012
## 22466       India non-atheist 2012
## 22467       India non-atheist 2012
## 22468       India non-atheist 2012
## 22469       India non-atheist 2012
## 22470       India non-atheist 2012
## 22471       India non-atheist 2012
## 22472       India non-atheist 2012
## 22473       India non-atheist 2012
## 22474       India non-atheist 2012
## 22475       India non-atheist 2012
## 22476       India non-atheist 2012
## 22477       India non-atheist 2012
## 22478       India non-atheist 2012
## 22479       India non-atheist 2012
## 22480       India non-atheist 2012
## 22481       India non-atheist 2012
## 22482       India non-atheist 2012
## 22483       India non-atheist 2012
## 22484       India non-atheist 2012
## 22485       India non-atheist 2012
## 22486       India non-atheist 2012
## 22487       India non-atheist 2012
## 22488       India non-atheist 2012
## 22489       India non-atheist 2012
## 22490       India non-atheist 2012
## 22491       India non-atheist 2012
## 22492       India non-atheist 2012
## 22493       India non-atheist 2012
## 22494       India non-atheist 2012
## 22495       India non-atheist 2012
## 22496       India non-atheist 2012
## 22497       India non-atheist 2012
## 22498       India non-atheist 2012
## 22499       India non-atheist 2012
## 22500       India non-atheist 2012
## 22501       India non-atheist 2012
## 22502       India non-atheist 2012
## 22503       India non-atheist 2012
## 22504       India non-atheist 2012
## 22505       India non-atheist 2012
## 22506       India non-atheist 2012
## 22507       India non-atheist 2012
## 22508       India non-atheist 2012
## 22509       India non-atheist 2012
## 22510       India non-atheist 2012
## 22511       India non-atheist 2012
## 22512       India non-atheist 2012
## 22513       India non-atheist 2012
## 22514       India non-atheist 2012
## 22515       India non-atheist 2012
## 22516       India non-atheist 2012
## 22517       India non-atheist 2012
## 22518       India non-atheist 2012
## 22519       India non-atheist 2012
## 22520       India non-atheist 2012
## 22521       India non-atheist 2012
## 22522       India non-atheist 2012
## 22523       India non-atheist 2012
## 22524       India non-atheist 2012
## 22525       India non-atheist 2012
## 22526       India non-atheist 2012
## 22527       India non-atheist 2012
## 22528       India non-atheist 2012
## 22529       India non-atheist 2012
## 22530       India non-atheist 2012
## 22531       India non-atheist 2012
## 22532       India     atheist 2012
## 22533       India non-atheist 2012
## 22534       India non-atheist 2012
## 22535       India non-atheist 2012
## 22536       India non-atheist 2012
## 22537       India non-atheist 2012
## 22538       India non-atheist 2012
## 22539       India non-atheist 2012
## 22540       India non-atheist 2012
## 22541       India non-atheist 2012
## 22542       India non-atheist 2012
## 22543       India non-atheist 2012
## 22544       India non-atheist 2012
## 22545       India non-atheist 2012
## 22546       India non-atheist 2012
## 22547       India non-atheist 2012
## 22548       India non-atheist 2012
## 22549       India non-atheist 2012
## 22550       India non-atheist 2012
## 22551       India non-atheist 2012
## 22552       India non-atheist 2012
## 22553       India non-atheist 2012
## 22554       India non-atheist 2012
## 22555       India non-atheist 2012
## 22556       India non-atheist 2012
## 22557       India non-atheist 2012
## 22558       India non-atheist 2012
## 22559       India non-atheist 2012
## 22560       India non-atheist 2012
## 22561       India non-atheist 2012
## 22562       India non-atheist 2012
## 22563       India non-atheist 2012
## 22564       India non-atheist 2012
## 22565       India non-atheist 2012
## 22566       India non-atheist 2012
## 22567       India non-atheist 2012
## 22568       India non-atheist 2012
## 22569       India non-atheist 2012
## 22570       India non-atheist 2012
## 22571       India non-atheist 2012
## 22572       India non-atheist 2012
## 22573       India non-atheist 2012
## 22574       India non-atheist 2012
## 22575       India non-atheist 2012
## 22576       India non-atheist 2012
## 22577       India non-atheist 2012
## 22578       India non-atheist 2012
## 22579       India non-atheist 2012
## 22580       India non-atheist 2012
## 22581       India non-atheist 2012
## 22582       India non-atheist 2012
## 22583       India non-atheist 2012
## 22584       India non-atheist 2012
## 22585       India non-atheist 2012
## 22586       India non-atheist 2012
## 22587       India non-atheist 2012
## 22588       India non-atheist 2012
## 22589       India non-atheist 2012
## 22590       India non-atheist 2012
## 22591       India non-atheist 2012
## 22592       India non-atheist 2012
## 22593       India non-atheist 2012
## 22594       India non-atheist 2012
## 22595       India non-atheist 2012
## 22596       India non-atheist 2012
## 22597       India non-atheist 2012
## 22598       India non-atheist 2012
## 22599       India non-atheist 2012
## 22600       India non-atheist 2012
## 22601       India non-atheist 2012
## 22602       India non-atheist 2012
## 22603       India non-atheist 2012
## 22604       India non-atheist 2012
## 22605       India non-atheist 2012
## 22606       India non-atheist 2012
## 22607       India non-atheist 2012
## 22608       India non-atheist 2012
## 22609       India non-atheist 2012
## 22610       India non-atheist 2012
## 22611       India     atheist 2012
## 22612       India non-atheist 2012
## 22613       India non-atheist 2012
## 22614       India non-atheist 2012
## 22615       India non-atheist 2012
## 22616       India non-atheist 2012
## 22617       India non-atheist 2012
## 22618       India non-atheist 2012
## 22619       India non-atheist 2012
## 22620       India non-atheist 2012
## 22621       India non-atheist 2012
## 22622       India non-atheist 2012
## 22623       India non-atheist 2012
## 22624       India non-atheist 2012
## 22625       India non-atheist 2012
## 22626       India non-atheist 2012
## 22627       India non-atheist 2012
## 22628       India non-atheist 2012
## 22629       India non-atheist 2012
## 22630       India non-atheist 2012
## 22631       India non-atheist 2012
## 22632       India non-atheist 2012
## 22633       India non-atheist 2012
## 22634       India non-atheist 2012
## 22635       India non-atheist 2012
## 22636       India non-atheist 2012
## 22637       India non-atheist 2012
## 22638       India non-atheist 2012
## 22639       India non-atheist 2012
## 22640       India non-atheist 2012
## 22641       India non-atheist 2012
## 22642       India non-atheist 2012
## 22643       India non-atheist 2012
## 22644       India non-atheist 2012
## 22645       India non-atheist 2012
## 22646       India non-atheist 2012
## 22647       India non-atheist 2012
## 22648       India non-atheist 2012
## 22649       India non-atheist 2012
## 22650       India non-atheist 2012
## 22651       India non-atheist 2012
## 22652       India non-atheist 2012
## 22653       India non-atheist 2012
## 22654       India non-atheist 2012
## 22655       India     atheist 2012
## 22656       India non-atheist 2012
## 22657       India non-atheist 2012
## 22658       India non-atheist 2012
## 22659       India non-atheist 2012
## 22660       India non-atheist 2012
## 22661       India non-atheist 2012
## 22662       India non-atheist 2012
## 22663       India non-atheist 2012
## 22664       India non-atheist 2012
## 22665       India non-atheist 2012
## 22666       India non-atheist 2012
## 22667       India non-atheist 2012
## 22668       India non-atheist 2012
## 22669       India non-atheist 2012
## 22670       India non-atheist 2012
## 22671       India non-atheist 2012
## 22672       India non-atheist 2012
## 22673       India non-atheist 2012
## 22674       India non-atheist 2012
## 22675       India non-atheist 2012
## 22676       India non-atheist 2012
## 22677       India non-atheist 2012
## 22678       India non-atheist 2012
## 22679       India non-atheist 2012
## 22680       India non-atheist 2012
## 22681       India non-atheist 2012
## 22682       India non-atheist 2012
## 22683       India non-atheist 2012
## 22684       India non-atheist 2012
## 22685       India     atheist 2012
## 22686       India non-atheist 2012
## 22687       India non-atheist 2012
## 22688       India non-atheist 2012
## 22689       India non-atheist 2012
## 22690       India non-atheist 2012
## 22691       India     atheist 2012
## 22692       India non-atheist 2012
## 22693       India non-atheist 2012
## 22694       India non-atheist 2012
## 22695       India non-atheist 2012
## 22696       India non-atheist 2012
## 22697       India non-atheist 2012
## 22698       India non-atheist 2012
## 22699       India non-atheist 2012
## 22700       India non-atheist 2012
## 22701       India non-atheist 2012
## 22702       India non-atheist 2012
## 22703       India non-atheist 2012
## 22704       India non-atheist 2012
## 22705       India non-atheist 2012
## 22706       India non-atheist 2012
## 22707       India non-atheist 2012
## 22708       India non-atheist 2012
## 22709       India non-atheist 2012
## 22710       India non-atheist 2012
## 22711       India non-atheist 2012
## 22712       India non-atheist 2012
## 22713       India non-atheist 2012
## 22714       India non-atheist 2012
## 22715       India non-atheist 2012
## 22716       India non-atheist 2012
## 22717       India non-atheist 2012
## 22718       India non-atheist 2012
## 22719       India non-atheist 2012
## 22720       India non-atheist 2012
## 22721       India non-atheist 2012
## 22722       India non-atheist 2012
## 22723       India non-atheist 2012
## 22724       India non-atheist 2012
## 22725       India non-atheist 2012
## 22726       India non-atheist 2012
## 22727       India non-atheist 2012
## 22728       India non-atheist 2012
## 22729       India non-atheist 2012
## 22730       India non-atheist 2012
## 22731       India non-atheist 2012
## 22732       India non-atheist 2012
## 22733       India non-atheist 2012
## 22734       India non-atheist 2012
## 22735       India non-atheist 2012
## 22736       India non-atheist 2012
## 22737       India non-atheist 2012
## 22738       India non-atheist 2012
## 22739       India non-atheist 2012
## 22740       India non-atheist 2012
## 22741       India non-atheist 2012
## 22742       India non-atheist 2012
## 22743       India non-atheist 2012
## 22744       India non-atheist 2012
## 22745       India non-atheist 2012
#Create data sets for two additional countries
#India
poland12 <- subset(atheism, nationality == "Poland" & year == "2012")
poland12
##       nationality    response year
## 39908      Poland non-atheist 2012
## 39909      Poland non-atheist 2012
## 39910      Poland non-atheist 2012
## 39911      Poland non-atheist 2012
## 39912      Poland non-atheist 2012
## 39913      Poland non-atheist 2012
## 39914      Poland non-atheist 2012
## 39915      Poland non-atheist 2012
## 39916      Poland non-atheist 2012
## 39917      Poland non-atheist 2012
## 39918      Poland non-atheist 2012
## 39919      Poland non-atheist 2012
## 39920      Poland non-atheist 2012
## 39921      Poland non-atheist 2012
## 39922      Poland non-atheist 2012
## 39923      Poland     atheist 2012
## 39924      Poland non-atheist 2012
## 39925      Poland non-atheist 2012
## 39926      Poland non-atheist 2012
## 39927      Poland     atheist 2012
## 39928      Poland     atheist 2012
## 39929      Poland non-atheist 2012
## 39930      Poland non-atheist 2012
## 39931      Poland non-atheist 2012
## 39932      Poland non-atheist 2012
## 39933      Poland non-atheist 2012
## 39934      Poland non-atheist 2012
## 39935      Poland non-atheist 2012
## 39936      Poland non-atheist 2012
## 39937      Poland non-atheist 2012
## 39938      Poland non-atheist 2012
## 39939      Poland non-atheist 2012
## 39940      Poland non-atheist 2012
## 39941      Poland non-atheist 2012
## 39942      Poland non-atheist 2012
## 39943      Poland non-atheist 2012
## 39944      Poland non-atheist 2012
## 39945      Poland non-atheist 2012
## 39946      Poland non-atheist 2012
## 39947      Poland non-atheist 2012
## 39948      Poland non-atheist 2012
## 39949      Poland non-atheist 2012
## 39950      Poland non-atheist 2012
## 39951      Poland non-atheist 2012
## 39952      Poland non-atheist 2012
## 39953      Poland non-atheist 2012
## 39954      Poland non-atheist 2012
## 39955      Poland non-atheist 2012
## 39956      Poland non-atheist 2012
## 39957      Poland non-atheist 2012
## 39958      Poland non-atheist 2012
## 39959      Poland non-atheist 2012
## 39960      Poland non-atheist 2012
## 39961      Poland non-atheist 2012
## 39962      Poland non-atheist 2012
## 39963      Poland non-atheist 2012
## 39964      Poland non-atheist 2012
## 39965      Poland non-atheist 2012
## 39966      Poland non-atheist 2012
## 39967      Poland non-atheist 2012
## 39968      Poland non-atheist 2012
## 39969      Poland non-atheist 2012
## 39970      Poland non-atheist 2012
## 39971      Poland non-atheist 2012
## 39972      Poland non-atheist 2012
## 39973      Poland non-atheist 2012
## 39974      Poland non-atheist 2012
## 39975      Poland non-atheist 2012
## 39976      Poland non-atheist 2012
## 39977      Poland non-atheist 2012
## 39978      Poland non-atheist 2012
## 39979      Poland non-atheist 2012
## 39980      Poland non-atheist 2012
## 39981      Poland non-atheist 2012
## 39982      Poland non-atheist 2012
## 39983      Poland non-atheist 2012
## 39984      Poland non-atheist 2012
## 39985      Poland non-atheist 2012
## 39986      Poland non-atheist 2012
## 39987      Poland non-atheist 2012
## 39988      Poland non-atheist 2012
## 39989      Poland non-atheist 2012
## 39990      Poland non-atheist 2012
## 39991      Poland non-atheist 2012
## 39992      Poland     atheist 2012
## 39993      Poland non-atheist 2012
## 39994      Poland non-atheist 2012
## 39995      Poland non-atheist 2012
## 39996      Poland non-atheist 2012
## 39997      Poland non-atheist 2012
## 39998      Poland     atheist 2012
## 39999      Poland non-atheist 2012
## 40000      Poland non-atheist 2012
## 40001      Poland non-atheist 2012
## 40002      Poland non-atheist 2012
## 40003      Poland non-atheist 2012
## 40004      Poland non-atheist 2012
## 40005      Poland non-atheist 2012
## 40006      Poland     atheist 2012
## 40007      Poland non-atheist 2012
## 40008      Poland non-atheist 2012
## 40009      Poland non-atheist 2012
## 40010      Poland non-atheist 2012
## 40011      Poland non-atheist 2012
## 40012      Poland non-atheist 2012
## 40013      Poland non-atheist 2012
## 40014      Poland non-atheist 2012
## 40015      Poland non-atheist 2012
## 40016      Poland non-atheist 2012
## 40017      Poland non-atheist 2012
## 40018      Poland non-atheist 2012
## 40019      Poland non-atheist 2012
## 40020      Poland non-atheist 2012
## 40021      Poland non-atheist 2012
## 40022      Poland non-atheist 2012
## 40023      Poland non-atheist 2012
## 40024      Poland non-atheist 2012
## 40025      Poland non-atheist 2012
## 40026      Poland non-atheist 2012
## 40027      Poland non-atheist 2012
## 40028      Poland non-atheist 2012
## 40029      Poland     atheist 2012
## 40030      Poland non-atheist 2012
## 40031      Poland non-atheist 2012
## 40032      Poland non-atheist 2012
## 40033      Poland non-atheist 2012
## 40034      Poland non-atheist 2012
## 40035      Poland non-atheist 2012
## 40036      Poland non-atheist 2012
## 40037      Poland non-atheist 2012
## 40038      Poland non-atheist 2012
## 40039      Poland non-atheist 2012
## 40040      Poland non-atheist 2012
## 40041      Poland non-atheist 2012
## 40042      Poland non-atheist 2012
## 40043      Poland non-atheist 2012
## 40044      Poland non-atheist 2012
## 40045      Poland non-atheist 2012
## 40046      Poland non-atheist 2012
## 40047      Poland non-atheist 2012
## 40048      Poland non-atheist 2012
## 40049      Poland non-atheist 2012
## 40050      Poland non-atheist 2012
## 40051      Poland non-atheist 2012
## 40052      Poland non-atheist 2012
## 40053      Poland non-atheist 2012
## 40054      Poland non-atheist 2012
## 40055      Poland non-atheist 2012
## 40056      Poland     atheist 2012
## 40057      Poland non-atheist 2012
## 40058      Poland non-atheist 2012
## 40059      Poland     atheist 2012
## 40060      Poland non-atheist 2012
## 40061      Poland non-atheist 2012
## 40062      Poland non-atheist 2012
## 40063      Poland non-atheist 2012
## 40064      Poland non-atheist 2012
## 40065      Poland non-atheist 2012
## 40066      Poland non-atheist 2012
## 40067      Poland non-atheist 2012
## 40068      Poland non-atheist 2012
## 40069      Poland non-atheist 2012
## 40070      Poland non-atheist 2012
## 40071      Poland non-atheist 2012
## 40072      Poland non-atheist 2012
## 40073      Poland non-atheist 2012
## 40074      Poland non-atheist 2012
## 40075      Poland non-atheist 2012
## 40076      Poland non-atheist 2012
## 40077      Poland non-atheist 2012
## 40078      Poland non-atheist 2012
## 40079      Poland non-atheist 2012
## 40080      Poland non-atheist 2012
## 40081      Poland non-atheist 2012
## 40082      Poland non-atheist 2012
## 40083      Poland     atheist 2012
## 40084      Poland     atheist 2012
## 40085      Poland non-atheist 2012
## 40086      Poland non-atheist 2012
## 40087      Poland non-atheist 2012
## 40088      Poland non-atheist 2012
## 40089      Poland non-atheist 2012
## 40090      Poland non-atheist 2012
## 40091      Poland non-atheist 2012
## 40092      Poland non-atheist 2012
## 40093      Poland non-atheist 2012
## 40094      Poland non-atheist 2012
## 40095      Poland non-atheist 2012
## 40096      Poland non-atheist 2012
## 40097      Poland non-atheist 2012
## 40098      Poland non-atheist 2012
## 40099      Poland non-atheist 2012
## 40100      Poland non-atheist 2012
## 40101      Poland non-atheist 2012
## 40102      Poland     atheist 2012
## 40103      Poland non-atheist 2012
## 40104      Poland non-atheist 2012
## 40105      Poland non-atheist 2012
## 40106      Poland non-atheist 2012
## 40107      Poland non-atheist 2012
## 40108      Poland non-atheist 2012
## 40109      Poland non-atheist 2012
## 40110      Poland non-atheist 2012
## 40111      Poland non-atheist 2012
## 40112      Poland non-atheist 2012
## 40113      Poland non-atheist 2012
## 40114      Poland non-atheist 2012
## 40115      Poland non-atheist 2012
## 40116      Poland non-atheist 2012
## 40117      Poland non-atheist 2012
## 40118      Poland non-atheist 2012
## 40119      Poland non-atheist 2012
## 40120      Poland non-atheist 2012
## 40121      Poland non-atheist 2012
## 40122      Poland non-atheist 2012
## 40123      Poland non-atheist 2012
## 40124      Poland non-atheist 2012
## 40125      Poland non-atheist 2012
## 40126      Poland non-atheist 2012
## 40127      Poland non-atheist 2012
## 40128      Poland non-atheist 2012
## 40129      Poland non-atheist 2012
## 40130      Poland non-atheist 2012
## 40131      Poland non-atheist 2012
## 40132      Poland non-atheist 2012
## 40133      Poland non-atheist 2012
## 40134      Poland non-atheist 2012
## 40135      Poland non-atheist 2012
## 40136      Poland non-atheist 2012
## 40137      Poland non-atheist 2012
## 40138      Poland non-atheist 2012
## 40139      Poland non-atheist 2012
## 40140      Poland non-atheist 2012
## 40141      Poland non-atheist 2012
## 40142      Poland non-atheist 2012
## 40143      Poland non-atheist 2012
## 40144      Poland     atheist 2012
## 40145      Poland non-atheist 2012
## 40146      Poland non-atheist 2012
## 40147      Poland non-atheist 2012
## 40148      Poland non-atheist 2012
## 40149      Poland non-atheist 2012
## 40150      Poland     atheist 2012
## 40151      Poland non-atheist 2012
## 40152      Poland non-atheist 2012
## 40153      Poland non-atheist 2012
## 40154      Poland non-atheist 2012
## 40155      Poland non-atheist 2012
## 40156      Poland non-atheist 2012
## 40157      Poland non-atheist 2012
## 40158      Poland     atheist 2012
## 40159      Poland non-atheist 2012
## 40160      Poland non-atheist 2012
## 40161      Poland non-atheist 2012
## 40162      Poland non-atheist 2012
## 40163      Poland non-atheist 2012
## 40164      Poland non-atheist 2012
## 40165      Poland non-atheist 2012
## 40166      Poland non-atheist 2012
## 40167      Poland non-atheist 2012
## 40168      Poland non-atheist 2012
## 40169      Poland non-atheist 2012
## 40170      Poland non-atheist 2012
## 40171      Poland non-atheist 2012
## 40172      Poland non-atheist 2012
## 40173      Poland non-atheist 2012
## 40174      Poland non-atheist 2012
## 40175      Poland non-atheist 2012
## 40176      Poland non-atheist 2012
## 40177      Poland non-atheist 2012
## 40178      Poland non-atheist 2012
## 40179      Poland non-atheist 2012
## 40180      Poland non-atheist 2012
## 40181      Poland non-atheist 2012
## 40182      Poland non-atheist 2012
## 40183      Poland non-atheist 2012
## 40184      Poland non-atheist 2012
## 40185      Poland non-atheist 2012
## 40186      Poland non-atheist 2012
## 40187      Poland non-atheist 2012
## 40188      Poland non-atheist 2012
## 40189      Poland non-atheist 2012
## 40190      Poland non-atheist 2012
## 40191      Poland non-atheist 2012
## 40192      Poland non-atheist 2012
## 40193      Poland non-atheist 2012
## 40194      Poland non-atheist 2012
## 40195      Poland non-atheist 2012
## 40196      Poland non-atheist 2012
## 40197      Poland non-atheist 2012
## 40198      Poland non-atheist 2012
## 40199      Poland non-atheist 2012
## 40200      Poland non-atheist 2012
## 40201      Poland non-atheist 2012
## 40202      Poland non-atheist 2012
## 40203      Poland non-atheist 2012
## 40204      Poland non-atheist 2012
## 40205      Poland non-atheist 2012
## 40206      Poland non-atheist 2012
## 40207      Poland non-atheist 2012
## 40208      Poland non-atheist 2012
## 40209      Poland non-atheist 2012
## 40210      Poland non-atheist 2012
## 40211      Poland non-atheist 2012
## 40212      Poland non-atheist 2012
## 40213      Poland non-atheist 2012
## 40214      Poland non-atheist 2012
## 40215      Poland non-atheist 2012
## 40216      Poland non-atheist 2012
## 40217      Poland non-atheist 2012
## 40218      Poland non-atheist 2012
## 40219      Poland non-atheist 2012
## 40220      Poland non-atheist 2012
## 40221      Poland     atheist 2012
## 40222      Poland non-atheist 2012
## 40223      Poland     atheist 2012
## 40224      Poland non-atheist 2012
## 40225      Poland non-atheist 2012
## 40226      Poland non-atheist 2012
## 40227      Poland non-atheist 2012
## 40228      Poland non-atheist 2012
## 40229      Poland non-atheist 2012
## 40230      Poland non-atheist 2012
## 40231      Poland non-atheist 2012
## 40232      Poland non-atheist 2012
## 40233      Poland non-atheist 2012
## 40234      Poland non-atheist 2012
## 40235      Poland non-atheist 2012
## 40236      Poland non-atheist 2012
## 40237      Poland non-atheist 2012
## 40238      Poland non-atheist 2012
## 40239      Poland non-atheist 2012
## 40240      Poland non-atheist 2012
## 40241      Poland non-atheist 2012
## 40242      Poland non-atheist 2012
## 40243      Poland non-atheist 2012
## 40244      Poland non-atheist 2012
## 40245      Poland non-atheist 2012
## 40246      Poland non-atheist 2012
## 40247      Poland non-atheist 2012
## 40248      Poland non-atheist 2012
## 40249      Poland non-atheist 2012
## 40250      Poland non-atheist 2012
## 40251      Poland non-atheist 2012
## 40252      Poland non-atheist 2012
## 40253      Poland non-atheist 2012
## 40254      Poland non-atheist 2012
## 40255      Poland non-atheist 2012
## 40256      Poland non-atheist 2012
## 40257      Poland     atheist 2012
## 40258      Poland non-atheist 2012
## 40259      Poland non-atheist 2012
## 40260      Poland non-atheist 2012
## 40261      Poland non-atheist 2012
## 40262      Poland non-atheist 2012
## 40263      Poland non-atheist 2012
## 40264      Poland non-atheist 2012
## 40265      Poland non-atheist 2012
## 40266      Poland non-atheist 2012
## 40267      Poland non-atheist 2012
## 40268      Poland non-atheist 2012
## 40269      Poland non-atheist 2012
## 40270      Poland non-atheist 2012
## 40271      Poland non-atheist 2012
## 40272      Poland non-atheist 2012
## 40273      Poland non-atheist 2012
## 40274      Poland non-atheist 2012
## 40275      Poland non-atheist 2012
## 40276      Poland non-atheist 2012
## 40277      Poland     atheist 2012
## 40278      Poland non-atheist 2012
## 40279      Poland non-atheist 2012
## 40280      Poland non-atheist 2012
## 40281      Poland non-atheist 2012
## 40282      Poland non-atheist 2012
## 40283      Poland non-atheist 2012
## 40284      Poland non-atheist 2012
## 40285      Poland non-atheist 2012
## 40286      Poland     atheist 2012
## 40287      Poland non-atheist 2012
## 40288      Poland non-atheist 2012
## 40289      Poland non-atheist 2012
## 40290      Poland non-atheist 2012
## 40291      Poland non-atheist 2012
## 40292      Poland non-atheist 2012
## 40293      Poland non-atheist 2012
## 40294      Poland non-atheist 2012
## 40295      Poland non-atheist 2012
## 40296      Poland non-atheist 2012
## 40297      Poland non-atheist 2012
## 40298      Poland non-atheist 2012
## 40299      Poland non-atheist 2012
## 40300      Poland non-atheist 2012
## 40301      Poland non-atheist 2012
## 40302      Poland non-atheist 2012
## 40303      Poland non-atheist 2012
## 40304      Poland non-atheist 2012
## 40305      Poland non-atheist 2012
## 40306      Poland non-atheist 2012
## 40307      Poland non-atheist 2012
## 40308      Poland non-atheist 2012
## 40309      Poland non-atheist 2012
## 40310      Poland non-atheist 2012
## 40311      Poland non-atheist 2012
## 40312      Poland non-atheist 2012
## 40313      Poland non-atheist 2012
## 40314      Poland non-atheist 2012
## 40315      Poland non-atheist 2012
## 40316      Poland non-atheist 2012
## 40317      Poland non-atheist 2012
## 40318      Poland non-atheist 2012
## 40319      Poland non-atheist 2012
## 40320      Poland non-atheist 2012
## 40321      Poland non-atheist 2012
## 40322      Poland non-atheist 2012
## 40323      Poland non-atheist 2012
## 40324      Poland non-atheist 2012
## 40325      Poland non-atheist 2012
## 40326      Poland non-atheist 2012
## 40327      Poland non-atheist 2012
## 40328      Poland non-atheist 2012
## 40329      Poland non-atheist 2012
## 40330      Poland non-atheist 2012
## 40331      Poland non-atheist 2012
## 40332      Poland non-atheist 2012
## 40333      Poland     atheist 2012
## 40334      Poland     atheist 2012
## 40335      Poland non-atheist 2012
## 40336      Poland non-atheist 2012
## 40337      Poland non-atheist 2012
## 40338      Poland non-atheist 2012
## 40339      Poland non-atheist 2012
## 40340      Poland non-atheist 2012
## 40341      Poland non-atheist 2012
## 40342      Poland non-atheist 2012
## 40343      Poland non-atheist 2012
## 40344      Poland non-atheist 2012
## 40345      Poland non-atheist 2012
## 40346      Poland non-atheist 2012
## 40347      Poland non-atheist 2012
## 40348      Poland non-atheist 2012
## 40349      Poland non-atheist 2012
## 40350      Poland non-atheist 2012
## 40351      Poland non-atheist 2012
## 40352      Poland non-atheist 2012
## 40353      Poland non-atheist 2012
## 40354      Poland non-atheist 2012
## 40355      Poland non-atheist 2012
## 40356      Poland non-atheist 2012
## 40357      Poland     atheist 2012
## 40358      Poland non-atheist 2012
## 40359      Poland non-atheist 2012
## 40360      Poland non-atheist 2012
## 40361      Poland non-atheist 2012
## 40362      Poland non-atheist 2012
## 40363      Poland non-atheist 2012
## 40364      Poland     atheist 2012
## 40365      Poland non-atheist 2012
## 40366      Poland non-atheist 2012
## 40367      Poland non-atheist 2012
## 40368      Poland non-atheist 2012
## 40369      Poland non-atheist 2012
## 40370      Poland non-atheist 2012
## 40371      Poland     atheist 2012
## 40372      Poland non-atheist 2012
## 40373      Poland non-atheist 2012
## 40374      Poland non-atheist 2012
## 40375      Poland non-atheist 2012
## 40376      Poland non-atheist 2012
## 40377      Poland non-atheist 2012
## 40378      Poland non-atheist 2012
## 40379      Poland non-atheist 2012
## 40380      Poland non-atheist 2012
## 40381      Poland     atheist 2012
## 40382      Poland non-atheist 2012
## 40383      Poland non-atheist 2012
## 40384      Poland non-atheist 2012
## 40385      Poland non-atheist 2012
## 40386      Poland non-atheist 2012
## 40387      Poland non-atheist 2012
## 40388      Poland non-atheist 2012
## 40389      Poland non-atheist 2012
## 40390      Poland non-atheist 2012
## 40391      Poland non-atheist 2012
## 40392      Poland non-atheist 2012
## 40393      Poland non-atheist 2012
## 40394      Poland non-atheist 2012
## 40395      Poland non-atheist 2012
## 40396      Poland non-atheist 2012
## 40397      Poland non-atheist 2012
## 40398      Poland non-atheist 2012
## 40399      Poland non-atheist 2012
## 40400      Poland non-atheist 2012
## 40401      Poland non-atheist 2012
## 40402      Poland non-atheist 2012
## 40403      Poland non-atheist 2012
## 40404      Poland non-atheist 2012
## 40405      Poland non-atheist 2012
## 40406      Poland non-atheist 2012
## 40407      Poland non-atheist 2012
## 40408      Poland non-atheist 2012
## 40409      Poland non-atheist 2012
## 40410      Poland non-atheist 2012
## 40411      Poland non-atheist 2012
## 40412      Poland non-atheist 2012
## 40413      Poland non-atheist 2012
## 40414      Poland non-atheist 2012
## 40415      Poland non-atheist 2012
## 40416      Poland non-atheist 2012
## 40417      Poland non-atheist 2012
## 40418      Poland non-atheist 2012
## 40419      Poland non-atheist 2012
## 40420      Poland non-atheist 2012
## 40421      Poland non-atheist 2012
## 40422      Poland non-atheist 2012
## 40423      Poland non-atheist 2012
## 40424      Poland non-atheist 2012
## 40425      Poland non-atheist 2012
## 40426      Poland non-atheist 2012
## 40427      Poland non-atheist 2012
## 40428      Poland non-atheist 2012
## 40429      Poland non-atheist 2012
## 40430      Poland non-atheist 2012
## 40431      Poland non-atheist 2012
## 40432      Poland non-atheist 2012
#calculate proportion of atheist responses
#get number of atheists in India
india_atheist <- nrow (india12[india12$response =="atheist",])
india_atheist
## [1] 33
#calculate proportion of atheist responses
#get number of atheists in Poland
poland_atheist <- nrow (poland12[poland12$response =="atheist",])
poland_atheist
## [1] 26
#calculate proportion of atheist responses_India
#get number of India rows

