Lab 7: Inference for Categorical Data

Teamwork Report

Team member name | Attendence | Author | Contribution % |
: ………………………| : ……..| :……..| :………..
Kathleen Vern | yes | yes | 25%
Amanda Beach | yes | no | 25%
Lexi Clifford | yes | no | 25%
Michelle Rodriguez | yes | no | 25%
Total | | | 100% |

Exercise 1:

The percentages presented in the first paragraph appear to be sample statistics because the data describes a large population that was surveyed, but it is unlikely that every single person in each country sampled responded to the survey. Additionally in the second paragraph we are informed that it was surveyed from a sample size of 50,000 people which is not the entire population and thus it appears that we are looking at sample parameters rather than the entire population.

Exercise 2:

To generalize the report’s findings to the global human population, we must assume that the sampling method is a simple random sample. This seems like a reasonable assumption because the data is collected from an international Gallup poll and is described as a “world-wide network of leading opinion pollsters.” There is also diversity among countries, genders, has a large enough number of responses while remaining less that 10% of the whole population, and asks the same question to every sample surveyed. Also, because there is no information to indicate that the data is not taken from a simple random sample, we are able to assume this random method was in fact used.

Exercise 3:

Each row of table 6 corresponds to different countries while each row of “atheism” corresponds to different people who were surveyed. Because these two are different, we will need to take extra measures to compare the data of these tables.

Exercise 4:

The calculated proportion is .0499, which agrees with the percentage of 5% in the table

us12 <- atheism%>%
  filter(nationality == "United States", year == "2012")
inference(y = response, data = us12, null = 0, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided")

## Single categorical variable, success: atheist
## n = 1002, p-hat = 0.0499
## H0: p = 0
## HA: p != 0
## z = 7.2544
## p_value = < 0.0001

Single categorical variable success: atheist n = 1002 p-hat = 0.0499 H0: p = 0 HA: p != 0 z = 7.2544 p_value = < 0.0001

Exercise 5:

We are confident that all conditions are met: The data comes from a random sample. The sampling distribution of p^ is approximately normal. With a large sample size of 50,000, there are at least 10 expected successes and 10 expected failures. The observations appear to be independent, as the sample size is less than 10% of the global population.

Exercise 6:

ME= 1.96 x SE → sq root of (p(1-p))/n → (0.0499(1-0.0499))/1002 → 1.96 x 0.000047 ME = 0.000093

inference(y = response, data = us12, null = 0, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided")

## Single categorical variable, success: atheist
## n = 1002, p-hat = 0.0499
## H0: p = 0
## HA: p != 0
## z = 7.2544
## p_value = < 0.0001

Results: Single categorical variable, success: atheist n = 1002, p-hat = 0.0499 H0: p = 0 HA: p != 0 z = 7.2544 p_value = > 0.0001

Exercise 7:

The conditions for inference are met. The data comes from a random sample as it is part of the data from the Gallup poll, the sampling distribution of p-hat is approximately normal since the sample size is large enough, and there are at least 10 expected successes and 10 expected failures. Finally, the observations appear to be independent and the sample size is less than 10% of the population.

Confidence interval China: 42.63%, 51.37% ME: Z*SE = SE → sq root of (p(1-p))/n → (0.47(1-0.47))/500 = .0004982 → 1.96 x 0.00004982 = .000976 ME = 0.000976 We are 42.63-51.37% confident that the proporiton of atheists in China in 2012 is .47.

Confidence interval Argentina: 5.47-8.66% ME: Z*SE = SE → sq root of (p(1-p))/n → (.0706(1-.0706))/991 = .000066 → 1.96 x .000066 = .00013 ME = 0.00013 We are 5.47-8.66% confident that the proportion of atheists in Argentina in 2012 is .0706%

ch12 <- atheism %>%
  filter(nationality == "China", year == "2012")
inference(y = response, data = ch12, null = 0, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist", alternative = "twosided")

## Single categorical variable, success: atheist
## n = 500, p-hat = 0.47
## 95% CI: (0.4263 , 0.5137)

ar12 <- atheism %>%
 filter(nationality == "Argentina", year == "2012")
inference(y = response, data = ar12, null = 0, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist", alternative = "twosided")