india_rows <- nrow(india12)
india_rows
## [1] 1092
#calculate proportion of atheist responses_Poland
#get number of Poland rows

poland_rows <- nrow(poland12)
poland_rows
## [1] 525
#calculate proportion of atheist responses
india_atheist/india_rows
## [1] 0.03021978
#calculate proportion of atheist responses
poland_atheist/poland_rows
## [1] 0.04952381
#calculate proportion of non_atheist responses
#get number of India non-atheists
india_non_atheist <- nrow (india12[india12$response =="non-atheist",])
india_non_atheist
## [1] 1059
#calculate proportion of non_atheist responses
#get number of Poland non-atheists
poland_non_atheist <- nrow (poland12[poland12$response =="non-atheist",])
poland_non_atheist
## [1] 499
#calculate proportion of non_atheist responses
india_non_atheist/india_rows
## [1] 0.9697802
#calculate proportion of non_atheist responses
poland_non_atheist/poland_rows
## [1] 0.9504762
#Success/fail condition satisfied:  Is the calculation greater than 10?
india_rows*(india_atheist/india_rows)
## [1] 33
#Success/fail condition satisfied:  Is the calculation greater than 10?
india_rows*(india_non_atheist/india_rows)
## [1] 1059
#Success/fail condition satisfied:  Is the calculation greater than 10?
poland_rows*(poland_atheist/poland_rows)
## [1] 26
#Success/fail condition satisfied:  Is the calculation greater than 10?
poland_rows*(poland_non_atheist/poland_rows)
## [1] 499
summary(india12)
##       nationality          response         year     
##  India      :1092   atheist    :  33   Min.   :2012  
##  Afghanistan:   0   non-atheist:1059   1st Qu.:2012  
##  Argentina  :   0                      Median :2012  
##  Armenia    :   0                      Mean   :2012  
##  Australia  :   0                      3rd Qu.:2012  
##  Austria    :   0                      Max.   :2012  
##  (Other)    :   0
summary(poland12)
##       nationality         response        year     
##  Poland     :525   atheist    : 26   Min.   :2012  
##  Afghanistan:  0   non-atheist:499   1st Qu.:2012  
##  Argentina  :  0                     Median :2012  
##  Armenia    :  0                     Mean   :2012  
##  Australia  :  0                     3rd Qu.:2012  
##  Austria    :  0                     Max.   :2012  
##  (Other)    :  0
#If the conditions for inference are reasonable, calculate the standard error and construct the interval using the inference function 
#India
inference(india12$response, est = "proportion", type = "ci", method = "theoretical", 
          success = "atheist")
## Single proportion -- success: atheist 
## Summary statistics:

## p_hat = 0.0302 ;  n = 1092 
## Check conditions: number of successes = 33 ; number of failures = 1059 
## Standard error = 0.0052 
## 95 % Confidence interval = ( 0.0201 , 0.0404 )

Single proportion – success: atheist Summary statistics: p_hat = 0.0302 ; n = 1092 Check conditions: number of successes = 33 ; number of failures = 1059 Standard error = 0.0052 95 % Confidence interval = ( 0.0201 , 0.0404 )

#find margin of error for India
lower_boundary <- 0.0201
upper_boundary <- 0.0404
diff <- upper_boundary-lower_boundary
moE <- diff/2
moE
## [1] 0.01015
#If the conditions for inference are reasonable, calculate the standard error and construct the interval using the inference function 
#Poland
inference(poland12$response, est = "proportion", type = "ci", method = "theoretical", 
          success = "atheist")
## Single proportion -- success: atheist 
## Summary statistics:

## p_hat = 0.0495 ;  n = 525 
## Check conditions: number of successes = 26 ; number of failures = 499 
## Standard error = 0.0095 
## 95 % Confidence interval = ( 0.031 , 0.0681 )

Single proportion – success: atheist Summary statistics: p_hat = 0.0495 ; n = 525 Check conditions: number of successes = 26 ; number of failures = 499 Standard error = 0.0095 95 % Confidence interval = ( 0.031 , 0.0681 )

#find margin of error for Poland
lower_boundary <- 0.031
upper_boundary <- 0.0681
diff <- upper_boundary-lower_boundary
moE <- diff/2
moE
## [1] 0.01855

How does the proportion affect the margin of error? Imagine you’ve set out to survey 1000 people on two questions: are you female? and are you left-handed? Since both of these sample proportions were calculated from the same sample size, they should have the same margin of error, right? Wrong! While the margin of error does change with sample size, it is also affected by the proportion.

Think back to the formula for the standard error: SE=p(1−p)/n−−−−−−−−−√. This is then used in the formula for the margin of error for a 95% confidence interval: ME=1.96×SE=1.96×p(1−p)/n−−−−−−−−−√. Since the population proportion p is in this ME formula, it should make sense that the margin of error is in some way dependent on the population proportion. We can visualize this relationship by creating a plot of ME vs. p.

The first step is to make a vector p that is a sequence from 0 to 1 with each number separated by 0.01. We can then create a vector of the margin of error (me) associated with each of these values of p using the familiar approximate formula (ME=2×SE). Lastly, we plot the two vectors against each other to reveal their relationship.

n <- 1000
p <- seq(0, 1, 0.01)
me <- 2 * sqrt(p * (1 - p)/n)
plot(me ~ p, ylab = "Margin of Error", xlab = "Population Proportion")

Exercise 8

Describe the relationship between p and me.

Answer As Population Proportion, p, increases from 0.0 to approximately 0.5, Margin of Error, me, increases to a maximum of approximately 0.03. As p continues increasing from .5 to 1.0, p decreases from .03 to 0.

#inserting space here

Success-failure condition The textbook emphasizes that you must always check conditions before making inference. For inference on proportions, the sample proportion can be assumed to be nearly normal if it is based upon a random sample of independent observations and if both np≥10 and n(1−p)≥10. This rule of thumb is easy enough to follow, but it makes one wonder: what’s so special about the number 10?

The short answer is: nothing. You could argue that we would be fine with 9 or that we really should be using 11. What is the “best” value for such a rule of thumb is, at least to some degree, arbitrary. However, when np and n(1−p) reaches 10 the sampling distribution is sufficiently normal to use confidence intervals and hypothesis tests that are based on that approximation.

We can investigate the interplay between n and p and the shape of the sampling distribution by using simulations. To start off, we simulate the process of drawing 5000 samples of size 1040 from a population with a true atheist proportion of 0.1. For each of the 5000 samples we compute p^ and then plot a histogram to visualize their distribution.

#interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))

Exercise 9

Describe the sampling distribution of sample proportions at n=1040 and p=0.1. Be sure to note the center, spread, and shape. Hint: Remember that R has functions such as mean to calculate summary statistics. https://statsandr.com/blog/descriptive-statistics-in-r/#boxplot

Answer Summary Statistics Min. 1st Qu. Median Mean 3rd Qu. Max. 0.06923 0.09327 0.10000 0.09991 0.10577 0.13558

Mean Error 0.01860521

Center: The sample distribution of the sample proportions’, p_hats, center-point is at approximately 0.10. This is the same as the population proportion value of p=0.1.

Shape: The distribution has a single, clear peak with values increasing up to that point and then decreasing. This indicates a unimodal, normal distribution.

Spread Calculations: Variance var(p_hats) 8.545609e-05 Standard Deviation sd(p_hats) 0.009244247 IQR IQR(p_hats) 0.0125 Minimum min(p_hats) 0.06923077 Maximum max(p_hats) 0.1355769 Range range(p_hats) 0.06923077 0.13557692

summary(p_hats)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.07019 0.09327 0.09904 0.09969 0.10577 0.12981
sd(p_hats)
## [1] 0.009287382
    var(p_hats)
## [1] 8.625547e-05
IQR(p_hats)
## [1] 0.0125
    min(p_hats)
## [1] 0.07019231
max(p_hats)
## [1] 0.1298077
 range(p_hats)
## [1] 0.07019231 0.12980769
#Mean Error
p <- 0.1
n <- 1040
me <- 2* sqrt(p*(1-p)/n)
me
## [1] 0.01860521

Exercise 10

Repeat the above simulation three more times but with modified sample sizes and proportions: for n=400 and p=0.1, n=1040 and p=0.02, and n=400 and p=0.02. Plot all four histograms together by running the par(mfrow = c(2, 2)) command before creating the histograms. You may need to expand the plot window to accommodate the larger two-by-two plot. Describe the three new sampling distributions. Based on these limited plots, how does n appear to affect the distribution of p^? How does p affect the sampling distribution?

Answer

As the sample size, n, increases from 400 to 1040, the spread becomes smaller and the margin of error becomes smaller. Changing n changes the distribution. As p changes, the location of the curve centers around the value of the population. When p is .1, the location of the curve is centered around the population value of .1. The same applies to .02. So, as p increases, the spread decreases and the margin of error increases until p reaches a certain point (population proportion = .5), and then the margin of error decreases (as the parabola shows in Exercise 7 above).

par(mfrow=c(2,2))  

#interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))





#2interplay between n ad p
#5,000 samples of size 400 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 400
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 400", xlim = c(0, 0.18))



#3interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.02
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.02, n = 1040", xlim = c(0, 0.18))







#4interplay between n ad p
#5,000 samples of size 400 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.02
n <- 400
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.02, n = 400", xlim = c(0, 0.18))

#reset plot window

par(mfrow = c(1, 1))

Exercise 11

If you refer to Table 6, you’ll find that Australia has a sample proportion of 0.1 on a sample size of 1040, and that Ecuador has a sample proportion of 0.02 on 400 subjects. Let’s suppose for this exercise that these point estimates are actually the truth. Then given the shape of their respective sampling distributions, do you think it is sensible to proceed with inference and report margin of errors, as the reports does?

Answer No, it does not make sense to proceed with inference and report margin of errors as the report does. After doing the inference tests, I found Ecuador did not meet the Success/Fail condition for Atheist. There were only 8 expected successes rather than 10 or more, so the inference test wasn’t met. Also, according to the margin of error plots shown via the code below, as the population increases above 200, there is little change in the margin of error. The curve flattens out and stays flat. The report indicates an error margin of 3-5% in the report as follows:

A total of 51,927 persons were interviewed globally. In each country a national probability sample of around 1000 men and women was interviewed either face to face (35 countries; n=33,890), via telephone (11 countries; n=7,661) or online (11 countries; n=10,376). Details are attached. The field work was conducted during November 2011- January 2012. In general the WIN-Gallup International GLOBAL INDEX OF RELIGIOSITY AND ATHEISM - 2012 Page 8 of 25 error margin for surveys of this kind is +3-5% at 95% confidence level.

When looking at the plot of the error margins and comparing them to the calculated numbers, they are more around .01 - .02, so this is close. Please see all analysis below.

Analysis:

  1. Are the observations independent? Yes If the random (picked radomly across the two countries) sample sizes are less than 10% of the populations of Australia and Ecuador, the observations are independent - and this condition necessary for inference is satisfied as observations must be independent. It appears the observations are independent, so this condition is met.

  2. Compare the margin of errors: Australia = 0.01860521 or approximately .02 Ecuador = 0.014 or approximately .01

Margin of errors are similar; distribution and spreads are similar

Summary Statistics - Australia Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00250 0.01500 0.02000 0.01997 0.02500 0.05000

Summary Statistics - Ecuador Min. 1st Qu. Median Mean 3rd Qu. Max. 0.00000 0.01500 0.02000 0.02007 0.02500 0.05250

Mean Error - Australia: 0.01860521 Mean Error - Ecuador: 0.014

Center - Australia: The sample distribution of the sample proportions’, p_hats, center-point is at approximately 0.10. This is the same as the population proportion value of p=0.1. Center - Ecuador: The sample distribution of the sample proportions, p_hatse, center-point is at approximately 0.02. This is the same as the population proportion value of p=0.02.

Shape - Australia: The distribution has a single, clear peak with values increasing up to that point and then decreasing. This indicates a unimodal, normal distribution. Shape - Ecuador: The distribution has a single, clear peak with values increasing up to that point and then decreasing. This indicates a unimodal, normal distribution.

Spread Calculations: Australia Variance var(p_hats) = 8.856288e-05 Standard Deviation sd(p_hats) = 0.009410785
IQR IQR(p_hats) = 0.0125

Spread Calculations: Ecquador Variance var(p_hatse) = 4.982679e-05 Standard Deviation sd(p_hatse) = 0.00705881 IQR IQR(p_hatse) = 0.01

  1. Success/Fail Condition: Ecuador Failed Australia Calc 1 - Atheist: Population of 1039 * 0.1000962 = 104 Calc 2 - non-Atheist: Population of 1039 * 0.8999038 = 935 Both calculations are greater than 10. The condition is met if there are at least 10 expected successes and 10 expected failures in the sample.

Ecuador Calc 1 - Atheist: Population of 404 * 0.01980198 = 8 Calc 2 - non-Atheist: Population of 404 * 0.980198 = 396 Both calculations are not greater than 10. The success/fail condition is not met for Ecuador because there are only 8 expected successes as “atheist” is considered “success” in this study.