## Single categorical variable, success: atheist
## n = 991, p-hat = 0.0706
## 95% CI: (0.0547 , 0.0866)

China results:

Single categorical variable, success: atheist n = 500, p-hat = 0.47 95% CI: (0.4263 , 0.5137)

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=299&randomizer=-1709530061

Argentina results:

Single categorical variable, success: atheist n = 991, p-hat = 0.0706 95% CI: (0.0547 , 0.0866)

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=299&randomizer=-27408275

Exercise 8:

The relationship between “p” and “me” is an inverse u shaped relationship, or a unimodal graph with a margin of error of ** against the population proportion plot we constructed. At a value of p = 0.50, margin of error me is maximized for a given sample size.

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=299&randomizer=-953100298

Exercise 9:

The sampling distribution shows that the mean of the data is approximately 0.11, the graph is unimodal and slightly right skewed.

Exercise 10:

As p changes and n remains constant, the sampling distribution becomes more skewed to either side (it becomes more left skewed as p decreases and more right skewed as p increases). Additionally, the mean of the data decreases as p decreases and increases as p increases. The graph remains unimodal, but becomes less normal.

Exercise 11:

If n is altered along with p, the sampling distribution approaches a nearly normal distribution as n increases. The larger the population size, the more normal the distribution becomes.

Exercise 12:

For Australia, we can proceed with inference and report margin of error (me) as Australia’s data satisfies the conditions for inference for sampling disribution (p). However, Ecuador’s data does not meet the success-failure condition as np is only 8, which is smaller than the 10 needed.

Exercise 13:

Ho = proporiton of atheists in Spain in 2005 = proportion of atheists in Spain in 2012 Ha = proporiton of atheists in Spain in 2005 does not equal proportion of atheists in Spain in 2012

There is convincing evidence that Spain has experienced a change in its atheist index between 2005 and 2012 because the p value is <0.0001, which is less than .05.

The confience interval is (.0831, .1072)

sp <- atheism%>%
 filter(nationality == "Spain", year == "2012" | year == "2005")
inference(y = response, data = sp, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided", null = 0)

## Single categorical variable, success: atheist
## n = 2291, p-hat = 0.0952
## H0: p = 0
## HA: p != 0
## z = 15.5218
## p_value = < 0.0001

inference(y = response, data = sp, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist")

## Single categorical variable, success: atheist
## n = 2291, p-hat = 0.0952
## 95% CI: (0.0831 , 0.1072)

Single categorical variable, success: atheist n = 2291, p-hat = 0.0952 H0: p = 0 HA: p != 0 z = 15.5218 p_value = < 0.0001

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=298&randomizer=1162104824

Confidence interval:

Single categorical variable, success: atheist n = 2291, p-hat = 0.0952 95% CI: (0.0831 , 0.1072)

Exercise 14:

Ho = proporiton of atheists in the US in 2005 = proportion of atheists in the US in 2012 Ha = proporiton of atheists in the US in 2005 does not equal proportion of atheists in the US in 2012

There is convincing evidence that the US has seen a change in its atheist index between 2005 and 2012. The p value of is < 0.0001, which is less than .05.

The confidence interval is (0.0225 , 0.0374)

us0512 <- atheism%>%
 filter(nationality == "United States", year == "2012" | year == "2005")
 inference(y = response, data = us0512, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided", null = 0)

## Single categorical variable, success: atheist
## n = 2004, p-hat = 0.0299
## H0: p = 0
## HA: p != 0
## z = 7.8646
## p_value = < 0.0001

Single categorical variable, success: atheist n = 2004, p-hat = 0.0299 H0: p = 0 HA: p != 0 z = 7.8646 p_value = < 0.0001

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=298&randomizer=-2950631

Single categorical variable, success: atheist n = 2004, p-hat = 0.0299 95% CI: (0.0225 , 0.0374)

Exercise 15:

A type 1 error is the false rejection of the null hypothesis; ie a “false positive”. There is a 5% chance because the probability of making a type 1 error is equal to alpha, because of this there is a 5% chance there will be a change in the proportion of atheists due to random chance

Exercise 16: use formula for margin of error + plug in values to calc sample size