#Margin of Error (Australia and Ecuador)
#Australia
p <- 0.1
n <- 1040
me <- 2 * sqrt(p*(1-p)/n)
me
## [1] 0.01860521
#Margin of Error (Australia and Ecuador)
#Ecuador
p <- 0.02
n <- 400
me <- 2 * sqrt(p*(1-p)/n)
me
## [1] 0.014
#Create data sets for Australia and Ecuador
#Australia
australia12 <- subset(atheism, nationality == "Australia" & year == "2012")
australia12
##      nationality    response year
## 2518   Australia non-atheist 2012
## 2519   Australia non-atheist 2012
## 2520   Australia non-atheist 2012
## 2521   Australia non-atheist 2012
## 2522   Australia non-atheist 2012
## 2523   Australia non-atheist 2012
## 2524   Australia non-atheist 2012
## 2525   Australia non-atheist 2012
## 2526   Australia non-atheist 2012
## 2527   Australia non-atheist 2012
## 2528   Australia non-atheist 2012
## 2529   Australia non-atheist 2012
## 2530   Australia non-atheist 2012
## 2531   Australia     atheist 2012
## 2532   Australia non-atheist 2012
## 2533   Australia non-atheist 2012
## 2534   Australia non-atheist 2012
## 2535   Australia     atheist 2012
## 2536   Australia non-atheist 2012
## 2537   Australia     atheist 2012
## 2538   Australia non-atheist 2012
## 2539   Australia     atheist 2012
## 2540   Australia non-atheist 2012
## 2541   Australia non-atheist 2012
## 2542   Australia non-atheist 2012
## 2543   Australia non-atheist 2012
## 2544   Australia non-atheist 2012
## 2545   Australia non-atheist 2012
## 2546   Australia non-atheist 2012
## 2547   Australia non-atheist 2012
## 2548   Australia non-atheist 2012
## 2549   Australia non-atheist 2012
## 2550   Australia non-atheist 2012
## 2551   Australia non-atheist 2012
## 2552   Australia     atheist 2012
## 2553   Australia non-atheist 2012
## 2554   Australia non-atheist 2012
## 2555   Australia     atheist 2012
## 2556   Australia non-atheist 2012
## 2557   Australia non-atheist 2012
## 2558   Australia non-atheist 2012
## 2559   Australia non-atheist 2012
## 2560   Australia non-atheist 2012
## 2561   Australia non-atheist 2012
## 2562   Australia non-atheist 2012
## 2563   Australia non-atheist 2012
## 2564   Australia non-atheist 2012
## 2565   Australia non-atheist 2012
## 2566   Australia     atheist 2012
## 2567   Australia non-atheist 2012
## 2568   Australia non-atheist 2012
## 2569   Australia non-atheist 2012
## 2570   Australia non-atheist 2012
## 2571   Australia non-atheist 2012
## 2572   Australia non-atheist 2012
## 2573   Australia non-atheist 2012
## 2574   Australia non-atheist 2012
## 2575   Australia non-atheist 2012
## 2576   Australia     atheist 2012
## 2577   Australia non-atheist 2012
## 2578   Australia non-atheist 2012
## 2579   Australia non-atheist 2012
## 2580   Australia     atheist 2012
## 2581   Australia non-atheist 2012
## 2582   Australia non-atheist 2012
## 2583   Australia non-atheist 2012
## 2584   Australia non-atheist 2012
## 2585   Australia non-atheist 2012
## 2586   Australia non-atheist 2012
## 2587   Australia     atheist 2012
## 2588   Australia non-atheist 2012
## 2589   Australia non-atheist 2012
## 2590   Australia non-atheist 2012
## 2591   Australia non-atheist 2012
## 2592   Australia non-atheist 2012
## 2593   Australia non-atheist 2012
## 2594   Australia non-atheist 2012
## 2595   Australia non-atheist 2012
## 2596   Australia non-atheist 2012
## 2597   Australia     atheist 2012
## 2598   Australia non-atheist 2012
## 2599   Australia non-atheist 2012
## 2600   Australia non-atheist 2012
## 2601   Australia non-atheist 2012
## 2602   Australia non-atheist 2012
## 2603   Australia non-atheist 2012
## 2604   Australia non-atheist 2012
## 2605   Australia non-atheist 2012
## 2606   Australia non-atheist 2012
## 2607   Australia non-atheist 2012
## 2608   Australia non-atheist 2012
## 2609   Australia non-atheist 2012
## 2610   Australia non-atheist 2012
## 2611   Australia non-atheist 2012
## 2612   Australia non-atheist 2012
## 2613   Australia non-atheist 2012
## 2614   Australia non-atheist 2012
## 2615   Australia non-atheist 2012
## 2616   Australia non-atheist 2012
## 2617   Australia non-atheist 2012
## 2618   Australia non-atheist 2012
## 2619   Australia non-atheist 2012
## 2620   Australia non-atheist 2012
## 2621   Australia non-atheist 2012
## 2622   Australia non-atheist 2012
## 2623   Australia non-atheist 2012
## 2624   Australia non-atheist 2012
## 2625   Australia non-atheist 2012
## 2626   Australia non-atheist 2012
## 2627   Australia non-atheist 2012
## 2628   Australia non-atheist 2012
## 2629   Australia non-atheist 2012
## 2630   Australia non-atheist 2012
## 2631   Australia non-atheist 2012
## 2632   Australia non-atheist 2012
## 2633   Australia non-atheist 2012
## 2634   Australia non-atheist 2012
## 2635   Australia non-atheist 2012
## 2636   Australia non-atheist 2012
## 2637   Australia non-atheist 2012
## 2638   Australia non-atheist 2012
## 2639   Australia non-atheist 2012
## 2640   Australia non-atheist 2012
## 2641   Australia     atheist 2012
## 2642   Australia non-atheist 2012
## 2643   Australia non-atheist 2012
## 2644   Australia non-atheist 2012
## 2645   Australia non-atheist 2012
## 2646   Australia non-atheist 2012
## 2647   Australia     atheist 2012
## 2648   Australia non-atheist 2012
## 2649   Australia non-atheist 2012
## 2650   Australia non-atheist 2012
## 2651   Australia non-atheist 2012
## 2652   Australia non-atheist 2012
## 2653   Australia non-atheist 2012
## 2654   Australia non-atheist 2012
## 2655   Australia non-atheist 2012
## 2656   Australia non-atheist 2012
## 2657   Australia non-atheist 2012
## 2658   Australia non-atheist 2012
## 2659   Australia non-atheist 2012
## 2660   Australia non-atheist 2012
## 2661   Australia non-atheist 2012
## 2662   Australia non-atheist 2012
## 2663   Australia non-atheist 2012
## 2664   Australia non-atheist 2012
## 2665   Australia non-atheist 2012
## 2666   Australia non-atheist 2012
## 2667   Australia non-atheist 2012
## 2668   Australia non-atheist 2012
## 2669   Australia non-atheist 2012
## 2670   Australia non-atheist 2012
## 2671   Australia non-atheist 2012
## 2672   Australia non-atheist 2012
## 2673   Australia non-atheist 2012
## 2674   Australia non-atheist 2012
## 2675   Australia non-atheist 2012
## 2676   Australia non-atheist 2012
## 2677   Australia non-atheist 2012
## 2678   Australia non-atheist 2012
## 2679   Australia non-atheist 2012
## 2680   Australia non-atheist 2012
## 2681   Australia non-atheist 2012
## 2682   Australia non-atheist 2012
## 2683   Australia non-atheist 2012
## 2684   Australia non-atheist 2012
## 2685   Australia     atheist 2012
## 2686   Australia non-atheist 2012
## 2687   Australia     atheist 2012
## 2688   Australia non-atheist 2012
## 2689   Australia non-atheist 2012
## 2690   Australia non-atheist 2012
## 2691   Australia non-atheist 2012
## 2692   Australia non-atheist 2012
## 2693   Australia non-atheist 2012
## 2694   Australia non-atheist 2012
## 2695   Australia     atheist 2012
## 2696   Australia non-atheist 2012
## 2697   Australia non-atheist 2012
## 2698   Australia     atheist 2012
## 2699   Australia non-atheist 2012
## 2700   Australia non-atheist 2012
## 2701   Australia non-atheist 2012
## 2702   Australia non-atheist 2012
## 2703   Australia non-atheist 2012
## 2704   Australia non-atheist 2012
## 2705   Australia non-atheist 2012
## 2706   Australia non-atheist 2012
## 2707   Australia non-atheist 2012
## 2708   Australia non-atheist 2012
## 2709   Australia non-atheist 2012
## 2710   Australia non-atheist 2012
## 2711   Australia non-atheist 2012
## 2712   Australia non-atheist 2012
## 2713   Australia     atheist 2012
## 2714   Australia     atheist 2012
## 2715   Australia non-atheist 2012
## 2716   Australia non-atheist 2012
## 2717   Australia non-atheist 2012
## 2718   Australia non-atheist 2012
## 2719   Australia non-atheist 2012
## 2720   Australia non-atheist 2012
## 2721   Australia non-atheist 2012
## 2722   Australia     atheist 2012
## 2723   Australia non-atheist 2012
## 2724   Australia non-atheist 2012
## 2725   Australia non-atheist 2012
## 2726   Australia non-atheist 2012
## 2727   Australia non-atheist 2012
## 2728   Australia non-atheist 2012
## 2729   Australia non-atheist 2012
## 2730   Australia non-atheist 2012
## 2731   Australia non-atheist 2012
## 2732   Australia non-atheist 2012
## 2733   Australia non-atheist 2012
## 2734   Australia non-atheist 2012
## 2735   Australia non-atheist 2012
## 2736   Australia non-atheist 2012
## 2737   Australia non-atheist 2012
## 2738   Australia non-atheist 2012
## 2739   Australia non-atheist 2012
## 2740   Australia non-atheist 2012
## 2741   Australia non-atheist 2012
## 2742   Australia non-atheist 2012
## 2743   Australia non-atheist 2012
## 2744   Australia non-atheist 2012
## 2745   Australia non-atheist 2012
## 2746   Australia non-atheist 2012
## 2747   Australia non-atheist 2012
## 2748   Australia non-atheist 2012
## 2749   Australia non-atheist 2012
## 2750   Australia non-atheist 2012
## 2751   Australia non-atheist 2012
## 2752   Australia non-atheist 2012
## 2753   Australia non-atheist 2012
## 2754   Australia non-atheist 2012
## 2755   Australia non-atheist 2012
## 2756   Australia non-atheist 2012
## 2757   Australia non-atheist 2012
## 2758   Australia non-atheist 2012
## 2759   Australia non-atheist 2012
## 2760   Australia non-atheist 2012
## 2761   Australia non-atheist 2012
## 2762   Australia     atheist 2012
## 2763   Australia non-atheist 2012
## 2764   Australia non-atheist 2012
## 2765   Australia non-atheist 2012
## 2766   Australia non-atheist 2012
## 2767   Australia non-atheist 2012
## 2768   Australia non-atheist 2012
## 2769   Australia non-atheist 2012
## 2770   Australia non-atheist 2012
## 2771   Australia non-atheist 2012
## 2772   Australia non-atheist 2012
## 2773   Australia non-atheist 2012
## 2774   Australia     atheist 2012
## 2775   Australia non-atheist 2012
## 2776   Australia     atheist 2012
## 2777   Australia non-atheist 2012
## 2778   Australia non-atheist 2012
## 2779   Australia non-atheist 2012
## 2780   Australia non-atheist 2012
## 2781   Australia non-atheist 2012
## 2782   Australia non-atheist 2012
## 2783   Australia non-atheist 2012
## 2784   Australia non-atheist 2012
## 2785   Australia non-atheist 2012
## 2786   Australia non-atheist 2012
## 2787   Australia non-atheist 2012
## 2788   Australia non-atheist 2012
## 2789   Australia non-atheist 2012
## 2790   Australia     atheist 2012
## 2791   Australia     atheist 2012
## 2792   Australia non-atheist 2012
## 2793   Australia non-atheist 2012
## 2794   Australia non-atheist 2012
## 2795   Australia non-atheist 2012
## 2796   Australia     atheist 2012
## 2797   Australia non-atheist 2012
## 2798   Australia non-atheist 2012
## 2799   Australia non-atheist 2012
## 2800   Australia non-atheist 2012
## 2801   Australia non-atheist 2012
## 2802   Australia non-atheist 2012
## 2803   Australia non-atheist 2012
## 2804   Australia non-atheist 2012
## 2805   Australia non-atheist 2012
## 2806   Australia non-atheist 2012
## 2807   Australia non-atheist 2012
## 2808   Australia non-atheist 2012
## 2809   Australia non-atheist 2012
## 2810   Australia non-atheist 2012
## 2811   Australia non-atheist 2012
## 2812   Australia non-atheist 2012
## 2813   Australia non-atheist 2012
## 2814   Australia non-atheist 2012
## 2815   Australia non-atheist 2012
## 2816   Australia non-atheist 2012
## 2817   Australia non-atheist 2012
## 2818   Australia     atheist 2012
## 2819   Australia non-atheist 2012
## 2820   Australia non-atheist 2012
## 2821   Australia non-atheist 2012
## 2822   Australia     atheist 2012
## 2823   Australia     atheist 2012
## 2824   Australia non-atheist 2012
## 2825   Australia non-atheist 2012
## 2826   Australia non-atheist 2012
## 2827   Australia non-atheist 2012
## 2828   Australia non-atheist 2012
## 2829   Australia     atheist 2012
## 2830   Australia non-atheist 2012
## 2831   Australia non-atheist 2012
## 2832   Australia non-atheist 2012
## 2833   Australia non-atheist 2012
## 2834   Australia non-atheist 2012
## 2835   Australia non-atheist 2012
## 2836   Australia non-atheist 2012
## 2837   Australia non-atheist 2012
## 2838   Australia non-atheist 2012
## 2839   Australia non-atheist 2012
## 2840   Australia non-atheist 2012
## 2841   Australia non-atheist 2012
## 2842   Australia non-atheist 2012
## 2843   Australia non-atheist 2012
## 2844   Australia non-atheist 2012
## 2845   Australia non-atheist 2012
## 2846   Australia non-atheist 2012
## 2847   Australia non-atheist 2012
## 2848   Australia non-atheist 2012
## 2849   Australia non-atheist 2012
## 2850   Australia non-atheist 2012
## 2851   Australia non-atheist 2012
## 2852   Australia non-atheist 2012
## 2853   Australia non-atheist 2012
## 2854   Australia non-atheist 2012
## 2855   Australia     atheist 2012
## 2856   Australia     atheist 2012
## 2857   Australia non-atheist 2012
## 2858   Australia non-atheist 2012
## 2859   Australia non-atheist 2012
## 2860   Australia non-atheist 2012
## 2861   Australia non-atheist 2012
## 2862   Australia non-atheist 2012
## 2863   Australia non-atheist 2012
## 2864   Australia non-atheist 2012
## 2865   Australia non-atheist 2012
## 2866   Australia non-atheist 2012
## 2867   Australia non-atheist 2012
## 2868   Australia     atheist 2012
## 2869   Australia non-atheist 2012
## 2870   Australia     atheist 2012
## 2871   Australia non-atheist 2012
## 2872   Australia non-atheist 2012
## 2873   Australia non-atheist 2012
## 2874   Australia non-atheist 2012
## 2875   Australia non-atheist 2012
## 2876   Australia non-atheist 2012
## 2877   Australia non-atheist 2012
## 2878   Australia     atheist 2012
## 2879   Australia non-atheist 2012
## 2880   Australia non-atheist 2012
## 2881   Australia non-atheist 2012
## 2882   Australia non-atheist 2012
## 2883   Australia non-atheist 2012
## 2884   Australia non-atheist 2012
## 2885   Australia non-atheist 2012
## 2886   Australia non-atheist 2012
## 2887   Australia non-atheist 2012
## 2888   Australia non-atheist 2012
## 2889   Australia non-atheist 2012
## 2890   Australia non-atheist 2012
## 2891   Australia non-atheist 2012
## 2892   Australia non-atheist 2012
## 2893   Australia non-atheist 2012
## 2894   Australia non-atheist 2012
## 2895   Australia non-atheist 2012
## 2896   Australia non-atheist 2012
## 2897   Australia non-atheist 2012
## 2898   Australia non-atheist 2012
## 2899   Australia     atheist 2012
## 2900   Australia non-atheist 2012
## 2901   Australia non-atheist 2012
## 2902   Australia non-atheist 2012
## 2903   Australia non-atheist 2012
## 2904   Australia non-atheist 2012
## 2905   Australia non-atheist 2012
## 2906   Australia non-atheist 2012
## 2907   Australia     atheist 2012
## 2908   Australia non-atheist 2012
## 2909   Australia non-atheist 2012
## 2910   Australia non-atheist 2012
## 2911   Australia non-atheist 2012
## 2912   Australia non-atheist 2012
## 2913   Australia non-atheist 2012
## 2914   Australia non-atheist 2012
## 2915   Australia non-atheist 2012
## 2916   Australia non-atheist 2012
## 2917   Australia non-atheist 2012
## 2918   Australia non-atheist 2012
## 2919   Australia non-atheist 2012
## 2920   Australia non-atheist 2012
## 2921   Australia non-atheist 2012
## 2922   Australia non-atheist 2012
## 2923   Australia non-atheist 2012
## 2924   Australia non-atheist 2012
## 2925   Australia     atheist 2012
## 2926   Australia non-atheist 2012
## 2927   Australia     atheist 2012
## 2928   Australia non-atheist 2012
## 2929   Australia     atheist 2012
## 2930   Australia non-atheist 2012
## 2931   Australia non-atheist 2012
## 2932   Australia     atheist 2012
## 2933   Australia non-atheist 2012
## 2934   Australia non-atheist 2012
## 2935   Australia     atheist 2012
## 2936   Australia non-atheist 2012
## 2937   Australia non-atheist 2012
## 2938   Australia non-atheist 2012
## 2939   Australia     atheist 2012
## 2940   Australia non-atheist 2012
## 2941   Australia non-atheist 2012
## 2942   Australia non-atheist 2012
## 2943   Australia non-atheist 2012
## 2944   Australia non-atheist 2012
## 2945   Australia non-atheist 2012
## 2946   Australia non-atheist 2012
## 2947   Australia non-atheist 2012
## 2948   Australia non-atheist 2012
## 2949   Australia non-atheist 2012
## 2950   Australia non-atheist 2012
## 2951   Australia non-atheist 2012
## 2952   Australia non-atheist 2012
## 2953   Australia     atheist 2012
## 2954   Australia non-atheist 2012
## 2955   Australia non-atheist 2012
## 2956   Australia     atheist 2012
## 2957   Australia     atheist 2012
## 2958   Australia non-atheist 2012
## 2959   Australia non-atheist 2012
## 2960   Australia non-atheist 2012
## 2961   Australia non-atheist 2012
## 2962   Australia non-atheist 2012
## 2963   Australia non-atheist 2012
## 2964   Australia non-atheist 2012
## 2965   Australia non-atheist 2012
## 2966   Australia non-atheist 2012
## 2967   Australia non-atheist 2012
## 2968   Australia non-atheist 2012
## 2969   Australia     atheist 2012
## 2970   Australia non-atheist 2012
## 2971   Australia non-atheist 2012
## 2972   Australia non-atheist 2012
## 2973   Australia     atheist 2012
## 2974   Australia     atheist 2012
## 2975   Australia non-atheist 2012
## 2976   Australia non-atheist 2012
## 2977   Australia non-atheist 2012
## 2978   Australia non-atheist 2012
## 2979   Australia non-atheist 2012
## 2980   Australia non-atheist 2012
## 2981   Australia non-atheist 2012
## 2982   Australia     atheist 2012
## 2983   Australia non-atheist 2012
## 2984   Australia non-atheist 2012
## 2985   Australia non-atheist 2012
## 2986   Australia non-atheist 2012
## 2987   Australia non-atheist 2012
## 2988   Australia non-atheist 2012
## 2989   Australia non-atheist 2012
## 2990   Australia non-atheist 2012
## 2991   Australia non-atheist 2012
## 2992   Australia     atheist 2012
## 2993   Australia non-atheist 2012
## 2994   Australia non-atheist 2012
## 2995   Australia     atheist 2012
## 2996   Australia non-atheist 2012
## 2997   Australia non-atheist 2012
## 2998   Australia non-atheist 2012
## 2999   Australia non-atheist 2012
## 3000   Australia non-atheist 2012
## 3001   Australia non-atheist 2012
## 3002   Australia     atheist 2012
## 3003   Australia non-atheist 2012
## 3004   Australia non-atheist 2012
## 3005   Australia non-atheist 2012
## 3006   Australia non-atheist 2012
## 3007   Australia non-atheist 2012
## 3008   Australia non-atheist 2012
## 3009   Australia non-atheist 2012
## 3010   Australia non-atheist 2012
## 3011   Australia non-atheist 2012
## 3012   Australia non-atheist 2012
## 3013   Australia non-atheist 2012
## 3014   Australia non-atheist 2012
## 3015   Australia non-atheist 2012
## 3016   Australia non-atheist 2012
## 3017   Australia non-atheist 2012
## 3018   Australia non-atheist 2012
## 3019   Australia non-atheist 2012
## 3020   Australia     atheist 2012
## 3021   Australia     atheist 2012
## 3022   Australia non-atheist 2012
## 3023   Australia non-atheist 2012
## 3024   Australia non-atheist 2012
## 3025   Australia non-atheist 2012
## 3026   Australia non-atheist 2012
## 3027   Australia non-atheist 2012
## 3028   Australia     atheist 2012
## 3029   Australia non-atheist 2012
## 3030   Australia     atheist 2012
## 3031   Australia non-atheist 2012
## 3032   Australia non-atheist 2012
## 3033   Australia non-atheist 2012
## 3034   Australia non-atheist 2012
## 3035   Australia non-atheist 2012
## 3036   Australia     atheist 2012
## 3037   Australia non-atheist 2012
## 3038   Australia non-atheist 2012
## 3039   Australia non-atheist 2012
## 3040   Australia non-atheist 2012
## 3041   Australia non-atheist 2012
## 3042   Australia non-atheist 2012
## 3043   Australia non-atheist 2012
## 3044   Australia non-atheist 2012
## 3045   Australia non-atheist 2012
## 3046   Australia non-atheist 2012
## 3047   Australia non-atheist 2012
## 3048   Australia non-atheist 2012
## 3049   Australia non-atheist 2012
## 3050   Australia non-atheist 2012
## 3051   Australia non-atheist 2012
## 3052   Australia non-atheist 2012
## 3053   Australia non-atheist 2012
## 3054   Australia non-atheist 2012
## 3055   Australia non-atheist 2012
## 3056   Australia non-atheist 2012
## 3057   Australia     atheist 2012
## 3058   Australia non-atheist 2012
## 3059   Australia non-atheist 2012
## 3060   Australia non-atheist 2012
## 3061   Australia non-atheist 2012
## 3062   Australia non-atheist 2012
## 3063   Australia non-atheist 2012
## 3064   Australia non-atheist 2012
## 3065   Australia non-atheist 2012
## 3066   Australia non-atheist 2012
## 3067   Australia non-atheist 2012
## 3068   Australia non-atheist 2012
## 3069   Australia non-atheist 2012
## 3070   Australia non-atheist 2012
## 3071   Australia non-atheist 2012
## 3072   Australia non-atheist 2012
## 3073   Australia non-atheist 2012
## 3074   Australia non-atheist 2012
## 3075   Australia non-atheist 2012
## 3076   Australia non-atheist 2012
## 3077   Australia non-atheist 2012
## 3078   Australia     atheist 2012
## 3079   Australia non-atheist 2012
## 3080   Australia non-atheist 2012
## 3081   Australia non-atheist 2012
## 3082   Australia non-atheist 2012
## 3083   Australia non-atheist 2012
## 3084   Australia     atheist 2012
## 3085   Australia non-atheist 2012
## 3086   Australia non-atheist 2012
## 3087   Australia non-atheist 2012
## 3088   Australia non-atheist 2012
## 3089   Australia non-atheist 2012
## 3090   Australia non-atheist 2012
## 3091   Australia     atheist 2012
## 3092   Australia non-atheist 2012
## 3093   Australia non-atheist 2012
## 3094   Australia non-atheist 2012
## 3095   Australia non-atheist 2012
## 3096   Australia non-atheist 2012
## 3097   Australia non-atheist 2012
## 3098   Australia non-atheist 2012
## 3099   Australia non-atheist 2012
## 3100   Australia non-atheist 2012
## 3101   Australia non-atheist 2012
## 3102   Australia non-atheist 2012
## 3103   Australia     atheist 2012
## 3104   Australia non-atheist 2012
## 3105   Australia non-atheist 2012
## 3106   Australia non-atheist 2012
## 3107   Australia non-atheist 2012
## 3108   Australia non-atheist 2012
## 3109   Australia non-atheist 2012
## 3110   Australia non-atheist 2012
## 3111   Australia non-atheist 2012
## 3112   Australia non-atheist 2012
## 3113   Australia non-atheist 2012
## 3114   Australia non-atheist 2012
## 3115   Australia non-atheist 2012
## 3116   Australia non-atheist 2012
## 3117   Australia non-atheist 2012
## 3118   Australia non-atheist 2012
## 3119   Australia non-atheist 2012
## 3120   Australia non-atheist 2012
## 3121   Australia non-atheist 2012
## 3122   Australia non-atheist 2012
## 3123   Australia non-atheist 2012
## 3124   Australia non-atheist 2012
## 3125   Australia non-atheist 2012
## 3126   Australia non-atheist 2012
## 3127   Australia non-atheist 2012
## 3128   Australia non-atheist 2012
## 3129   Australia non-atheist 2012
## 3130   Australia non-atheist 2012
## 3131   Australia non-atheist 2012
## 3132   Australia non-atheist 2012
## 3133   Australia non-atheist 2012
## 3134   Australia non-atheist 2012
## 3135   Australia non-atheist 2012
## 3136   Australia non-atheist 2012
## 3137   Australia non-atheist 2012
## 3138   Australia non-atheist 2012
## 3139   Australia non-atheist 2012
## 3140   Australia non-atheist 2012
## 3141   Australia non-atheist 2012
## 3142   Australia non-atheist 2012
## 3143   Australia non-atheist 2012
## 3144   Australia non-atheist 2012
## 3145   Australia non-atheist 2012
## 3146   Australia non-atheist 2012
## 3147   Australia non-atheist 2012
## 3148   Australia non-atheist 2012
## 3149   Australia non-atheist 2012
## 3150   Australia non-atheist 2012
## 3151   Australia non-atheist 2012
## 3152   Australia non-atheist 2012
## 3153   Australia non-atheist 2012
## 3154   Australia non-atheist 2012
## 3155   Australia non-atheist 2012
## 3156   Australia non-atheist 2012
## 3157   Australia non-atheist 2012
## 3158   Australia non-atheist 2012
## 3159   Australia non-atheist 2012
## 3160   Australia non-atheist 2012
## 3161   Australia non-atheist 2012
## 3162   Australia non-atheist 2012
## 3163   Australia non-atheist 2012
## 3164   Australia non-atheist 2012
## 3165   Australia non-atheist 2012
## 3166   Australia non-atheist 2012
## 3167   Australia non-atheist 2012
## 3168   Australia non-atheist 2012
## 3169   Australia non-atheist 2012
## 3170   Australia non-atheist 2012
## 3171   Australia non-atheist 2012
## 3172   Australia non-atheist 2012
## 3173   Australia non-atheist 2012
## 3174   Australia non-atheist 2012
## 3175   Australia non-atheist 2012
## 3176   Australia non-atheist 2012
## 3177   Australia non-atheist 2012
## 3178   Australia non-atheist 2012
## 3179   Australia non-atheist 2012
## 3180   Australia non-atheist 2012
## 3181   Australia     atheist 2012
## 3182   Australia non-atheist 2012
## 3183   Australia non-atheist 2012
## 3184   Australia     atheist 2012
## 3185   Australia non-atheist 2012
## 3186   Australia non-atheist 2012
## 3187   Australia     atheist 2012
## 3188   Australia     atheist 2012
## 3189   Australia non-atheist 2012
## 3190   Australia non-atheist 2012
## 3191   Australia non-atheist 2012
## 3192   Australia non-atheist 2012
## 3193   Australia non-atheist 2012
## 3194   Australia non-atheist 2012
## 3195   Australia     atheist 2012
## 3196   Australia non-atheist 2012
## 3197   Australia non-atheist 2012
## 3198   Australia non-atheist 2012
## 3199   Australia non-atheist 2012
## 3200   Australia non-atheist 2012
## 3201   Australia     atheist 2012
## 3202   Australia non-atheist 2012
## 3203   Australia non-atheist 2012
## 3204   Australia non-atheist 2012
## 3205   Australia non-atheist 2012
## 3206   Australia non-atheist 2012
## 3207   Australia non-atheist 2012
## 3208   Australia non-atheist 2012
## 3209   Australia non-atheist 2012
## 3210   Australia non-atheist 2012
## 3211   Australia non-atheist 2012
## 3212   Australia non-atheist 2012
## 3213   Australia non-atheist 2012
## 3214   Australia non-atheist 2012
## 3215   Australia non-atheist 2012
## 3216   Australia non-atheist 2012
## 3217   Australia non-atheist 2012
## 3218   Australia non-atheist 2012
## 3219   Australia non-atheist 2012
## 3220   Australia     atheist 2012
## 3221   Australia non-atheist 2012
## 3222   Australia non-atheist 2012
## 3223   Australia non-atheist 2012
## 3224   Australia non-atheist 2012
## 3225   Australia non-atheist 2012
## 3226   Australia non-atheist 2012
## 3227   Australia non-atheist 2012
## 3228   Australia     atheist 2012
## 3229   Australia non-atheist 2012
## 3230   Australia non-atheist 2012
## 3231   Australia non-atheist 2012
## 3232   Australia non-atheist 2012
## 3233   Australia non-atheist 2012
## 3234   Australia non-atheist 2012
## 3235   Australia non-atheist 2012
## 3236   Australia non-atheist 2012
## 3237   Australia non-atheist 2012
## 3238   Australia non-atheist 2012
## 3239   Australia non-atheist 2012
## 3240   Australia non-atheist 2012
## 3241   Australia non-atheist 2012
## 3242   Australia     atheist 2012
## 3243   Australia non-atheist 2012
## 3244   Australia non-atheist 2012
## 3245   Australia non-atheist 2012
## 3246   Australia non-atheist 2012
## 3247   Australia non-atheist 2012
## 3248   Australia non-atheist 2012
## 3249   Australia non-atheist 2012
## 3250   Australia     atheist 2012
## 3251   Australia non-atheist 2012
## 3252   Australia non-atheist 2012
## 3253   Australia non-atheist 2012
## 3254   Australia non-atheist 2012
## 3255   Australia non-atheist 2012
## 3256   Australia non-atheist 2012
## 3257   Australia non-atheist 2012
## 3258   Australia non-atheist 2012
## 3259   Australia non-atheist 2012
## 3260   Australia non-atheist 2012
## 3261   Australia non-atheist 2012
## 3262   Australia non-atheist 2012
## 3263   Australia non-atheist 2012
## 3264   Australia non-atheist 2012
## 3265   Australia non-atheist 2012
## 3266   Australia     atheist 2012
## 3267   Australia non-atheist 2012
## 3268   Australia non-atheist 2012
## 3269   Australia non-atheist 2012
## 3270   Australia non-atheist 2012
## 3271   Australia non-atheist 2012
## 3272   Australia non-atheist 2012
## 3273   Australia non-atheist 2012
## 3274   Australia non-atheist 2012
## 3275   Australia non-atheist 2012
## 3276   Australia non-atheist 2012
## 3277   Australia non-atheist 2012
## 3278   Australia non-atheist 2012
## 3279   Australia non-atheist 2012
## 3280   Australia non-atheist 2012
## 3281   Australia non-atheist 2012
## 3282   Australia non-atheist 2012
## 3283   Australia non-atheist 2012
## 3284   Australia non-atheist 2012
## 3285   Australia non-atheist 2012
## 3286   Australia non-atheist 2012
## 3287   Australia non-atheist 2012
## 3288   Australia non-atheist 2012
## 3289   Australia non-atheist 2012
## 3290   Australia     atheist 2012
## 3291   Australia non-atheist 2012
## 3292   Australia non-atheist 2012
## 3293   Australia non-atheist 2012
## 3294   Australia non-atheist 2012
## 3295   Australia non-atheist 2012
## 3296   Australia non-atheist 2012
## 3297   Australia non-atheist 2012
## 3298   Australia non-atheist 2012
## 3299   Australia non-atheist 2012
## 3300   Australia non-atheist 2012
## 3301   Australia non-atheist 2012
## 3302   Australia non-atheist 2012
## 3303   Australia non-atheist 2012
## 3304   Australia non-atheist 2012
## 3305   Australia non-atheist 2012
## 3306   Australia non-atheist 2012
## 3307   Australia non-atheist 2012
## 3308   Australia non-atheist 2012
## 3309   Australia non-atheist 2012
## 3310   Australia     atheist 2012
## 3311   Australia     atheist 2012
## 3312   Australia non-atheist 2012
## 3313   Australia non-atheist 2012
## 3314   Australia non-atheist 2012
## 3315   Australia non-atheist 2012
## 3316   Australia non-atheist 2012
## 3317   Australia non-atheist 2012
## 3318   Australia     atheist 2012
## 3319   Australia non-atheist 2012
## 3320   Australia non-atheist 2012
## 3321   Australia non-atheist 2012
## 3322   Australia non-atheist 2012
## 3323   Australia non-atheist 2012
## 3324   Australia non-atheist 2012
## 3325   Australia non-atheist 2012
## 3326   Australia non-atheist 2012
## 3327   Australia non-atheist 2012
## 3328   Australia non-atheist 2012
## 3329   Australia non-atheist 2012
## 3330   Australia non-atheist 2012
## 3331   Australia non-atheist 2012
## 3332   Australia non-atheist 2012
## 3333   Australia non-atheist 2012
## 3334   Australia     atheist 2012
## 3335   Australia non-atheist 2012
## 3336   Australia non-atheist 2012
## 3337   Australia non-atheist 2012
## 3338   Australia     atheist 2012
## 3339   Australia non-atheist 2012
## 3340   Australia non-atheist 2012
## 3341   Australia non-atheist 2012
## 3342   Australia non-atheist 2012
## 3343   Australia non-atheist 2012
## 3344   Australia     atheist 2012
## 3345   Australia non-atheist 2012
## 3346   Australia non-atheist 2012
## 3347   Australia non-atheist 2012
## 3348   Australia non-atheist 2012
## 3349   Australia non-atheist 2012
## 3350   Australia non-atheist 2012
## 3351   Australia non-atheist 2012
## 3352   Australia non-atheist 2012
## 3353   Australia non-atheist 2012
## 3354   Australia non-atheist 2012
## 3355   Australia     atheist 2012
## 3356   Australia non-atheist 2012
## 3357   Australia non-atheist 2012
## 3358   Australia non-atheist 2012
## 3359   Australia non-atheist 2012
## 3360   Australia non-atheist 2012
## 3361   Australia non-atheist 2012
## 3362   Australia non-atheist 2012
## 3363   Australia non-atheist 2012
## 3364   Australia non-atheist 2012
## 3365   Australia     atheist 2012
## 3366   Australia non-atheist 2012
## 3367   Australia     atheist 2012
## 3368   Australia non-atheist 2012
## 3369   Australia non-atheist 2012
## 3370   Australia non-atheist 2012
## 3371   Australia non-atheist 2012
## 3372   Australia non-atheist 2012
## 3373   Australia     atheist 2012
## 3374   Australia non-atheist 2012
## 3375   Australia non-atheist 2012
## 3376   Australia non-atheist 2012
## 3377   Australia non-atheist 2012
## 3378   Australia non-atheist 2012
## 3379   Australia non-atheist 2012
## 3380   Australia non-atheist 2012
## 3381   Australia non-atheist 2012
## 3382   Australia non-atheist 2012
## 3383   Australia non-atheist 2012
## 3384   Australia non-atheist 2012
## 3385   Australia non-atheist 2012
## 3386   Australia non-atheist 2012
## 3387   Australia non-atheist 2012
## 3388   Australia non-atheist 2012
## 3389   Australia     atheist 2012
## 3390   Australia non-atheist 2012
## 3391   Australia     atheist 2012
## 3392   Australia non-atheist 2012
## 3393   Australia non-atheist 2012
## 3394   Australia non-atheist 2012
## 3395   Australia     atheist 2012
## 3396   Australia     atheist 2012
## 3397   Australia non-atheist 2012
## 3398   Australia non-atheist 2012
## 3399   Australia non-atheist 2012
## 3400   Australia non-atheist 2012
## 3401   Australia non-atheist 2012
## 3402   Australia non-atheist 2012
## 3403   Australia non-atheist 2012
## 3404   Australia     atheist 2012
## 3405   Australia non-atheist 2012
## 3406   Australia non-atheist 2012
## 3407   Australia     atheist 2012
## 3408   Australia non-atheist 2012
## 3409   Australia non-atheist 2012
## 3410   Australia non-atheist 2012
## 3411   Australia non-atheist 2012
## 3412   Australia non-atheist 2012
## 3413   Australia non-atheist 2012
## 3414   Australia non-atheist 2012
## 3415   Australia non-atheist 2012
## 3416   Australia non-atheist 2012
## 3417   Australia non-atheist 2012
## 3418   Australia non-atheist 2012
## 3419   Australia non-atheist 2012
## 3420   Australia non-atheist 2012
## 3421   Australia non-atheist 2012
## 3422   Australia non-atheist 2012
## 3423   Australia non-atheist 2012
## 3424   Australia non-atheist 2012
## 3425   Australia non-atheist 2012
## 3426   Australia     atheist 2012
## 3427   Australia non-atheist 2012
## 3428   Australia non-atheist 2012
## 3429   Australia non-atheist 2012
## 3430   Australia non-atheist 2012
## 3431   Australia non-atheist 2012
## 3432   Australia non-atheist 2012
## 3433   Australia non-atheist 2012
## 3434   Australia non-atheist 2012
## 3435   Australia non-atheist 2012
## 3436   Australia non-atheist 2012
## 3437   Australia non-atheist 2012
## 3438   Australia non-atheist 2012
## 3439   Australia non-atheist 2012
## 3440   Australia non-atheist 2012
## 3441   Australia non-atheist 2012
## 3442   Australia non-atheist 2012
## 3443   Australia non-atheist 2012
## 3444   Australia non-atheist 2012
## 3445   Australia non-atheist 2012
## 3446   Australia     atheist 2012
## 3447   Australia non-atheist 2012
## 3448   Australia non-atheist 2012
## 3449   Australia non-atheist 2012
## 3450   Australia non-atheist 2012
## 3451   Australia non-atheist 2012
## 3452   Australia non-atheist 2012
## 3453   Australia non-atheist 2012
## 3454   Australia     atheist 2012
## 3455   Australia non-atheist 2012
## 3456   Australia non-atheist 2012
## 3457   Australia non-atheist 2012
## 3458   Australia non-atheist 2012
## 3459   Australia non-atheist 2012
## 3460   Australia non-atheist 2012
## 3461   Australia non-atheist 2012
## 3462   Australia non-atheist 2012
## 3463   Australia non-atheist 2012
## 3464   Australia non-atheist 2012
## 3465   Australia non-atheist 2012
## 3466   Australia non-atheist 2012
## 3467   Australia non-atheist 2012
## 3468   Australia non-atheist 2012
## 3469   Australia     atheist 2012
## 3470   Australia non-atheist 2012
## 3471   Australia non-atheist 2012
## 3472   Australia non-atheist 2012
## 3473   Australia non-atheist 2012
## 3474   Australia non-atheist 2012
## 3475   Australia non-atheist 2012
## 3476   Australia     atheist 2012
## 3477   Australia non-atheist 2012
## 3478   Australia non-atheist 2012
## 3479   Australia non-atheist 2012
## 3480   Australia non-atheist 2012
## 3481   Australia non-atheist 2012
## 3482   Australia non-atheist 2012
## 3483   Australia non-atheist 2012
## 3484   Australia non-atheist 2012
## 3485   Australia non-atheist 2012
## 3486   Australia non-atheist 2012
## 3487   Australia non-atheist 2012
## 3488   Australia non-atheist 2012
## 3489   Australia non-atheist 2012
## 3490   Australia non-atheist 2012
## 3491   Australia non-atheist 2012
## 3492   Australia non-atheist 2012
## 3493   Australia non-atheist 2012
## 3494   Australia non-atheist 2012
## 3495   Australia non-atheist 2012
## 3496   Australia     atheist 2012
## 3497   Australia non-atheist 2012
## 3498   Australia non-atheist 2012
## 3499   Australia non-atheist 2012
## 3500   Australia     atheist 2012
## 3501   Australia non-atheist 2012
## 3502   Australia non-atheist 2012
## 3503   Australia non-atheist 2012
## 3504   Australia non-atheist 2012
## 3505   Australia non-atheist 2012
## 3506   Australia non-atheist 2012
## 3507   Australia non-atheist 2012
## 3508   Australia non-atheist 2012
## 3509   Australia non-atheist 2012
## 3510   Australia non-atheist 2012
## 3511   Australia non-atheist 2012
## 3512   Australia non-atheist 2012
## 3513   Australia non-atheist 2012
## 3514   Australia     atheist 2012
## 3515   Australia non-atheist 2012
## 3516   Australia non-atheist 2012
## 3517   Australia non-atheist 2012
## 3518   Australia non-atheist 2012
## 3519   Australia non-atheist 2012
## 3520   Australia non-atheist 2012
## 3521   Australia non-atheist 2012
## 3522   Australia non-atheist 2012
## 3523   Australia non-atheist 2012
## 3524   Australia non-atheist 2012
## 3525   Australia non-atheist 2012
## 3526   Australia non-atheist 2012
## 3527   Australia non-atheist 2012
## 3528   Australia non-atheist 2012
## 3529   Australia non-atheist 2012
## 3530   Australia non-atheist 2012
## 3531   Australia non-atheist 2012
## 3532   Australia non-atheist 2012
## 3533   Australia non-atheist 2012
## 3534   Australia non-atheist 2012
## 3535   Australia non-atheist 2012
## 3536   Australia non-atheist 2012
## 3537   Australia non-atheist 2012
## 3538   Australia non-atheist 2012
## 3539   Australia non-atheist 2012
## 3540   Australia non-atheist 2012
## 3541   Australia     atheist 2012
## 3542   Australia non-atheist 2012
## 3543   Australia non-atheist 2012
## 3544   Australia     atheist 2012
## 3545   Australia non-atheist 2012
## 3546   Australia     atheist 2012
## 3547   Australia non-atheist 2012
## 3548   Australia     atheist 2012
## 3549   Australia non-atheist 2012
## 3550   Australia non-atheist 2012
## 3551   Australia non-atheist 2012
## 3552   Australia non-atheist 2012
## 3553   Australia non-atheist 2012
## 3554   Australia non-atheist 2012
## 3555   Australia     atheist 2012
## 3556   Australia non-atheist 2012
#Create data sets for Australia and Ecuador
#Ecuador
ecuador12 <- subset(atheism, nationality == "Ecuador" & year == "2012")
ecuador12
##       nationality    response year
## 13215     Ecuador non-atheist 2012
## 13216     Ecuador non-atheist 2012
## 13217     Ecuador non-atheist 2012
## 13218     Ecuador non-atheist 2012
## 13219     Ecuador non-atheist 2012
## 13220     Ecuador non-atheist 2012
## 13221     Ecuador non-atheist 2012
## 13222     Ecuador     atheist 2012
## 13223     Ecuador non-atheist 2012
## 13224     Ecuador non-atheist 2012
## 13225     Ecuador non-atheist 2012
## 13226     Ecuador non-atheist 2012
## 13227     Ecuador     atheist 2012
## 13228     Ecuador non-atheist 2012
## 13229     Ecuador non-atheist 2012
## 13230     Ecuador non-atheist 2012
## 13231     Ecuador non-atheist 2012
## 13232     Ecuador non-atheist 2012
## 13233     Ecuador     atheist 2012
## 13234     Ecuador non-atheist 2012
## 13235     Ecuador non-atheist 2012
## 13236     Ecuador non-atheist 2012
## 13237     Ecuador non-atheist 2012
## 13238     Ecuador non-atheist 2012
## 13239     Ecuador non-atheist 2012
## 13240     Ecuador non-atheist 2012
## 13241     Ecuador non-atheist 2012
## 13242     Ecuador non-atheist 2012
## 13243     Ecuador non-atheist 2012
## 13244     Ecuador non-atheist 2012
## 13245     Ecuador non-atheist 2012
## 13246     Ecuador non-atheist 2012
## 13247     Ecuador non-atheist 2012
## 13248     Ecuador non-atheist 2012
## 13249     Ecuador non-atheist 2012
## 13250     Ecuador non-atheist 2012
## 13251     Ecuador non-atheist 2012
## 13252     Ecuador non-atheist 2012
## 13253     Ecuador non-atheist 2012
## 13254     Ecuador non-atheist 2012
## 13255     Ecuador non-atheist 2012
## 13256     Ecuador non-atheist 2012
## 13257     Ecuador non-atheist 2012
## 13258     Ecuador non-atheist 2012
## 13259     Ecuador non-atheist 2012
## 13260     Ecuador non-atheist 2012
## 13261     Ecuador non-atheist 2012
## 13262     Ecuador non-atheist 2012
## 13263     Ecuador non-atheist 2012
## 13264     Ecuador non-atheist 2012
## 13265     Ecuador non-atheist 2012
## 13266     Ecuador non-atheist 2012
## 13267     Ecuador non-atheist 2012
## 13268     Ecuador non-atheist 2012
## 13269     Ecuador non-atheist 2012
## 13270     Ecuador non-atheist 2012
## 13271     Ecuador non-atheist 2012
## 13272     Ecuador non-atheist 2012
## 13273     Ecuador non-atheist 2012
## 13274     Ecuador non-atheist 2012
## 13275     Ecuador non-atheist 2012
## 13276     Ecuador non-atheist 2012
## 13277     Ecuador non-atheist 2012
## 13278     Ecuador non-atheist 2012
## 13279     Ecuador     atheist 2012
## 13280     Ecuador non-atheist 2012
## 13281     Ecuador non-atheist 2012
## 13282     Ecuador non-atheist 2012
## 13283     Ecuador non-atheist 2012
## 13284     Ecuador non-atheist 2012
## 13285     Ecuador non-atheist 2012
## 13286     Ecuador non-atheist 2012
## 13287     Ecuador non-atheist 2012
## 13288     Ecuador non-atheist 2012
## 13289     Ecuador non-atheist 2012
## 13290     Ecuador non-atheist 2012
## 13291     Ecuador non-atheist 2012
## 13292     Ecuador non-atheist 2012
## 13293     Ecuador non-atheist 2012
## 13294     Ecuador non-atheist 2012
## 13295     Ecuador non-atheist 2012
## 13296     Ecuador non-atheist 2012
## 13297     Ecuador non-atheist 2012
## 13298     Ecuador non-atheist 2012
## 13299     Ecuador non-atheist 2012
## 13300     Ecuador non-atheist 2012
## 13301     Ecuador non-atheist 2012
## 13302     Ecuador non-atheist 2012
## 13303     Ecuador non-atheist 2012
## 13304     Ecuador non-atheist 2012
## 13305     Ecuador non-atheist 2012
## 13306     Ecuador non-atheist 2012
## 13307     Ecuador non-atheist 2012
## 13308     Ecuador non-atheist 2012
## 13309     Ecuador non-atheist 2012
## 13310     Ecuador non-atheist 2012
## 13311     Ecuador non-atheist 2012
## 13312     Ecuador non-atheist 2012
## 13313     Ecuador non-atheist 2012
## 13314     Ecuador non-atheist 2012
## 13315     Ecuador non-atheist 2012
## 13316     Ecuador non-atheist 2012
## 13317     Ecuador non-atheist 2012
## 13318     Ecuador non-atheist 2012
## 13319     Ecuador non-atheist 2012
## 13320     Ecuador non-atheist 2012
## 13321     Ecuador non-atheist 2012
## 13322     Ecuador non-atheist 2012
## 13323     Ecuador non-atheist 2012
## 13324     Ecuador non-atheist 2012
## 13325     Ecuador non-atheist 2012
## 13326     Ecuador non-atheist 2012
## 13327     Ecuador non-atheist 2012
## 13328     Ecuador non-atheist 2012
## 13329     Ecuador non-atheist 2012
## 13330     Ecuador non-atheist 2012
## 13331     Ecuador non-atheist 2012
## 13332     Ecuador non-atheist 2012
## 13333     Ecuador non-atheist 2012
## 13334     Ecuador non-atheist 2012
## 13335     Ecuador non-atheist 2012
## 13336     Ecuador non-atheist 2012
## 13337     Ecuador non-atheist 2012
## 13338     Ecuador non-atheist 2012
## 13339     Ecuador non-atheist 2012
## 13340     Ecuador non-atheist 2012
## 13341     Ecuador non-atheist 2012
## 13342     Ecuador non-atheist 2012
## 13343     Ecuador non-atheist 2012
## 13344     Ecuador non-atheist 2012
## 13345     Ecuador non-atheist 2012
## 13346     Ecuador non-atheist 2012
## 13347     Ecuador non-atheist 2012
## 13348     Ecuador non-atheist 2012
## 13349     Ecuador non-atheist 2012
## 13350     Ecuador non-atheist 2012
## 13351     Ecuador non-atheist 2012
## 13352     Ecuador non-atheist 2012
## 13353     Ecuador non-atheist 2012
## 13354     Ecuador non-atheist 2012
## 13355     Ecuador non-atheist 2012
## 13356     Ecuador non-atheist 2012
## 13357     Ecuador non-atheist 2012
## 13358     Ecuador non-atheist 2012
## 13359     Ecuador non-atheist 2012
## 13360     Ecuador non-atheist 2012
## 13361     Ecuador non-atheist 2012
## 13362     Ecuador non-atheist 2012
## 13363     Ecuador non-atheist 2012
## 13364     Ecuador non-atheist 2012
## 13365     Ecuador non-atheist 2012
## 13366     Ecuador non-atheist 2012
## 13367     Ecuador non-atheist 2012
## 13368     Ecuador non-atheist 2012
## 13369     Ecuador non-atheist 2012
## 13370     Ecuador non-atheist 2012
## 13371     Ecuador non-atheist 2012
## 13372     Ecuador non-atheist 2012
## 13373     Ecuador non-atheist 2012
## 13374     Ecuador non-atheist 2012
## 13375     Ecuador non-atheist 2012
## 13376     Ecuador non-atheist 2012
## 13377     Ecuador non-atheist 2012
## 13378     Ecuador non-atheist 2012
## 13379     Ecuador non-atheist 2012
## 13380     Ecuador non-atheist 2012
## 13381     Ecuador non-atheist 2012
## 13382     Ecuador non-atheist 2012
## 13383     Ecuador non-atheist 2012
## 13384     Ecuador non-atheist 2012
## 13385     Ecuador non-atheist 2012
## 13386     Ecuador non-atheist 2012
## 13387     Ecuador non-atheist 2012
## 13388     Ecuador non-atheist 2012
## 13389     Ecuador non-atheist 2012
## 13390     Ecuador non-atheist 2012
## 13391     Ecuador non-atheist 2012
## 13392     Ecuador non-atheist 2012
## 13393     Ecuador non-atheist 2012
## 13394     Ecuador non-atheist 2012
## 13395     Ecuador non-atheist 2012
## 13396     Ecuador non-atheist 2012
## 13397     Ecuador non-atheist 2012
## 13398     Ecuador non-atheist 2012
## 13399     Ecuador non-atheist 2012
## 13400     Ecuador non-atheist 2012
## 13401     Ecuador non-atheist 2012
## 13402     Ecuador non-atheist 2012
## 13403     Ecuador non-atheist 2012
## 13404     Ecuador non-atheist 2012
## 13405     Ecuador non-atheist 2012
## 13406     Ecuador non-atheist 2012
## 13407     Ecuador non-atheist 2012
## 13408     Ecuador non-atheist 2012
## 13409     Ecuador non-atheist 2012
## 13410     Ecuador non-atheist 2012
## 13411     Ecuador non-atheist 2012
## 13412     Ecuador