Based on the plot of p and margin of error (me) you would need to sample 16 people

---
title: "Lab 7: Inference for Categorical Data"
author: "Above Average"
date: "3/18/2019"
output: oilabs::lab_report
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(tidyverse)
library(oilabs)
library(ggplot2)
library(dplyr)

data(atheism)


```

### Teamwork Report

| Team member name | Attendence | Author | Contribution % |
| : ...........................| : ........| :........| :...........
| Kathleen Vern      | yes | yes | 25%
| Amanda Beach       | yes | no | 25%
| Lexi Clifford      | yes | no | 25%
| Michelle Rodriguez | yes | no | 25%
| Total | | | 100% |

* * *

### Exercise 1: 
The percentages presented in the first paragraph appear to be sample statistics because the data describes a large population that was surveyed, but it is unlikely that every single person in each country sampled responded to the survey. Additionally in the second paragraph we are informed that it was surveyed from a sample size of 50,000 people which is not the entire population and thus it appears that we are looking at sample parameters rather than the entire population. 

### Exercise 2:
To generalize the report’s findings to the global human population, we must assume that the sampling method is a simple random sample. This seems like a reasonable assumption because the data is collected from an international Gallup poll and is described as a “world-wide network of leading opinion pollsters.” There is also diversity among countries, genders, has a large enough number of responses while remaining less that 10% of the whole population, and asks the same question to every sample surveyed. Also, because there is no information to indicate that the data is not taken from a simple random sample, we are able to assume this random method was in fact used. 

### Exercise 3:
Each row of table 6 corresponds to different countries while each row of “atheism” corresponds to different people who were surveyed. Because these two are different, we will need to take extra measures to compare the data of these tables. 

### Exercise 4:
The calculated proportion is .0499, which agrees with the percentage of 5% in the table
```{r}
us12 <- atheism%>%
  filter(nationality == "United States", year == "2012")
inference(y = response, data = us12, null = 0, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided")

```
Single categorical variable success: atheist
n = 1002 p-hat = 0.0499
H0: p = 0
HA: p != 0
z = 7.2544
p_value = < 0.0001

### Exercise 5:
We are confident that all conditions are met: 
The data comes from a random sample.
The sampling distribution of p^ is approximately normal. With a large sample size of 50,000, there are at least 10 expected successes and 10 expected failures. 
The observations appear to be independent, as the sample size is less than 10% of the global population. 

### Exercise 6:
ME= 1.96 x SE → sq root of (p(1-p))/n → (0.0499(1-0.0499))/1002 → 1.96 x 0.000047 
ME = 0.000093

```{r}
inference(y = response, data = us12, null = 0, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided")
```
Results:
Single categorical variable, success: atheist
n = 1002,  p-hat = 0.0499
H0: p = 0
HA: p != 0
z = 7.2544
p_value = > 0.0001

### Exercise 7:
The conditions for inference are met. The data comes from a random sample as it is part of the data from the Gallup poll, the sampling distribution of p-hat is approximately normal since the sample size is large enough, and there are at least 10 expected successes and 10 expected failures. Finally, the observations appear to be independent and the sample size is less than 10% of the population. 

Confidence interval China: 42.63%, 51.37%
ME: Z*SE = SE → sq root of (p(1-p))/n → (0.47(1-0.47))/500 = .0004982 → 1.96 x 0.00004982 = .000976
ME = 0.000976
We are 42.63-51.37% confident that the proporiton of atheists in China in 2012 is .47.

Confidence interval Argentina: 5.47-8.66%
ME: Z*SE  = SE → sq root of (p(1-p))/n → (.0706(1-.0706))/991 = .000066 → 1.96 x .000066 = .00013
ME = 0.00013
We are 5.47-8.66% confident that the proportion of atheists in Argentina in 2012 is .0706% 