non-atheist 2012
## 13413     Ecuador non-atheist 2012
## 13414     Ecuador non-atheist 2012
## 13415     Ecuador non-atheist 2012
## 13416     Ecuador non-atheist 2012
## 13417     Ecuador     atheist 2012
## 13418     Ecuador non-atheist 2012
## 13419     Ecuador non-atheist 2012
## 13420     Ecuador non-atheist 2012
## 13421     Ecuador non-atheist 2012
## 13422     Ecuador non-atheist 2012
## 13423     Ecuador non-atheist 2012
## 13424     Ecuador non-atheist 2012
## 13425     Ecuador non-atheist 2012
## 13426     Ecuador non-atheist 2012
## 13427     Ecuador non-atheist 2012
## 13428     Ecuador non-atheist 2012
## 13429     Ecuador non-atheist 2012
## 13430     Ecuador non-atheist 2012
## 13431     Ecuador non-atheist 2012
## 13432     Ecuador non-atheist 2012
## 13433     Ecuador non-atheist 2012
## 13434     Ecuador non-atheist 2012
## 13435     Ecuador non-atheist 2012
## 13436     Ecuador     atheist 2012
## 13437     Ecuador non-atheist 2012
## 13438     Ecuador non-atheist 2012
## 13439     Ecuador non-atheist 2012
## 13440     Ecuador non-atheist 2012
## 13441     Ecuador non-atheist 2012
## 13442     Ecuador     atheist 2012
## 13443     Ecuador non-atheist 2012
## 13444     Ecuador non-atheist 2012
## 13445     Ecuador non-atheist 2012
## 13446     Ecuador non-atheist 2012
## 13447     Ecuador non-atheist 2012
## 13448     Ecuador non-atheist 2012
## 13449     Ecuador non-atheist 2012
## 13450     Ecuador non-atheist 2012
## 13451     Ecuador non-atheist 2012
## 13452     Ecuador non-atheist 2012
## 13453     Ecuador non-atheist 2012
## 13454     Ecuador non-atheist 2012
## 13455     Ecuador non-atheist 2012
## 13456     Ecuador non-atheist 2012
## 13457     Ecuador non-atheist 2012
## 13458     Ecuador     atheist 2012
## 13459     Ecuador non-atheist 2012
## 13460     Ecuador non-atheist 2012
## 13461     Ecuador non-atheist 2012
## 13462     Ecuador non-atheist 2012
## 13463     Ecuador non-atheist 2012
## 13464     Ecuador non-atheist 2012
## 13465     Ecuador non-atheist 2012
## 13466     Ecuador non-atheist 2012
## 13467     Ecuador non-atheist 2012
## 13468     Ecuador non-atheist 2012
## 13469     Ecuador non-atheist 2012
## 13470     Ecuador non-atheist 2012
## 13471     Ecuador non-atheist 2012
## 13472     Ecuador non-atheist 2012
## 13473     Ecuador non-atheist 2012
## 13474     Ecuador non-atheist 2012
## 13475     Ecuador non-atheist 2012
## 13476     Ecuador non-atheist 2012
## 13477     Ecuador non-atheist 2012
## 13478     Ecuador non-atheist 2012
## 13479     Ecuador non-atheist 2012
## 13480     Ecuador non-atheist 2012
## 13481     Ecuador non-atheist 2012
## 13482     Ecuador non-atheist 2012
## 13483     Ecuador non-atheist 2012
## 13484     Ecuador non-atheist 2012
## 13485     Ecuador non-atheist 2012
## 13486     Ecuador non-atheist 2012
## 13487     Ecuador non-atheist 2012
## 13488     Ecuador non-atheist 2012
## 13489     Ecuador non-atheist 2012
## 13490     Ecuador non-atheist 2012
## 13491     Ecuador non-atheist 2012
## 13492     Ecuador non-atheist 2012
## 13493     Ecuador non-atheist 2012
## 13494     Ecuador non-atheist 2012
## 13495     Ecuador non-atheist 2012
## 13496     Ecuador non-atheist 2012
## 13497     Ecuador non-atheist 2012
## 13498     Ecuador non-atheist 2012
## 13499     Ecuador non-atheist 2012
## 13500     Ecuador non-atheist 2012
## 13501     Ecuador non-atheist 2012
## 13502     Ecuador non-atheist 2012
## 13503     Ecuador non-atheist 2012
## 13504     Ecuador non-atheist 2012
## 13505     Ecuador non-atheist 2012
## 13506     Ecuador non-atheist 2012
## 13507     Ecuador non-atheist 2012
## 13508     Ecuador non-atheist 2012
## 13509     Ecuador non-atheist 2012
## 13510     Ecuador non-atheist 2012
## 13511     Ecuador non-atheist 2012
## 13512     Ecuador non-atheist 2012
## 13513     Ecuador non-atheist 2012
## 13514     Ecuador non-atheist 2012
## 13515     Ecuador non-atheist 2012
## 13516     Ecuador non-atheist 2012
## 13517     Ecuador non-atheist 2012
## 13518     Ecuador non-atheist 2012
## 13519     Ecuador non-atheist 2012
## 13520     Ecuador non-atheist 2012
## 13521     Ecuador non-atheist 2012
## 13522     Ecuador non-atheist 2012
## 13523     Ecuador non-atheist 2012
## 13524     Ecuador non-atheist 2012
## 13525     Ecuador non-atheist 2012
## 13526     Ecuador non-atheist 2012
## 13527     Ecuador non-atheist 2012
## 13528     Ecuador non-atheist 2012
## 13529     Ecuador non-atheist 2012
## 13530     Ecuador non-atheist 2012
## 13531     Ecuador non-atheist 2012
## 13532     Ecuador non-atheist 2012
## 13533     Ecuador non-atheist 2012
## 13534     Ecuador non-atheist 2012
## 13535     Ecuador non-atheist 2012
## 13536     Ecuador non-atheist 2012
## 13537     Ecuador non-atheist 2012
## 13538     Ecuador non-atheist 2012
## 13539     Ecuador non-atheist 2012
## 13540     Ecuador non-atheist 2012
## 13541     Ecuador non-atheist 2012
## 13542     Ecuador non-atheist 2012
## 13543     Ecuador non-atheist 2012
## 13544     Ecuador non-atheist 2012
## 13545     Ecuador non-atheist 2012
## 13546     Ecuador non-atheist 2012
## 13547     Ecuador non-atheist 2012
## 13548     Ecuador non-atheist 2012
## 13549     Ecuador non-atheist 2012
## 13550     Ecuador non-atheist 2012
## 13551     Ecuador non-atheist 2012
## 13552     Ecuador non-atheist 2012
## 13553     Ecuador non-atheist 2012
## 13554     Ecuador non-atheist 2012
## 13555     Ecuador non-atheist 2012
## 13556     Ecuador non-atheist 2012
## 13557     Ecuador non-atheist 2012
## 13558     Ecuador non-atheist 2012
## 13559     Ecuador non-atheist 2012
## 13560     Ecuador non-atheist 2012
## 13561     Ecuador non-atheist 2012
## 13562     Ecuador non-atheist 2012
## 13563     Ecuador non-atheist 2012
## 13564     Ecuador non-atheist 2012
## 13565     Ecuador non-atheist 2012
## 13566     Ecuador non-atheist 2012
## 13567     Ecuador non-atheist 2012
## 13568     Ecuador non-atheist 2012
## 13569     Ecuador non-atheist 2012
## 13570     Ecuador non-atheist 2012
## 13571     Ecuador non-atheist 2012
## 13572     Ecuador non-atheist 2012
## 13573     Ecuador non-atheist 2012
## 13574     Ecuador non-atheist 2012
## 13575     Ecuador non-atheist 2012
## 13576     Ecuador non-atheist 2012
## 13577     Ecuador non-atheist 2012
## 13578     Ecuador non-atheist 2012
## 13579     Ecuador non-atheist 2012
## 13580     Ecuador non-atheist 2012
## 13581     Ecuador non-atheist 2012
## 13582     Ecuador non-atheist 2012
## 13583     Ecuador non-atheist 2012
## 13584     Ecuador non-atheist 2012
## 13585     Ecuador non-atheist 2012
## 13586     Ecuador non-atheist 2012
## 13587     Ecuador non-atheist 2012
## 13588     Ecuador non-atheist 2012
## 13589     Ecuador non-atheist 2012
## 13590     Ecuador non-atheist 2012
## 13591     Ecuador non-atheist 2012
## 13592     Ecuador non-atheist 2012
## 13593     Ecuador non-atheist 2012
## 13594     Ecuador non-atheist 2012
## 13595     Ecuador non-atheist 2012
## 13596     Ecuador non-atheist 2012
## 13597     Ecuador non-atheist 2012
## 13598     Ecuador non-atheist 2012
## 13599     Ecuador non-atheist 2012
## 13600     Ecuador non-atheist 2012
## 13601     Ecuador non-atheist 2012
## 13602     Ecuador non-atheist 2012
## 13603     Ecuador non-atheist 2012
## 13604     Ecuador non-atheist 2012
## 13605     Ecuador non-atheist 2012
## 13606     Ecuador non-atheist 2012
## 13607     Ecuador non-atheist 2012
## 13608     Ecuador non-atheist 2012
## 13609     Ecuador non-atheist 2012
## 13610     Ecuador non-atheist 2012
## 13611     Ecuador non-atheist 2012
## 13612     Ecuador non-atheist 2012
## 13613     Ecuador non-atheist 2012
## 13614     Ecuador non-atheist 2012
## 13615     Ecuador non-atheist 2012
## 13616     Ecuador non-atheist 2012
## 13617     Ecuador non-atheist 2012
## 13618     Ecuador non-atheist 2012
#Create data sets for Australia and Ecuador
#Australia
australia12 <- subset(atheism, nationality == "Australia" & year == "2012")
australia12
##      nationality    response year
## 2518   Australia non-atheist 2012
## 2519   Australia non-atheist 2012
## 2520   Australia non-atheist 2012
## 2521   Australia non-atheist 2012
## 2522   Australia non-atheist 2012
## 2523   Australia non-atheist 2012
## 2524   Australia non-atheist 2012
## 2525   Australia non-atheist 2012
## 2526   Australia non-atheist 2012
## 2527   Australia non-atheist 2012
## 2528   Australia non-atheist 2012
## 2529   Australia non-atheist 2012
## 2530   Australia non-atheist 2012
## 2531   Australia     atheist 2012
## 2532   Australia non-atheist 2012
## 2533   Australia non-atheist 2012
## 2534   Australia non-atheist 2012
## 2535   Australia     atheist 2012
## 2536   Australia non-atheist 2012
## 2537   Australia     atheist 2012
## 2538   Australia non-atheist 2012
## 2539   Australia     atheist 2012
## 2540   Australia non-atheist 2012
## 2541   Australia non-atheist 2012
## 2542   Australia non-atheist 2012
## 2543   Australia non-atheist 2012
## 2544   Australia non-atheist 2012
## 2545   Australia non-atheist 2012
## 2546   Australia non-atheist 2012
## 2547   Australia non-atheist 2012
## 2548   Australia non-atheist 2012
## 2549   Australia non-atheist 2012
## 2550   Australia non-atheist 2012
## 2551   Australia non-atheist 2012
## 2552   Australia     atheist 2012
## 2553   Australia non-atheist 2012
## 2554   Australia non-atheist 2012
## 2555   Australia     atheist 2012
## 2556   Australia non-atheist 2012
## 2557   Australia non-atheist 2012
## 2558   Australia non-atheist 2012
## 2559   Australia non-atheist 2012
## 2560   Australia non-atheist 2012
## 2561   Australia non-atheist 2012
## 2562   Australia non-atheist 2012
## 2563   Australia non-atheist 2012
## 2564   Australia non-atheist 2012
## 2565   Australia non-atheist 2012
## 2566   Australia     atheist 2012
## 2567   Australia non-atheist 2012
## 2568   Australia non-atheist 2012
## 2569   Australia non-atheist 2012
## 2570   Australia non-atheist 2012
## 2571   Australia non-atheist 2012
## 2572   Australia non-atheist 2012
## 2573   Australia non-atheist 2012
## 2574   Australia non-atheist 2012
## 2575   Australia non-atheist 2012
## 2576   Australia     atheist 2012
## 2577   Australia non-atheist 2012
## 2578   Australia non-atheist 2012
## 2579   Australia non-atheist 2012
## 2580   Australia     atheist 2012
## 2581   Australia non-atheist 2012
## 2582   Australia non-atheist 2012
## 2583   Australia non-atheist 2012
## 2584   Australia non-atheist 2012
## 2585   Australia non-atheist 2012
## 2586   Australia non-atheist 2012
## 2587   Australia     atheist 2012
## 2588   Australia non-atheist 2012
## 2589   Australia non-atheist 2012
## 2590   Australia non-atheist 2012
## 2591   Australia non-atheist 2012
## 2592   Australia non-atheist 2012
## 2593   Australia non-atheist 2012
## 2594   Australia non-atheist 2012
## 2595   Australia non-atheist 2012
## 2596   Australia non-atheist 2012
## 2597   Australia     atheist 2012
## 2598   Australia non-atheist 2012
## 2599   Australia non-atheist 2012
## 2600   Australia non-atheist 2012
## 2601   Australia non-atheist 2012
## 2602   Australia non-atheist 2012
## 2603   Australia non-atheist 2012
## 2604   Australia non-atheist 2012
## 2605   Australia non-atheist 2012
## 2606   Australia non-atheist 2012
## 2607   Australia non-atheist 2012
## 2608   Australia non-atheist 2012
## 2609   Australia non-atheist 2012
## 2610   Australia non-atheist 2012
## 2611   Australia non-atheist 2012
## 2612   Australia non-atheist 2012
## 2613   Australia non-atheist 2012
## 2614   Australia non-atheist 2012
## 2615   Australia non-atheist 2012
## 2616   Australia non-atheist 2012
## 2617   Australia non-atheist 2012
## 2618   Australia non-atheist 2012
## 2619   Australia non-atheist 2012
## 2620   Australia non-atheist 2012
## 2621   Australia non-atheist 2012
## 2622   Australia non-atheist 2012
## 2623   Australia non-atheist 2012
## 2624   Australia non-atheist 2012
## 2625   Australia non-atheist 2012
## 2626   Australia non-atheist 2012
## 2627   Australia non-atheist 2012
## 2628   Australia non-atheist 2012
## 2629   Australia non-atheist 2012
## 2630   Australia non-atheist 2012
## 2631   Australia non-atheist 2012
## 2632   Australia non-atheist 2012
## 2633   Australia non-atheist 2012
## 2634   Australia non-atheist 2012
## 2635   Australia non-atheist 2012
## 2636   Australia non-atheist 2012
## 2637   Australia non-atheist 2012
## 2638   Australia non-atheist 2012
## 2639   Australia non-atheist 2012
## 2640   Australia non-atheist 2012
## 2641   Australia     atheist 2012
## 2642   Australia non-atheist 2012
## 2643   Australia non-atheist 2012
## 2644   Australia non-atheist 2012
## 2645   Australia non-atheist 2012
## 2646   Australia non-atheist 2012
## 2647   Australia     atheist 2012
## 2648   Australia non-atheist 2012
## 2649   Australia non-atheist 2012
## 2650   Australia non-atheist 2012
## 2651   Australia non-atheist 2012
## 2652   Australia non-atheist 2012
## 2653   Australia non-atheist 2012
## 2654   Australia non-atheist 2012
## 2655   Australia non-atheist 2012
## 2656   Australia non-atheist 2012
## 2657   Australia non-atheist 2012
## 2658   Australia non-atheist 2012
## 2659   Australia non-atheist 2012
## 2660   Australia non-atheist 2012
## 2661   Australia non-atheist 2012
## 2662   Australia non-atheist 2012
## 2663   Australia non-atheist 2012
## 2664   Australia non-atheist 2012
## 2665   Australia non-atheist 2012
## 2666   Australia non-atheist 2012
## 2667   Australia non-atheist 2012
## 2668   Australia non-atheist 2012
## 2669   Australia non-atheist 2012
## 2670   Australia non-atheist 2012
## 2671   Australia non-atheist 2012
## 2672   Australia non-atheist 2012
## 2673   Australia non-atheist 2012
## 2674   Australia non-atheist 2012
## 2675   Australia non-atheist 2012
## 2676   Australia non-atheist 2012
## 2677   Australia non-atheist 2012
## 2678   Australia non-atheist 2012
## 2679   Australia non-atheist 2012
## 2680   Australia non-atheist 2012
## 2681   Australia non-atheist 2012
## 2682   Australia non-atheist 2012
## 2683   Australia non-atheist 2012
## 2684   Australia non-atheist 2012
## 2685   Australia     atheist 2012
## 2686   Australia non-atheist 2012
## 2687   Australia     atheist 2012
## 2688   Australia non-atheist 2012
## 2689   Australia non-atheist 2012
## 2690   Australia non-atheist 2012
## 2691   Australia non-atheist 2012
## 2692   Australia non-atheist 2012
## 2693   Australia non-atheist 2012
## 2694   Australia non-atheist 2012
## 2695   Australia     atheist 2012
## 2696   Australia non-atheist 2012
## 2697   Australia non-atheist 2012
## 2698   Australia     atheist 2012
## 2699   Australia non-atheist 2012
## 2700   Australia non-atheist 2012
## 2701   Australia non-atheist 2012
## 2702   Australia non-atheist 2012
## 2703   Australia non-atheist 2012
## 2704   Australia non-atheist 2012
## 2705   Australia non-atheist 2012
## 2706   Australia non-atheist 2012
## 2707   Australia non-atheist 2012
## 2708   Australia non-atheist 2012
## 2709   Australia non-atheist 2012
## 2710   Australia non-atheist 2012
## 2711   Australia non-atheist 2012
## 2712   Australia non-atheist 2012
## 2713   Australia     atheist 2012
## 2714   Australia     atheist 2012
## 2715   Australia non-atheist 2012
## 2716   Australia non-atheist 2012
## 2717   Australia non-atheist 2012
## 2718   Australia non-atheist 2012
## 2719   Australia non-atheist 2012
## 2720   Australia non-atheist 2012
## 2721   Australia non-atheist 2012
## 2722   Australia     atheist 2012
## 2723   Australia non-atheist 2012
## 2724   Australia non-atheist 2012
## 2725   Australia non-atheist 2012
## 2726   Australia non-atheist 2012
## 2727   Australia non-atheist 2012
## 2728   Australia non-atheist 2012
## 2729   Australia non-atheist 2012
## 2730   Australia non-atheist 2012
## 2731   Australia non-atheist 2012
## 2732   Australia non-atheist 2012
## 2733   Australia non-atheist 2012
## 2734   Australia non-atheist 2012
## 2735   Australia non-atheist 2012
## 2736   Australia non-atheist 2012
## 2737   Australia non-atheist 2012
## 2738   Australia non-atheist 2012
## 2739   Australia non-atheist 2012
## 2740   Australia non-atheist 2012
## 2741   Australia non-atheist 2012
## 2742   Australia non-atheist 2012
## 2743   Australia non-atheist 2012
## 2744   Australia non-atheist 2012
## 2745   Australia non-atheist 2012
## 2746   Australia non-atheist 2012
## 2747   Australia non-atheist 2012
## 2748   Australia non-atheist 2012
## 2749   Australia non-atheist 2012
## 2750   Australia non-atheist 2012
## 2751   Australia non-atheist 2012
## 2752   Australia non-atheist 2012
## 2753   Australia non-atheist 2012
## 2754   Australia non-atheist 2012
## 2755   Australia non-atheist 2012
## 2756   Australia non-atheist 2012
## 2757   Australia non-atheist 2012
## 2758   Australia non-atheist 2012
## 2759   Australia non-atheist 2012
## 2760   Australia non-atheist 2012
## 2761   Australia non-atheist 2012
## 2762   Australia     atheist 2012
## 2763   Australia non-atheist 2012
## 2764   Australia non-atheist 2012
## 2765   Australia non-atheist 2012
## 2766   Australia non-atheist 2012
## 2767   Australia non-atheist 2012
## 2768   Australia non-atheist 2012
## 2769   Australia non-atheist 2012
## 2770   Australia non-atheist 2012
## 2771   Australia non-atheist 2012
## 2772   Australia non-atheist 2012
## 2773   Australia non-atheist 2012
## 2774   Australia     atheist 2012
## 2775   Australia non-atheist 2012
## 2776   Australia     atheist 2012
## 2777   Australia non-atheist 2012
## 2778   Australia non-atheist 2012
## 2779   Australia non-atheist 2012
## 2780   Australia non-atheist 2012
## 2781   Australia non-atheist 2012
## 2782   Australia non-atheist 2012
## 2783   Australia non-atheist 2012
## 2784   Australia non-atheist 2012
## 2785   Australia non-atheist 2012
## 2786   Australia non-atheist 2012
## 2787   Australia non-atheist 2012
## 2788   Australia non-atheist 2012
## 2789   Australia non-atheist 2012
## 2790   Australia     atheist 2012
## 2791   Australia     atheist 2012
## 2792   Australia non-atheist 2012
## 2793   Australia non-atheist 2012
## 2794   Australia non-atheist 2012
## 2795   Australia non-atheist 2012
## 2796   Australia     atheist 2012
## 2797   Australia non-atheist 2012
## 2798   Australia non-atheist 2012
## 2799   Australia non-atheist 2012
## 2800   Australia non-atheist 2012
## 2801   Australia non-atheist 2012
## 2802   Australia non-atheist 2012
## 2803   Australia non-atheist 2012
## 2804   Australia non-atheist 2012
## 2805   Australia non-atheist 2012
## 2806   Australia non-atheist 2012
## 2807   Australia non-atheist 2012
## 2808   Australia non-atheist 2012
## 2809   Australia non-atheist 2012
## 2810   Australia non-atheist 2012
## 2811   Australia non-atheist 2012
## 2812   Australia non-atheist 2012
## 2813   Australia non-atheist 2012
## 2814   Australia non-atheist 2012
## 2815   Australia non-atheist 2012
## 2816   Australia non-atheist 2012
## 2817   Australia non-atheist 2012
## 2818   Australia     atheist 2012
## 2819   Australia non-atheist 2012
## 2820   Australia non-atheist 2012
## 2821   Australia non-atheist 2012
## 2822   Australia     atheist 2012
## 2823   Australia     atheist 2012
## 2824   Australia non-atheist 2012
## 2825   Australia non-atheist 2012
## 2826   Australia non-atheist 2012
## 2827   Australia non-atheist 2012
## 2828   Australia non-atheist 2012
## 2829   Australia     atheist 2012
## 2830   Australia non-atheist 2012
## 2831   Australia non-atheist 2012
## 2832   Australia non-atheist 2012
## 2833   Australia non-atheist 2012
## 2834   Australia non-atheist 2012
## 2835   Australia non-atheist 2012
## 2836   Australia non-atheist 2012
## 2837   Australia non-atheist 2012
## 2838   Australia non-atheist 2012
## 2839   Australia non-atheist 2012
## 2840   Australia non-atheist 2012
## 2841   Australia non-atheist 2012
## 2842   Australia non-atheist 2012
## 2843   Australia non-atheist 2012
## 2844   Australia non-atheist 2012
## 2845   Australia non-atheist 2012
## 2846   Australia non-atheist 2012
## 2847   Australia non-atheist 2012
## 2848   Australia non-atheist 2012
## 2849   Australia non-atheist 2012
## 2850   Australia non-atheist 2012
## 2851   Australia non-atheist 2012
## 2852   Australia non-atheist 2012
## 2853   Australia non-atheist 2012
## 2854   Australia non-atheist 2012
## 2855   Australia     atheist 2012
## 2856   Australia     atheist 2012
## 2857   Australia non-atheist 2012
## 2858   Australia non-atheist 2012
## 2859   Australia non-atheist 2012
## 2860   Australia non-atheist 2012
## 2861   Australia non-atheist 2012
## 2862   Australia non-atheist 2012
## 2863   Australia non-atheist 2012
## 2864   Australia non-atheist 2012
## 2865   Australia non-atheist 2012
## 2866   Australia non-atheist 2012
## 2867   Australia non-atheist 2012
## 2868   Australia     atheist 2012
## 2869   Australia non-atheist 2012
## 2870   Australia     atheist 2012
## 2871   Australia non-atheist 2012
## 2872   Australia non-atheist 2012
## 2873   Australia non-atheist 2012
## 2874   Australia non-atheist 2012
## 2875   Australia non-atheist 2012
## 2876   Australia non-atheist 2012
## 2877   Australia non-atheist 2012
## 2878   Australia     atheist 2012
## 2879   Australia non-atheist 2012
## 2880   Australia non-atheist 2012
## 2881   Australia non-atheist 2012
## 2882   Australia non-atheist 2012
## 2883   Australia non-atheist 2012
## 2884   Australia non-atheist 2012
## 2885   Australia non-atheist 2012
## 2886   Australia non-atheist 2012
## 2887   Australia non-atheist 2012
## 2888   Australia non-atheist 2012
## 2889   Australia non-atheist 2012
## 2890   Australia non-atheist 2012
## 2891   Australia non-atheist 2012
## 2892   Australia non-atheist 2012
## 2893   Australia non-atheist 2012
## 2894   Australia non-atheist 2012
## 2895   Australia non-atheist 2012
## 2896   Australia non-atheist 2012
## 2897   Australia non-atheist 2012
## 2898   Australia non-atheist 2012
## 2899   Australia     atheist 2012
## 2900   Australia non-atheist 2012
## 2901   Australia non-atheist 2012
## 2902   Australia non-atheist 2012
## 2903   Australia non-atheist 2012
## 2904   Australia non-atheist 2012
## 2905   Australia non-atheist 2012
## 2906   Australia non-atheist 2012
## 2907   Australia     atheist 2012
## 2908   Australia non-atheist 2012
## 2909   Australia non-atheist 2012
## 2910   Australia non-atheist 2012
## 2911   Australia non-atheist 2012
## 2912   Australia non-atheist 2012
## 2913   Australia non-atheist 2012
## 2914   Australia non-atheist 2012
## 2915   Australia non-atheist 2012
## 2916   Australia non-atheist 2012
## 2917   Australia non-atheist 2012
## 2918   Australia non-atheist 2012
## 2919   Australia non-atheist 2012
## 2920   Australia non-atheist 2012
## 2921   Australia non-atheist 2012
## 2922   Australia non-atheist 2012
## 2923   Australia non-atheist 2012
## 2924   Australia non-atheist 2012
## 2925   Australia     atheist 2012
## 2926   Australia non-atheist 2012
## 2927   Australia     atheist 2012
## 2928   Australia non-atheist 2012
## 2929   Australia     atheist 2012
## 2930   Australia non-atheist 2012
## 2931   Australia non-atheist 2012
## 2932   Australia     atheist 2012
## 2933   Australia non-atheist 2012
## 2934   Australia non-atheist 2012
## 2935   Australia     atheist 2012
## 2936   Australia non-atheist 2012
## 2937   Australia non-atheist 2012
## 2938   Australia non-atheist 2012
## 2939   Australia     atheist 2012
## 2940   Australia non-atheist 2012
## 2941   Australia non-atheist 2012
## 2942   Australia non-atheist 2012
## 2943   Australia non-atheist 2012
## 2944   Australia non-atheist 2012
## 2945   Australia non-atheist 2012
## 2946   Australia non-atheist 2012
## 2947   Australia non-atheist 2012
## 2948   Australia non-atheist 2012
## 2949   Australia non-atheist 2012
## 2950   Australia non-atheist 2012
## 2951   Australia non-atheist 2012
## 2952   Australia non-atheist 2012
## 2953   Australia     atheist 2012
## 2954   Australia non-atheist 2012
## 2955   Australia non-atheist 2012
## 2956   Australia     atheist 2012
## 2957   Australia     atheist 2012
## 2958   Australia non-atheist 2012
## 2959   Australia non-atheist 2012
## 2960   Australia non-atheist 2012
## 2961   Australia non-atheist 2012
## 2962   Australia non-atheist 2012
## 2963   Australia non-atheist 2012
## 2964   Australia non-atheist 2012
## 2965   Australia non-atheist 2012
## 2966   Australia non-atheist 2012
## 2967   Australia non-atheist 2012
## 2968   Australia non-atheist 2012
## 2969   Australia     atheist 2012
## 2970   Australia non-atheist 2012
## 2971   Australia non-atheist 2012
## 2972   Australia non-atheist 2012
## 2973   Australia     atheist 2012
## 2974   Australia     atheist 2012
## 2975   Australia non-atheist 2012
## 2976   Australia non-atheist 2012
## 2977   Australia non-atheist 2012
## 2978   Australia non-atheist 2012
## 2979   Australia non-atheist 2012
## 2980   Australia non-atheist 2012
## 2981   Australia non-atheist 2012
## 2982   Australia     atheist 2012
## 2983   Australia non-atheist 2012
## 2984   Australia non-atheist 2012
## 2985   Australia non-atheist 2012
## 2986   Australia non-atheist 2012
## 2987   Australia non-atheist 2012
## 2988   Australia non-atheist 2012
## 2989   Australia non-atheist 2012
## 2990   Australia non-atheist 2012
## 2991   Australia non-atheist 2012
## 2992   Australia     atheist 2012
## 2993   Australia non-atheist 2012
## 2994   Australia non-atheist 2012
## 2995   Australia     atheist 2012
## 2996   Australia non-atheist 2012
## 2997   Australia non-atheist 2012
## 2998   Australia non-atheist 2012
## 2999   Australia non-atheist 2012
## 3000   Australia non-atheist 2012
## 3001   Australia non-atheist 2012
## 3002   Australia     atheist 2012
## 3003   Australia non-atheist 2012
## 3004   Australia non-atheist 2012
## 3005   Australia non-atheist 2012
## 3006   Australia non-atheist 2012
## 3007   Australia non-atheist 2012
## 3008   Australia non-atheist 2012
## 3009   Australia non-atheist 2012
## 3010   Australia non-atheist 2012
## 3011   Australia non-atheist 2012
## 3012   Australia non-atheist 2012
## 3013   Australia non-atheist 2012
## 3014   Australia non-atheist 2012
## 3015   Australia non-atheist 2012
## 3016   Australia non-atheist 2012
## 3017   Australia non-atheist 2012
## 3018   Australia non-atheist 2012
## 3019   Australia non-atheist 2012
## 3020   Australia     atheist 2012
## 3021   Australia     atheist 2012
## 3022   Australia non-atheist 2012
## 3023   Australia non-atheist 2012
## 3024   Australia non-atheist 2012
## 3025   Australia non-atheist 2012
## 3026   Australia non-atheist 2012
## 3027   Australia non-atheist 2012
## 3028   Australia     atheist 2012
## 3029   Australia non-atheist 2012
## 3030   Australia     atheist 2012
## 3031   Australia non-atheist 2012
## 3032   Australia non-atheist 2012
## 3033   Australia non-atheist 2012
## 3034   Australia non-atheist 2012
## 3035   Australia non-atheist 2012
## 3036   Australia     atheist 2012
## 3037   Australia non-atheist 2012
## 3038   Australia non-atheist 2012
## 3039   Australia non-atheist 2012
## 3040   Australia non-atheist 2012
## 3041   Australia non-atheist 2012
## 3042   Australia non-atheist 2012
## 3043   Australia non-atheist 2012
## 3044   Australia non-atheist 2012
## 3045   Australia non-atheist 2012
## 3046   Australia non-atheist 2012
## 3047   Australia non-atheist 2012
## 3048   Australia non-atheist 2012
## 3049   Australia non-atheist 2012
## 3050   Australia non-atheist 2012
## 3051   Australia non-atheist 2012
## 3052   Australia non-atheist 2012
## 3053   Australia non-atheist 2012
## 3054   Australia non-atheist 2012
## 3055   Australia non-atheist 2012
## 3056   Australia non-atheist 2012
## 3057   Australia     atheist 2012
## 3058   Australia non-atheist 2012
## 3059   Australia non-atheist 2012
## 3060   Australia non-atheist 2012
## 3061   Australia non-atheist 2012
## 3062   Australia non-atheist 2012
## 3063   Australia non-atheist 2012
## 3064   Australia non-atheist 2012
## 3065   Australia non-atheist 2012
## 3066   Australia non-atheist 2012
## 3067   Australia non-atheist 2012
## 3068   Australia non-atheist 2012
## 3069   Australia non-atheist 2012
## 3070   Australia non-atheist 2012
## 3071   Australia non-atheist 2012
## 3072   Australia non-atheist 2012
## 3073   Australia non-atheist 2012
## 3074   Australia non-atheist 2012
## 3075   Australia non-atheist 2012
## 3076   Australia non-atheist 2012
## 3077   Australia non-atheist 2012
## 3078   Australia     atheist 2012
## 3079   Australia non-atheist 2012
## 3080   Australia non-atheist 2012
## 3081   Australia non-atheist 2012
## 3082   Australia non-atheist 2012
## 3083   Australia non-atheist 2012
## 3084   Australia     atheist 2012
## 3085   Australia non-atheist 2012
## 3086   Australia non-atheist 2012
## 3087   Australia non-atheist 2012
## 3088   Australia non-atheist 2012
## 3089   Australia non-atheist 2012
## 3090   Australia non-atheist 2012
## 3091   Australia     atheist 2012
## 3092   Australia non-atheist 2012
## 3093   Australia non-atheist 2012
## 3094   Australia non-atheist 2012
## 3095   Australia non-atheist 2012
## 3096   Australia non-atheist 2012
## 3097   Australia non-atheist 2012
## 3098   Australia non-atheist 2012
## 3099   Australia non-atheist 2012
## 3100   Australia non-atheist 2012
## 3101   Australia non-atheist 2012
## 3102   Australia non-atheist 2012
## 3103   Australia     atheist 2012
## 3104   Australia non-atheist 2012
## 3105   Australia non-atheist 2012
## 3106   Australia non-atheist 2012
## 3107   Australia non-atheist 2012
## 3108   Australia non-atheist 2012
## 3109   Australia non-atheist 2012
## 3110   Australia non-atheist 2012
## 3111   Australia non-atheist 2012
## 3112   Australia non-atheist 2012
## 3113   Australia non-atheist 2012
## 3114   Australia non-atheist 2012
## 3115   Australia non-atheist 2012
## 3116   Australia non-atheist 2012
## 3117   Australia non-atheist 2012
## 3118   Australia non-atheist 2012
## 3119   Australia non-atheist 2012
## 3120   Australia non-atheist 2012
## 3121   Australia non-atheist 2012
## 3122   Australia non-atheist 2012
## 3123   Australia non-atheist 2012
## 3124   Australia non-atheist 2012
## 3125   Australia non-atheist 2012
## 3126   Australia non-atheist 2012
## 3127   Australia non-atheist 2012
## 3128   Australia non-atheist 2012
## 3129   Australia non-atheist 2012
## 3130   Australia non-atheist 2012
## 3131   Australia non-atheist 2012
## 3132   Australia non-atheist 2012
## 3133   Australia non-atheist 2012
## 3134   Australia non-atheist 2012
## 3135   Australia non-atheist 2012
## 3136   Australia non-atheist 2012
## 3137   Australia non-atheist 2012
## 3138   Australia non-atheist 2012
## 3139   Australia non-atheist 2012
## 3140   Australia non-atheist 2012
## 3141   Australia non-atheist 2012
## 3142   Australia non-atheist 2012
## 3143   Australia non-atheist 2012
## 3144   Australia non-atheist 2012
## 3145   Australia non-atheist 2012
## 3146   Australia non-atheist 2012
## 3147   Australia non-atheist 2012
## 3148   Australia non-atheist 2012
## 3149   Australia non-atheist 2012
## 3150   Australia non-atheist 2012
## 3151   Australia non-atheist 2012
## 3152   Australia non-atheist 2012
## 3153   Australia non-atheist 2012
## 3154   Australia non-atheist 2012
## 3155   Australia non-atheist 2012
## 3156   Australia non-atheist 2012
## 3157   Australia non-atheist 2012
## 3158   Australia non-atheist 2012
## 3159   Australia non-atheist 2012
## 3160   Australia non-atheist 2012
## 3161   Australia non-atheist 2012
## 3162   Australia non-atheist 2012
## 3163   Australia non-atheist 2012
## 3164   Australia non-atheist 2012
## 3165   Australia non-atheist 2012
## 3166   Australia non-atheist 2012
## 3167   Australia non-atheist 2012
## 3168   Australia non-atheist 2012
## 3169   Australia non-atheist 2012
## 3170   Australia non-atheist 2012
## 3171   Australia non-atheist 2012
## 3172   Australia non-atheist 2012
## 3173   Australia non-atheist 2012
## 3174   Australia non-atheist 2012
## 3175   Australia non-atheist 2012
## 3176   Australia non-atheist 2012
## 3177   Australia non-atheist 2012
## 3178   Australia non-atheist 2012
## 3179   Australia non-atheist 2012
## 3180   Australia non-atheist 2012
## 3181   Australia     atheist 2012
## 3182   Australia non-atheist 2012
## 3183   Australia non-atheist 2012
## 3184   Australia     atheist 2012
## 3185   Australia non-atheist 2012
## 3186   Australia non-atheist 2012
## 3187   Australia     atheist 2012
## 3188   Australia     atheist 2012
## 3189   Australia non-atheist 2012
## 3190   Australia non-atheist 2012
## 3191   Australia non-atheist 2012
## 3192   Australia non-atheist 2012
## 3193   Australia non-atheist 2012
## 3194   Australia non-atheist 2012
## 3195   Australia     atheist 2012
## 3196   Australia non-atheist 2012
## 3197   Australia non-atheist 2012
## 3198   Australia non-atheist 2012
## 3199   Australia non-atheist 2012
## 3200   Australia non-atheist 2012
## 3201   Australia     atheist 2012
## 3202   Australia non-atheist 2012
## 3203   Australia non-atheist 2012
## 3204   Australia non-atheist 2012
## 3205   Australia non-atheist 2012
## 3206   Australia non-atheist 2012
## 3207   Australia non-atheist 2012
## 3208   Australia non-atheist 2012
## 3209   Australia non-atheist 2012
## 3210   Australia non-atheist 2012
## 3211   Australia non-atheist 2012
## 3212   Australia non-atheist 2012
## 3213   Australia non-atheist 2012
## 3214   Australia non-atheist 2012
## 3215   Australia non-atheist 2012
## 3216   Australia non-atheist 2012
## 3217   Australia non-atheist 2012
## 3218   Australia non-atheist 2012
## 3219   Australia non-atheist 2012
## 3220   Australia     atheist 2012
## 3221   Australia non-atheist 2012
## 3222   Australia non-atheist 2012
## 3223   Australia non-atheist 2012
## 3224   Australia non-atheist 2012
## 3225   Australia non-atheist 2012
## 3226   Australia non-atheist 2012
## 3227   Australia non-atheist 2012
## 3228   Australia     atheist 2012
## 3229   Australia non-atheist 2012
## 3230   Australia non-atheist 2012
## 3231   Australia non-atheist 2012
## 3232   Australia non-atheist 2012
## 3233   Australia non-atheist 2012
## 3234   Australia non-atheist 2012
## 3235   Australia non-atheist 2012
## 3236   Australia non-atheist 2012
## 3237   Australia non-atheist 2012
## 3238   Australia non-atheist 2012
## 3239   Australia non-atheist 2012
## 3240   Australia non-atheist 2012
## 3241   Australia non-atheist 2012
## 3242   Australia     atheist 2012
## 3243   Australia non-atheist 2012
## 3244   Australia non-atheist 2012
## 3245   Australia non-atheist 2012
## 3246   Australia non-atheist 2012
## 3247   Australia non-atheist 2012
## 3248   Australia non-atheist 2012
## 3249   Australia non-atheist 2012
## 3250   Australia     atheist 2012
## 3251   Australia non-atheist 2012
## 3252   Australia non-atheist 2012
## 3253   Australia non-atheist 2012
## 3254   Australia non-atheist 2012
## 3255   Australia non-atheist 2012
## 3256   Australia non-atheist 2012
## 3257   Australia non-atheist 2012
## 3258   Australia non-atheist 2012
## 3259   Australia non-atheist 2012
## 3260   Australia non-atheist 2012
## 3261   Australia non-atheist 2012
## 3262   Australia non-atheist 2012
## 3263   Australia non-atheist 2012
## 3264   Australia non-atheist 2012
## 3265   Australia non-atheist 2012
## 3266   Australia     atheist 2012
## 3267   Australia non-atheist 2012
## 3268   Australia non-atheist 2012
## 3269   Australia non-atheist 2012
## 3270   Australia non-atheist 2012
## 3271   Australia non-atheist 2012
## 3272   Australia non-atheist 2012
## 3273   Australia non-atheist 2012
## 3274   Australia non-atheist 2012
## 3275   Australia non-atheist 2012
## 3276   Australia non-atheist 2012
## 3277   Australia non-atheist 2012
## 3278   Australia non-atheist 2012
## 3279   Australia non-atheist 2012
## 3280   Australia non-atheist 2012
## 3281   Australia non-atheist 2012
## 3282   Australia non-atheist 2012
## 3283   Australia non-atheist 2012
## 3284   Australia non-atheist 2012
## 3285   Australia non-atheist 2012
## 3286   Australia non-atheist 2012
## 3287   Australia non-atheist 2012
## 3288   Australia non-atheist 2012
## 3289   Australia non-atheist 2012
## 3290   Australia     atheist 2012
## 3291   Australia non-atheist 2012
## 3292   Australia non-atheist 2012
## 3293   Australia non-atheist 2012
## 3294   Australia non-atheist 2012
## 3295   Australia non-atheist 2012
## 3296   Australia non-atheist 2012
## 3297   Australia non-atheist 2012
## 3298   Australia non-atheist 2012
## 3299   Australia non-atheist 2012
## 3300   Australia non-atheist 2012
## 3301   Australia non-atheist 2012
## 3302   Australia non-atheist 2012
## 3303   Australia non-atheist 2012
## 3304   Australia non-atheist 2012
## 3305   Australia non-atheist 2012
## 3306   Australia non-atheist 2012
## 3307   Australia non-atheist 2012
## 3308   Australia non-atheist 2012
## 3309   Australia non-atheist 2012
## 3310   Australia     atheist 2012
## 3311   Australia     atheist 2012
## 3312   Australia non-atheist 2012
## 3313   Australia non-atheist 2012
## 3314   Australia non-atheist 2012
## 3315   Australia non-atheist 2012
## 3316   Australia non-atheist 2012
## 3317   Australia non-atheist 2012
## 3318   Australia     atheist 2012
## 3319   Australia non-atheist 2012
## 3320   Australia non-atheist 2012
## 3321   Australia non-atheist 2012
## 3322   Australia non-atheist 2012
## 3323   Australia non-atheist 2012
## 3324   Australia non-atheist 2012
## 3325   Australia non-atheist 2012
## 3326   Australia non-atheist 2012
## 3327   Australia non-atheist 2012
## 3328   Australia non-atheist 2012
## 3329   Australia non-atheist 2012
## 3330   Australia non-atheist 2012
## 3331   Australia non-atheist 2012
## 3332   Australia non-atheist 2012
## 3333   Australia non-atheist 2012
## 3334   Australia     atheist 2012
## 3335   Australia non-atheist 2012
## 3336   Australia non-atheist 2012
## 3337   Australia non-atheist 2012
## 3338   Australia     atheist 2012
## 3339   Australia non-atheist 2012
## 3340   Australia non-atheist 2012
## 3341   Australia non-atheist 2012
## 3342   Australia non-atheist 2012
## 3343   Australia non-atheist 2012
## 3344   Australia     atheist 2012
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## 3346   Australia non-atheist 2012
## 3347   Australia non-atheist 2012
## 3348   Australia non-atheist 2012
## 3349   Australia non-atheist 2012
## 3350   Australia non-atheist 2012
## 3351   Australia non-atheist 2012
## 3352   Australia non-atheist 2012
## 3353   Australia non-atheist 2012
## 3354   Australia non-atheist 2012
## 3355   Australia     atheist 2012
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## 3357   Australia non-atheist 2012
## 3358   Australia non-atheist 2012
## 3359   Australia non-atheist 2012
## 3360   Australia non-atheist 2012
## 3361   Australia non-atheist 2012
## 3362   Australia non-atheist 2012
## 3363   Australia non-atheist 2012
## 3364   Australia non-atheist 2012
## 3365   Australia     atheist 2012
## 3366   Australia non-atheist 2012
## 3367   Australia     atheist 2012
## 3368   Australia non-atheist 2012
## 3369   Australia non-atheist 2012
## 3370   Australia non-atheist 2012
## 3371   Australia non-atheist 2012
## 3372   Australia non-atheist 2012
## 3373   Australia     atheist 2012
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## 3375   Australia non-atheist 2012
## 3376   Australia non-atheist 2012
## 3377   Australia non-atheist 2012
## 3378   Australia non-atheist 2012
## 3379   Australia non-atheist 2012
## 3380   Australia non-atheist 2012
## 3381   Australia non-atheist 2012
## 3382   Australia non-atheist 2012
## 3383   Australia non-atheist 2012
## 3384   Australia non-atheist 2012
## 3385   Australia non-atheist 2012
## 3386   Australia non-atheist 2012
## 3387   Australia non-atheist 2012
## 3388   Australia non-atheist 2012
## 3389   Australia     atheist 2012
## 3390   Australia non-atheist 2012
## 3391   Australia     atheist 2012
## 3392   Australia non-atheist 2012
## 3393   Australia non-atheist 2012
## 3394   Australia non-atheist 2012
## 3395   Australia     atheist 2012
## 3396   Australia     atheist 2012
## 3397   Australia non-atheist 2012
## 3398   Australia non-atheist 2012
## 3399   Australia non-atheist 2012
## 3400   Australia non-atheist 2012
## 3401   Australia non-atheist 2012
## 3402   Australia non-atheist 2012
## 3403   Australia non-atheist 2012
## 3404   Australia     atheist 2012
## 3405   Australia non-atheist 2012
## 3406   Australia non-atheist 2012
## 3407   Australia     atheist 2012
## 3408   Australia non-atheist 2012
## 3409   Australia non-atheist 2012
## 3410   Australia non-atheist 2012
## 3411   Australia non-atheist 2012
## 3412   Australia non-atheist 2012
## 3413   Australia non-atheist 2012
## 3414   Australia non-atheist 2012
## 3415   Australia non-atheist 2012
## 3416   Australia non-atheist 2012
## 3417   Australia non-atheist 2012
## 3418   Australia non-atheist 2012
## 3419   Australia non-atheist 2012
## 3420   Australia non-atheist 2012
## 3421   Australia non-atheist 2012
## 3422   Australia non-atheist 2012
## 3423   Australia non-atheist 2012
## 3424   Australia non-atheist 2012
## 3425   Australia non-atheist 2012
## 3426   Australia     atheist 2012
## 3427   Australia non-atheist 2012
## 3428   Australia non-atheist 2012
## 3429   Australia non-atheist 2012
## 3430   Australia non-atheist 2012
## 3431   Australia non-atheist 2012
## 3432   Australia non-atheist 2012
## 3433   Australia non-atheist 2012
## 3434   Australia non-atheist 2012
## 3435   Australia non-atheist 2012
## 3436   Australia non-atheist 2012
## 3437   Australia non-atheist 2012
## 3438   Australia non-atheist 2012
## 3439   Australia non-atheist 2012
## 3440   Australia non-atheist 2012
## 3441   Australia non-atheist 2012
## 3442   Australia non-atheist 2012
## 3443   Australia non-atheist 2012
## 3444   Australia non-atheist 2012
## 3445   Australia non-atheist 2012
## 3446   Australia     atheist 2012
## 3447   Australia non-atheist 2012
## 3448   Australia non-atheist 2012
## 3449   Australia non-atheist 2012
## 3450   Australia non-atheist 2012
## 3451   Australia non-atheist 2012
## 3452   Australia non-atheist 2012
## 3453   Australia non-atheist 2012
## 3454   Australia     atheist 2012
## 3455   Australia non-atheist 2012
## 3456   Australia non-atheist 2012
## 3457   Australia non-atheist 2012
## 3458   Australia non-atheist 2012
## 3459   Australia non-atheist 2012
## 3460   Australia non-atheist 2012
## 3461   Australia non-atheist 2012
## 3462   Australia non-atheist 2012
## 3463   Australia non-atheist 2012
## 3464   Australia non-atheist 2012
## 3465   Australia non-atheist 2012
## 3466   Australia non-atheist 2012
## 3467   Australia non-atheist 2012
## 3468   Australia non-atheist 2012
## 3469   Australia     atheist 2012
## 3470   Australia non-atheist 2012
## 3471   Australia non-atheist 2012
## 3472   Australia non-atheist 2012
## 3473   Australia non-atheist 2012
## 3474   Australia non-atheist 2012
## 3475   Australia non-atheist 2012
## 3476   Australia     atheist 2012
## 3477   Australia non-atheist 2012
## 3478   Australia non-atheist 2012
## 3479   Australia non-atheist 2012
## 3480   Australia non-atheist 2012
## 3481   Australia non-atheist 2012
## 3482   Australia non-atheist 2012
## 3483   Australia non-atheist 2012
## 3484   Australia non-atheist 2012
## 3485   Australia non-atheist 2012
## 3486   Australia non-atheist 2012
## 3487   Australia non-atheist 2012
## 3488   Australia non-atheist 2012
## 3489   Australia non-atheist 2012
## 3490   Australia non-atheist 2012
## 3491   Australia non-atheist 2012
## 3492   Australia non-atheist 2012
## 3493   Australia non-atheist 2012
## 3494   Australia non-atheist 2012
## 3495   Australia non-atheist 2012
## 3496   Australia     atheist 2012
## 3497   Australia non-atheist 2012
## 3498   Australia non-atheist 2012
## 3499   Australia non-atheist 2012
## 3500   Australia     atheist 2012
## 3501   Australia non-atheist 2012
## 3502   Australia non-atheist 2012
## 3503   Australia non-atheist 2012
## 3504   Australia non-atheist 2012
## 3505   Australia non-atheist 2012
## 3506   Australia non-atheist 2012
## 3507   Australia non-atheist 2012
## 3508   Australia non-atheist 2012
## 3509   Australia non-atheist 2012
## 3510   Australia non-atheist 2012
## 3511   Australia non-atheist 2012
## 3512   Australia non-atheist 2012
## 3513   Australia non-atheist 2012
## 3514   Australia     atheist 2012
## 3515   Australia non-atheist 2012
## 3516   Australia non-atheist 2012
## 3517   Australia non-atheist 2012
## 3518   Australia non-atheist 2012
## 3519   Australia non-atheist 2012
## 3520   Australia non-atheist 2012
## 3521   Australia non-atheist 2012
## 3522   Australia non-atheist 2012
## 3523   Australia non-atheist 2012
## 3524   Australia non-atheist 2012
## 3525   Australia non-atheist 2012
## 3526   Australia non-atheist 2012
## 3527   Australia non-atheist 2012
## 3528   Australia non-atheist 2012
## 3529   Australia non-atheist 2012
## 3530   Australia non-atheist 2012
## 3531   Australia non-atheist 2012
## 3532   Australia non-atheist 2012
## 3533   Australia non-atheist 2012
## 3534   Australia non-atheist 2012
## 3535   Australia non-atheist 2012
## 3536   Australia non-atheist 2012
## 3537   Australia non-atheist 2012
## 3538   Australia non-atheist 2012
## 3539   Australia non-atheist 2012
## 3540   Australia non-atheist 2012
## 3541   Australia     atheist 2012
## 3542   Australia non-atheist 2012
## 3543   Australia non-atheist 2012
## 3544   Australia     atheist 2012
## 3545   Australia non-atheist 2012
## 3546   Australia     atheist 2012
## 3547   Australia non-atheist 2012
## 3548   Australia     atheist 2012
## 3549   Australia non-atheist 2012
## 3550   Australia non-atheist 2012
## 3551   Australia non-atheist 2012
## 3552   Australia non-atheist 2012
## 3553   Australia non-atheist 2012
## 3554   Australia non-atheist 2012
## 3555   Australia     atheist 2012
## 3556   Australia non-atheist 2012
par(mfrow=c(1,2))

#Australia
#interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))



#Ecuador
#interplay between n ad p
#5,000 samples of size 400 from a population with a true atheist proportion of 0.02
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.02
n <- 400
p_hatse <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilities p and 1-p.
  p_hatse[i] <- sum(samp == "atheist")/n                                            #Calculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hatse, main = "p = 0.02, n = 400", xlim = c(0, 0.18))

par(mfrow = c(1, 1))
#calculate proportion of atheist responses
#get number of atheists in Australia
australia_atheist <- nrow (australia12[australia12$response =="atheist",])
australia_atheist
## [1] 104
#calculate proportion of atheist responses
#get number of atheists in Ecuador
ecuador_atheist <- nrow (ecuador12[ecuador12$response =="atheist",])
ecuador_atheist
## [1] 8
#calculate proportion of non-atheist responses
#get number of non-atheists in Australia
australia_non_atheist <- nrow (australia12[australia12$response =="non-atheist",])
australia_non_atheist
## [1] 935
#calculate proportion of non-atheist responses
#get number of non-atheists in Ecuador
ecuador_non_atheist <- nrow (ecuador12[ecuador12$response =="non-atheist",])
ecuador_non_atheist
## [1] 396
#calculate proportion of atheist responses_Australia
#get number of Australia rows

australia_rows <- nrow(australia12)
australia_rows
## [1] 1039
#calculate proportion of atheist responses_Australia

australia_atheist/australia_rows
## [1] 0.1000962
#calculate proportion of non-atheist responses_Australia

australia_non_atheist/australia_rows
## [1] 0.8999038
#calculate proportion of atheist responses_Ecuador
#get number of Ecuador rows

ecuador_rows <- nrow(ecuador12)
ecuador_rows
## [1] 404
#calculate proportion of atheist responses_Ecuador
ecuador_atheist/ecuador_rows
## [1] 0.01980198
#calculate proportion of non-atheist responses_Ecuador
ecuador_non_atheist/ecuador_rows
## [1] 0.980198
#Success/Fail Calculation:  Australia atheist

australia_rows * (australia_atheist/australia_rows)
## [1] 104
#Success/Fail Calculation:  Australia non-atheist

australia_rows * (australia_non_atheist/australia_rows)
## [1] 935
#Success/Fail Calculation:  Ecuador atheist

ecuador_rows * (ecuador_atheist/ecuador_rows)
## [1] 8
#Success/Fail Calculation:  Ecuador non-atheist

ecuador_rows * (ecuador_non_atheist/ecuador_rows)
## [1] 396
summary(p_hats)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.06827 0.09423 0.10000 0.10006 0.10673 0.14423
summary(p_hatse)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00250 0.01500 0.02000 0.01992 0.02500 0.05000
#Mean Error - Australia
p <- 0.1
n <- 1040
me <- 2* sqrt(p*(1-p)/n)
me
## [1] 0.01860521
#Mean Error - Australia
p <- 0.02
n <- 400
me <- 2* sqrt(p*(1-p)/n)
me
## [1] 0.014
#Spread Calculations: Australia
#Variance               
var(p_hats) 
## [1] 8.570617e-05
#Standard Deviation 
sd(p_hats)  
## [1] 0.009257763
#IQR                    
IQR(p_hats)
## [1] 0.0125
#Spread Calculations: Ecuador
#Variance               
var(p_hatse)    
## [1] 5.091495e-05
#Standard Deviation 
sd(p_hatse) 
## [1] 0.007135471
#IQR                    
IQR(p_hatse)
## [1] 0.01
#plot margin of error Australia and Ecuador
#Australia

#Margin of Error (Australia and Ecuador)
#Australia
p <- 0.1
n <- 1040
me<- 2 * sqrt(p*(1-p)/n)
me
## [1] 0.01860521
#plot margin of error Australia and Ecuador
#Australia

n <- seq(0,1039,1)
p <- 0.1
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Australia", xlab = "N")

#plot margin of error Australia and Ecuador
#Ecuador

n <- seq(0,404,1)
p <- 0.02
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Ecuador", xlab = "N")

#plot margin of error Australia and Ecuador
#Australia
#setting both p values at .5 to test

n <- seq(0,1039,1)
p <- 0.5
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Australia", xlab = "N")

#plot margin of error Australia and Ecuador
#Ecuador
#setting both p values at .5 to test

n <- seq(0,404,1)
p <- 0.5
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Ecuador", xlab = "N")

---
title: "Week 9 Lab - Inference for Categorical Data"
author: "Aaryn Zimmerman"
date: "`r Sys.Date()`"
output: openintro::lab_report
---

```{r load-packages, message=FALSE}
library(tidyverse)
library(openintro)
library(ggplot2)
library(plotrix)
```

Week 9 Lab:  Looking at atheism survey and exploring what’s at play when making inference about population proportions using categorical data.
Correct link for article:  https://www.webpages.uidaho.edu/~stevel/251/Global_INDEX_of_Religiosity_and_Atheism_PR__6.pdf


```{r code-chunk-label}
# Insert code for Exercise 1 here
```

### Exercise 1

Correct link for article:  https://www.webpages.uidaho.edu/~stevel/251/Global_INDEX_of_Religiosity_and_Atheism_PR__6.pdf

In the first paragraph, several key findings are reported. Do these percentages appear to be sample statistics (derived from the data sample) or population parameters?

**Answer***
Most of the percentages appear to be sample statistics that are derived from the sample data as opposed to percentages from population percentages.  The % findings outlined in the paragraph seem to be sample statistics.  Had these been population percentages, they would have been conclusions drawn from the sample statistics and would relate to the entire population, or the population parameter.  

Worth noting, I also looked for Greek letters (sigma, mu) in search of parameters; I looked for English letters to indicate statistics (x-bar; p-hat). 

Paragraph 1:
"Zurich, 27 July 2012 — We have no opinion polling data prior to
the 20th century, but according to the latest global poll released 
by WIN-Gallup International, a world-wide network of leading 
opinion pollsters, atheists are a small minority in the early years of
21st century. Only 13% say they are atheists. They are mostly 
concentrated in East Asia where 47% of the Chinese and 31% of 
the Japanese say they are atheists; and Western Europe, 14% of 
whose population says the same. Elsewhere sizeable majorities 
claim to be religious; the global average is 59%. Another sizeable 
group claims to be “not-religious” but stops short of defining itself 
as “atheist”. Their global average is 23%."
...



```{r}

```
### Exercise 2
The title of the report is “Global Index of Religiosity and Atheism”. To generalize the report’s findings to the global human population, what must we assume about the sampling method? Does that seem like a reasonable assumption?

**Answer**
"Global" indicates this is an index of religiosity and atheism of the world population.  To generalize findings, we must assume the sampling method used was random and representative across the entire world. In looking at the sample size and mode of field work (see snippet below), and thinking about it from a "reasonable assumption" perspective, it does not seem reasonable.  If a sample of 1,000 was taken from each country, it seems there could be a problem with the sampling since there are population differences between large countries and small countries.  The global index could be skewed if the countries aren't represented proportionally in the sampling.   


Sample Size and Mode of Field Work:
A total of 51,927 persons were interviewed globally. In each 
country a national probability sample of around 1000 men and 
women was interviewed either face to face (35 countries; 
n=33,890), via telephone (11 countries; n=7,661) or online 
(11 countries; n=10,376). 


```{r}
#Go to Table 6 (pages 15 and 16), which reports the sample size and response percentages for all 57 countries. 
#While this is a useful format to summarize the data, we will base our analysis on the original data set of individual responses to the survey. #Load this data set into R with the following command.

download.file("http://www.openintro.org/stat/data/atheism.RData", destfile = "atheism.RData")
load("atheism.RData")
```
```{r}
view(atheism)
```

### Exercise 3
What does each row of Table 6 correspond to? What does each row of atheism correspond to?

**Answer**
Table 6 shows the following:  
1.  Countries included in the polling (shows countries of the world that were included in the sample)
2.  Sample size of each country (gives us indication of proportions)
3.  Responses as a percentage for each country

Each row of the data set "atheism" corresponds to the following:
1.  nationality (individual responses from each country)
2.  response (as an atheist or non-atheist value as opposed to response percentages as seen in the table)
3.  year (the year the response was gathered)


```{r}
glimpse(atheism)
```

### Exercise 4
To investigate the link between these two ways of organizing this data, take a look at the estimated proportion of atheists in the United States. Towards the bottom of Table 6, we see that this is 5%. We should be able to come to the same number using the atheism data.


Using the command below, create a new dataframe called us12 that contains only the rows in atheism associated with resApondents to the 2012 survey from the United States. Next, calculate the proportion of atheist responses. Does it agree with the percentage in Table 6? If not, why?


***Answer***
Calculated proportion of atheist responses = 0.0499002, which is approximately 5%.   (see code chunks below)
Percentage in table 6:  5% atheist responses of 1002 responses
Yes, the calculated proportion of atheist responses agrees with the percentage in Table 6.

```{r}
us12 <- subset(atheism, nationality == "United States" & year == "2012")
```

```{r}
summary(us12)
```
```{r}
#calculate proportion of atheist responses
#get number of us atheists
us_atheist <- nrow (us12[us12$response =="atheist",])
us_atheist

```
```{r}
#calculate proportion of atheist responses
#get number of us rows

us_rows <- nrow(us12)
us_rows
```
```{r}
#calculate proportion of atheist responses
us_atheist/us_rows
```

### Exercise 5

Inference on proportions
As was hinted at in Exercise 1, Table 6 provides statistics, that is, calculations made from the sample of 51,927 people. What we’d like, though, is insight into the population parameters. You answer the question, “What proportion of people in your sample reported being atheists?” with a statistic; while the question “What proportion of people on earth would report being atheists” is answered with an estimate of the parameter.

The inferential tools for estimating population proportion are analogous to those used for means in the last chapter: the confidence interval and the hypothesis test.


Write out the conditions for inference to construct a 95% confidence interval for the proportion of atheists in the United States in 2012. Are you confident all conditions are met?

**Answer**
In the last chapter lab, we checked if the conditions necessary for inference were satisfied by obtaining sample sizes to check the conditions. We computed group size by using the by command as follows:  by(nc$weight, nc$habit, length)


If the random (picked radomly across the country) sample size is less than 10% of the US population, the observations are independent - and this condition necessary for inference is satisfied as observations must be independent.  In the us12 data set, there are 1,002 observations.  This number of observations is significantly below 10% of the US population, so the observations are, in fact, independent.

In the US in 2012, the success/fail condition is satisfied:   
Calc 1 - Population of 1,002 * 0.0499 = 50
Calc 2 - Population of 1,002 * 0.9500 = 952
Both calculations are greater than 10.  The condition is met if there are at least 10 expected successes and 10 expected failures in the sample. 

Expected number of successes is at least 10: np ≥ 10
Expected number of failures is at least 10: n(1-p) ≥ 10
where n is the sample size & p is the probability of success on a given trial.


I am confident all conditions are met.
```{r}
#calculate proportion of non_atheist responses
#get number of us non-atheists
us_non_atheist <- nrow (us12[us12$response =="non-atheist",])
us_non_atheist
```
```{r}
#calculate proportion of non_atheist responses
us_non_atheist/us_rows
```
```{r}
#Success/fail condition satisfied:  Is the calculation greater than 10?

us_rows *(us_atheist/us_rows)
```
```{r}
#Success/fail condition satisfied:  Is the calculation greater than 10?

us_rows *(us_non_atheist/us_rows)
```

```{r}
#If the conditions for inference are reasonable, calculate the standard error and construct the interval using the inference function 
inference(us12$response, est = "proportion", type = "ci", method = "theoretical", 
          success = "atheist")
```


Note that since the goal is to construct an interval estimate for a proportion, it’s necessary to specify what constitutes a “success”, which here is a response of "atheist".

Although formal confidence intervals and hypothesis tests don’t show up in the report, suggestions of inference appear at the bottom of page 7: “In general, the error margin for surveys of this kind is ± 3-5% at 95% confidence”.


### Exercise 6

Based on the R output, what is the margin of error, statistic expressing the amount of random sampling error in the results, for the estimate of the proportion of atheists in US in 2012?



***Answer***
Copied/pasted summary statistics from 'R Console' output above:
Summary statistics: p_hat = 0.0499 ;  n = 1002 
Check conditions: number of successes = 50 ; number of failures = 952 
Standard error = 0.0069 
95 % Confidence interval = ( 0.0364 , 0.0634 )

Calculated moE = 0.0135 (see code chunk below)

```{r}
#find margin of error 
lower_boundary <- 0.0364
upper_boundary <- 0.0634
diff <- upper_boundary-lower_boundary
moE <- diff/2
moE

```
### Exercise 7
Using the inference function, calculate confidence intervals for the proportion of atheists in 2012 in two other countries of your choice, and report the associated margins of error. Be sure to note whether the conditions for inference are met. It may be helpful to create new data sets for each of the two countries first, and then use these data sets in the inference function to construct the confidence intervals.


**Answer**
If the random (picked radomly across the country) sample size is less than 10% of the countries (India and Poland) populations, the observations are independent - and this condition necessary for inference is satisfied as observations must be independent.  In the india12 data set, there are 1,092 observations.  This number of observations is significantly below 10% of India's population, so the observations are, in fact, independent. In the poland12 data set, there are 525 observations.  This number of observations is also significantly below 10% of Poland's population, so the observations are also independent.


In India in 2012, the success/fail condition is satisfied:  
Calc 1 - Population of 1,092 * 0.03021978 = 33
Calc 2 - Population of 1,092 * 0.9697802  = 1059
Both calculations are greater than 10.  The condition is met if there are at least 10 expected successes and 10 expected failures in the sample. 

Expected number of successes is at least 10: np ≥ 10
Expected number of failures is at least 10: n(1-p) ≥ 10
where n is the sample size & p is the probability of success on a given trial.


I am confident the conditions for inference are met.



In Poland in 2012, the success/fail condition is satisfied:   
Calc 1 - Population of 525 * 0.04952381 = 26
Calc 2 - Population of 525 * 0.9504762. = 499
Both calculations are greater than 10.  The condition is met if there are at least 10 expected successes and 10 expected failures in the sample. 

Expected number of successes is at least 10: np ≥ 10
Expected number of failures is at least 10: n(1-p) ≥ 10
where n is the sample size & p is the probability of success on a given trial.


I am confident the conditions for inference are met.



moE for India = 0.01015

moE for Poland = 0.01855
```{r}
#Create data sets for two additional countries
#India
india12 <- subset(atheism, nationality == "India" & year == "2012")
india12
```
```{r}
#Create data sets for two additional countries
#India
poland12 <- subset(atheism, nationality == "Poland" & year == "2012")
poland12
```
```{r}
#calculate proportion of atheist responses
#get number of atheists in India
india_atheist <- nrow (india12[india12$response =="atheist",])
india_atheist
```
```{r}
#calculate proportion of atheist responses
#get number of atheists in Poland
poland_atheist <- nrow (poland12[poland12$response =="atheist",])
poland_atheist


```

```{r}
#calculate proportion of atheist responses_India
#get number of India rows

india_rows <- nrow(india12)
india_rows

```

```{r}
#calculate proportion of atheist responses_Poland
#get number of Poland rows

poland_rows <- nrow(poland12)
poland_rows



```

```{r}

#calculate proportion of atheist responses
india_atheist/india_rows

```

```{r}
#calculate proportion of atheist responses
poland_atheist/poland_rows
```
```{r}
#calculate proportion of non_atheist responses
#get number of India non-atheists
india_non_atheist <- nrow (india12[india12$response =="non-atheist",])
india_non_atheist
```
```{r}

#calculate proportion of non_atheist responses
#get number of Poland non-atheists
poland_non_atheist <- nrow (poland12[poland12$response =="non-atheist",])
poland_non_atheist

```
```{r}
#calculate proportion of non_atheist responses
india_non_atheist/india_rows
```
```{r}
#calculate proportion of non_atheist responses
poland_non_atheist/poland_rows

```

```{r}

#Success/fail condition satisfied:  Is the calculation greater than 10?
india_rows*(india_atheist/india_rows)
```
```{r}
#Success/fail condition satisfied:  Is the calculation greater than 10?
india_rows*(india_non_atheist/india_rows)
```
```{r}
#Success/fail condition satisfied:  Is the calculation greater than 10?
poland_rows*(poland_atheist/poland_rows)
```
```{r}
#Success/fail condition satisfied:  Is the calculation greater than 10?
poland_rows*(poland_non_atheist/poland_rows)
```

```{r}
summary(india12)
```
```{r}
summary(poland12)
```

```{r}
#If the conditions for inference are reasonable, calculate the standard error and construct the interval using the inference function 
#India
inference(india12$response, est = "proportion", type = "ci", method = "theoretical", 
          success = "atheist")
```
Single proportion -- success: atheist 
Summary statistics: p_hat = 0.0302 ;  n = 1092 
Check conditions: number of successes = 33 ; number of failures = 1059 
Standard error = 0.0052 
95 % Confidence interval = ( 0.0201 , 0.0404 )

```{r}

#find margin of error for India
lower_boundary <- 0.0201
upper_boundary <- 0.0404
diff <- upper_boundary-lower_boundary
moE <- diff/2
moE

```
```{r}

#If the conditions for inference are reasonable, calculate the standard error and construct the interval using the inference function 
#Poland
inference(poland12$response, est = "proportion", type = "ci", method = "theoretical", 
          success = "atheist")

```


Single proportion -- success: atheist 
Summary statistics: p_hat = 0.0495 ;  n = 525 
Check conditions: number of successes = 26 ; number of failures = 499 
Standard error = 0.0095 
95 % Confidence interval = ( 0.031 , 0.0681 )

```{r}
#find margin of error for Poland
lower_boundary <- 0.031
upper_boundary <- 0.0681
diff <- upper_boundary-lower_boundary
moE <- diff/2
moE



```


How does the proportion affect the margin of error?
Imagine you’ve set out to survey 1000 people on two questions: are you female? and are you left-handed? Since both of these sample proportions were calculated from the same sample size, they should have the same margin of error, right? Wrong! While the margin of error does change with sample size, it is also affected by the proportion.

Think back to the formula for the standard error: SE=p(1−p)/n−−−−−−−−−√. This is then used in the formula for the margin of error for a 95% confidence interval: ME=1.96×SE=1.96×p(1−p)/n−−−−−−−−−√. Since the population proportion p is in this ME formula, it should make sense that the margin of error is in some way dependent on the population proportion. We can visualize this relationship by creating a plot of ME vs. p.

The first step is to make a vector p that is a sequence from 0 to 1 with each number separated by 0.01. We can then create a vector of the margin of error (me) associated with each of these values of p using the familiar approximate formula (ME=2×SE). Lastly, we plot the two vectors against each other to reveal their relationship.

```{r}
n <- 1000
p <- seq(0, 1, 0.01)
me <- 2 * sqrt(p * (1 - p)/n)
plot(me ~ p, ylab = "Margin of Error", xlab = "Population Proportion")
```


### Exercise 8

Describe the relationship between p and me.

***Answer***
As Population Proportion, p, increases from 0.0 to approximately 0.5, Margin of Error, me, increases to a maximum of approximately 0.03.  As p continues increasing from .5 to 1.0, p decreases from .03 to 0.  


```{r}
#inserting space here
```


Success-failure condition
The textbook emphasizes that you must always check conditions before making inference. For inference on proportions, the sample proportion can be assumed to be nearly normal if it is based upon a random sample of independent observations and if both np≥10 and n(1−p)≥10. This rule of thumb is easy enough to follow, but it makes one wonder: what’s so special about the number 10?

The short answer is: nothing. You could argue that we would be fine with 9 or that we really should be using 11. What is the “best” value for such a rule of thumb is, at least to some degree, arbitrary. However, when np and n(1−p) reaches 10 the sampling distribution is sufficiently normal to use confidence intervals and hypothesis tests that are based on that approximation.

We can investigate the interplay between n and p and the shape of the sampling distribution by using simulations. To start off, we simulate the process of drawing 5000 samples of size 1040 from a population with a true atheist proportion of 0.1. For each of the 5000 samples we compute p^ and then plot a histogram to visualize their distribution.

```{r}
#interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))








```
```{r}

```

### Exercise 9
Describe the sampling distribution of sample proportions at n=1040 and p=0.1. Be sure to note the center, spread, and shape.
Hint: Remember that R has functions such as mean to calculate summary statistics.
https://statsandr.com/blog/descriptive-statistics-in-r/#boxplot


***Answer***
Summary Statistics
  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.06923 0.09327 0.10000 0.09991 0.10577 0.13558 


Mean Error  0.01860521


Center:  The sample distribution of the sample proportions', p_hats, center-point is at approximately 0.10. This is the same as the population proportion value of p=0.1. 

Shape:  The distribution has a single, clear peak with values increasing up to that point and then decreasing.  This indicates a unimodal, normal distribution. 

Spread Calculations:
Variance           	var(p_hats)	8.545609e-05
Standard Deviation	sd(p_hats)	0.009244247
IQR	                IQR(p_hats)	0.0125
Minimum             min(p_hats)	0.06923077
Maximum	            max(p_hats)	0.1355769
Range	              range(p_hats)	0.06923077 0.13557692



```{r}
summary(p_hats)
```
```{r}
sd(p_hats)
```

```{r}
	var(p_hats)
```
```{r}
IQR(p_hats)
```

```{r}
	min(p_hats)
```
```{r}
max(p_hats)
```
```{r}
 range(p_hats)
```
```{r}
#Mean Error
p <- 0.1
n <- 1040
me <- 2* sqrt(p*(1-p)/n)
me
```

### Exercise 10

Repeat the above simulation three more times but with modified sample sizes and proportions: for n=400 and p=0.1, n=1040 and p=0.02, and n=400 and p=0.02. Plot all four histograms together by running the par(mfrow = c(2, 2)) command before creating the histograms. You may need to expand the plot window to accommodate the larger two-by-two plot. Describe the three new sampling distributions. Based on these limited plots, how does n appear to affect the distribution of p^? How does p affect the sampling distribution?

***Answer***

As the sample size, n, increases from 400 to 1040, the spread becomes smaller and the margin of error becomes smaller.  Changing n changes the distribution.  As p changes, the location of the curve centers around the value of the population.  When p is .1, the location of the curve is centered around the population value of .1.  The same applies to .02.  So, as p increases, the spread decreases and the margin of error increases until p reaches a certain point (population proportion = .5), and then the margin of error decreases (as the parabola shows in Exercise 7 above). 

```{r}

par(mfrow=c(2,2))  

#interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))





#2interplay between n ad p
#5,000 samples of size 400 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 400
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 400", xlim = c(0, 0.18))



#3interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.02
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.02, n = 1040", xlim = c(0, 0.18))







#4interplay between n ad p
#5,000 samples of size 400 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.02
n <- 400
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.02, n = 400", xlim = c(0, 0.18))

```

```{r}
#reset plot window

par(mfrow = c(1, 1))
```

### Exercise 11

If you refer to Table 6, you’ll find that Australia has a sample proportion of 0.1 on a sample size of 1040, and that Ecuador has a sample proportion of 0.02 on 400 subjects. Let’s suppose for this exercise that these point estimates are actually the truth. Then given the shape of their respective sampling distributions, do you think it is sensible to proceed with inference and report margin of errors, as the reports does?



***Answer***
No, it does not make sense to proceed with inference and report margin of errors as the report does.  After doing the inference tests, I found Ecuador did not meet the Success/Fail condition for Atheist.  There were only 8 expected successes rather than 10 or more, so the inference test wasn't met.  Also, according to the margin of error plots shown via the code below, as the population increases above 200, there is little change in the margin of error.  The curve flattens out and stays flat. The report indicates an error margin of 3-5% in the report as follows:


A total of 51,927 persons were interviewed globally. In each 
country a national probability sample of around 1000 men and 
women was interviewed either face to face (35 countries; 
n=33,890), via telephone (11 countries; n=7,661) or online 
(11 countries; n=10,376). Details are attached. The field work was 
conducted during November 2011- January 2012. In general the WIN-Gallup International 
GLOBAL INDEX OF RELIGIOSITY AND ATHEISM - 2012
Page 8 of 25
error margin for surveys of this kind is +3-5% at 95% confidence 
level.

When looking at the plot of the error margins and comparing them to the calculated numbers, they are more around .01 - .02, so this is close.  Please see all analysis below.





Analysis:

1.  Are the observations independent?  Yes
If the random (picked radomly across the two countries) sample sizes are less than 10% of the populations of Australia and Ecuador, the observations are independent - and this condition necessary for inference is satisfied as observations must be independent.  It appears the observations are independent, so this condition is met.



2.  Compare the margin of errors: 
Australia = 0.01860521 or approximately .02
Ecuador = 0.014 or approximately .01

Margin of errors are similar; distribution and spreads are similar

Summary Statistics - Australia
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.00250 0.01500 0.02000 0.01997 0.02500 0.05000 

Summary Statistics - Ecuador
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.00000 0.01500 0.02000 0.02007 0.02500 0.05250 


Mean Error - Australia:  0.01860521
Mean Error - Ecuador:  0.014


Center - Australia:  The sample distribution of the sample proportions', p_hats, center-point is at approximately 0.10. This is the same as the population proportion value of p=0.1.
Center - Ecuador:    The sample distribution of the sample proportions, p_hatse, center-point is at approximately 0.02.  This is the same as the population proportion value of p=0.02.

Shape - Australia:  The distribution has a single, clear peak with values increasing up to that point and then decreasing.  This indicates a unimodal, normal distribution. 
Shape - Ecuador: The distribution has a single, clear peak with values increasing up to that point and then decreasing.  This indicates a unimodal, normal distribution. 


Spread Calculations: Australia
Variance           	var(p_hats)	= 8.856288e-05
Standard Deviation	sd(p_hats) = 0.009410785	
IQR	                IQR(p_hats) = 0.0125	


Spread Calculations: Ecquador
Variance           	var(p_hatse) = 4.982679e-05
Standard Deviation	sd(p_hatse)	 = 0.00705881
IQR	                IQR(p_hatse) = 0.01




3.  Success/Fail Condition:  Ecuador Failed
Australia 
Calc 1 - Atheist:       Population of 1039 * 0.1000962 = 104
Calc 2 - non-Atheist:   Population of 1039 * 0.8999038 = 935
Both calculations are greater than 10.  The condition is met if there are at least 10 expected successes and 10 expected failures in the sample.


Ecuador
Calc 1 - Atheist:       Population of 404 * 0.01980198 = 8
Calc 2 - non-Atheist:   Population of 404 * 0.980198   = 396
Both calculations are not greater than 10.  The success/fail condition is not met for Ecuador because there are only 8 expected successes as "atheist" is considered "success" in this study.



```{r}
#Margin of Error (Australia and Ecuador)
#Australia
p <- 0.1
n <- 1040
me <- 2 * sqrt(p*(1-p)/n)
me

```
```{r}
#Margin of Error (Australia and Ecuador)
#Ecuador
p <- 0.02
n <- 400
me <- 2 * sqrt(p*(1-p)/n)
me

```
```{r}
#Create data sets for Australia and Ecuador
#Australia
australia12 <- subset(atheism, nationality == "Australia" & year == "2012")
australia12
```
```{r}
#Create data sets for Australia and Ecuador
#Ecuador
ecuador12 <- subset(atheism, nationality == "Ecuador" & year == "2012")
ecuador12
```

```{r}
#Create data sets for Australia and Ecuador
#Australia
australia12 <- subset(atheism, nationality == "Australia" & year == "2012")
australia12
```
```{r}

par(mfrow=c(1,2))

#Australia
#interplay between n ad p
#5,000 samples of size 1040 from a population with a true atheist proportion of 0.1
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.1
n <- 1040
p_hats <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilityes p and 1-p.
  p_hats[i] <- sum(samp == "atheist")/n                                            #Caculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hats, main = "p = 0.1, n = 1040", xlim = c(0, 0.18))



#Ecuador
#interplay between n ad p
#5,000 samples of size 400 from a population with a true atheist proportion of 0.02
#For each of the 5,000 samples, compute p and then plot a histogram to visualize their distribution
p <- 0.02
n <- 400
p_hatse <- rep(0, 5000)

for(i in 1:5000){   #build the sampling distribution of p^ using the for loop
  samp <- sample(c("atheist", "non_atheist"), n, replace = TRUE, prob = c(p, 1-p)) #take a sample of size n with replacement from the choices 
                                                                                   #of atheist and non with probabilities p and 1-p.
  p_hatse[i] <- sum(samp == "atheist")/n                                            #Calculate the proportion of atheists in this sample and  
                                                                                    #record this value.  Loop allows us to repeat 5,000 times  
                                                                                    #to build a good representation of the sampling distrib. 
}

hist(p_hatse, main = "p = 0.02, n = 400", xlim = c(0, 0.18))


```
```{r}
par(mfrow = c(1, 1))
```

```{r}
#calculate proportion of atheist responses
#get number of atheists in Australia
australia_atheist <- nrow (australia12[australia12$response =="atheist",])
australia_atheist
```

```{r}
#calculate proportion of atheist responses
#get number of atheists in Ecuador
ecuador_atheist <- nrow (ecuador12[ecuador12$response =="atheist",])
ecuador_atheist
```
```{r}
#calculate proportion of non-atheist responses
#get number of non-atheists in Australia
australia_non_atheist <- nrow (australia12[australia12$response =="non-atheist",])
australia_non_atheist
```
```{r}
#calculate proportion of non-atheist responses
#get number of non-atheists in Ecuador
ecuador_non_atheist <- nrow (ecuador12[ecuador12$response =="non-atheist",])
ecuador_non_atheist
```
```{r}
#calculate proportion of atheist responses_Australia
#get number of Australia rows

australia_rows <- nrow(australia12)
australia_rows
```


```{r}
#calculate proportion of atheist responses_Australia

australia_atheist/australia_rows
```
```{r}
#calculate proportion of non-atheist responses_Australia

australia_non_atheist/australia_rows

```
```{r}
#calculate proportion of atheist responses_Ecuador
#get number of Ecuador rows

ecuador_rows <- nrow(ecuador12)
ecuador_rows

```


```{r}
#calculate proportion of atheist responses_Ecuador
ecuador_atheist/ecuador_rows
```


```{r}
#calculate proportion of non-atheist responses_Ecuador
ecuador_non_atheist/ecuador_rows
```

```{r}
#Success/Fail Calculation:  Australia atheist

australia_rows * (australia_atheist/australia_rows)
```
```{r}

#Success/Fail Calculation:  Australia non-atheist

australia_rows * (australia_non_atheist/australia_rows)

```
```{r}
#Success/Fail Calculation:  Ecuador atheist

ecuador_rows * (ecuador_atheist/ecuador_rows)

```
```{r}
#Success/Fail Calculation:  Ecuador non-atheist

ecuador_rows * (ecuador_non_atheist/ecuador_rows)
```

```{r}
summary(p_hats)
```
```{r}
summary(p_hatse)
```
```{r}
#Mean Error - Australia
p <- 0.1
n <- 1040
me <- 2* sqrt(p*(1-p)/n)
me
```
```{r}
#Mean Error - Australia
p <- 0.02
n <- 400
me <- 2* sqrt(p*(1-p)/n)
me
```
```{r}
#Spread Calculations: Australia
#Variance           	
var(p_hats)	

#Standard Deviation	
sd(p_hats)	

#IQR	                
IQR(p_hats)


```
```{r}

#Spread Calculations: Ecuador
#Variance           	
var(p_hatse)	

#Standard Deviation	
sd(p_hatse)	

#IQR	                
IQR(p_hatse)




```

```{r}
#plot margin of error Australia and Ecuador
#Australia

#Margin of Error (Australia and Ecuador)
#Australia
p <- 0.1
n <- 1040
me<- 2 * sqrt(p*(1-p)/n)
me


```
```{r}
#plot margin of error Australia and Ecuador
#Australia

n <- seq(0,1039,1)
p <- 0.1
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Australia", xlab = "N")

```

```{r}
#plot margin of error Australia and Ecuador
#Ecuador

n <- seq(0,404,1)
p <- 0.02
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Ecuador", xlab = "N")
```
```{r}

#plot margin of error Australia and Ecuador
#Australia
#setting both p values at .5 to test

n <- seq(0,1039,1)
p <- 0.5
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Australia", xlab = "N")



```
```{r}
#plot margin of error Australia and Ecuador
#Ecuador
#setting both p values at .5 to test

n <- seq(0,404,1)
p <- 0.5
me<- 2 * sqrt(p*(1-p)/n)
plot(me ~ n, ylab = "Margin of Error - Ecuador", xlab = "N")
```