```{r}
ch12 <- atheism %>%
  filter(nationality == "China", year == "2012")
inference(y = response, data = ch12, null = 0, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist", alternative = "twosided")

ar12 <- atheism %>%
 filter(nationality == "Argentina", year == "2012")
inference(y = response, data = ar12, null = 0, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist", alternative = "twosided")
```
China results:

Single categorical variable, success: atheist
n = 500, p-hat = 0.47
95% CI: (0.4263 , 0.5137)

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=299&randomizer=-1709530061 

Argentina results:

Single categorical variable, success: atheist
n = 991, p-hat = 0.0706
95% CI: (0.0547 , 0.0866)

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=299&randomizer=-27408275 

### Exercise 8: 
The relationship between “p” and “me” is an inverse u shaped relationship, or a unimodal graph with a margin of error of ** against the population proportion plot we constructed. At a value of p = 0.50, margin of error me is maximized for a given sample size. 

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=299&randomizer=-953100298 

### Exercise 9:
The sampling distribution shows that the mean of the data is approximately 0.11, the graph is unimodal and slightly right skewed.

### Exercise 10: 
As p changes and n remains constant, the sampling distribution becomes more skewed to either side (it becomes more left skewed as p decreases and more right skewed as p increases). Additionally, the mean of the data decreases as p decreases and increases as p increases. The graph remains unimodal, but becomes less normal. 

### Exercise 11:
If n is altered along with p, the sampling distribution approaches a nearly normal distribution as n increases. The larger the population size, the more normal the distribution becomes.

### Exercise 12:
For Australia, we can proceed with inference and report margin of error (me) as Australia's data satisfies the conditions for inference for sampling disribution (p). However, Ecuador's data does not meet the success-failure condition as np is only 8, which is smaller than the 10 needed. 

### Exercise 13:
Ho = proporiton of atheists in Spain in 2005 = proportion of atheists in Spain in 2012
Ha = proporiton of atheists in Spain in 2005 does not equal proportion of atheists in Spain in 2012

The conditions for inference are met. The data comes from a random sample as it is part of the data from the Gallup poll, the sampling distribution of p-hat is approximately normal since the sample size is large enough, and there are at least 10 expected successes and 10 expected failures. Finally, the observations appear to be independent and the sample size is less than 10% of the population. 

There is convincing evidence that Spain has experienced a change in its atheist index between 2005 and 2012 because the p value is <0.0001, which is less than .05. 

The confience interval is (.0831, .1072)
```{r}
sp <- atheism%>%
 filter(nationality == "Spain", year == "2012" | year == "2005")
inference(y = response, data = sp, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided", null = 0)
inference(y = response, data = sp, statistic = "proportion", type = "ci", method = "theoretical", success = "atheist")           
```
Single categorical variable, success: atheist
n = 2291, p-hat = 0.0952
H0: p = 0
HA: p != 0
z = 15.5218
p_value = < 0.0001

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=298&randomizer=1162104824 

Confidence interval:

Single categorical variable, success: atheist
n = 2291, p-hat = 0.0952
95% CI: (0.0831 , 0.1072)

### Exercise 14:
Ho = proporiton of atheists in the US in 2005 = proportion of atheists in the US in 2012
Ha = proporiton of atheists in the US in 2005 does not equal proportion of atheists in the US in 2012

The conditions for inference are met. The data comes from a random sample as it is part of the data from the Gallup poll, the sampling distribution of p-hat is approximately normal since the sample size is large enough, and there are at least 10 expected successes and 10 expected failures. Finally, the observations appear to be independent and the sample size is less than 10% of the population. 

There is convincing evidence that the US has seen a change in its atheist index between 2005 and 2012. The p value of is < 0.0001, which is less than .05. 

The confidence interval is (0.0225 , 0.0374)

```{r}
us0512 <- atheism%>%
 filter(nationality == "United States", year == "2012" | year == "2005")
 inference(y = response, data = us0512, statistic = "proportion", type = "ht", method = "theoretical", success = "atheist", alternative = "twosided", null = 0)
```
Single categorical variable, success: atheist
n = 2004, p-hat = 0.0299
H0: p = 0
HA: p != 0
z = 7.8646
p_value = < 0.0001

https://labs-az-02.oit.duke.edu:30623/graphics/plot.png?width=578&height=298&randomizer=-2950631

Single categorical variable, success: atheist
n = 2004, p-hat = 0.0299
95% CI: (0.0225 , 0.0374)

### Exercise 15: 
A type 1 error is the false rejection of the null hypothesis; ie a "false positive". There is a 5% chance because the probability of making a type 1 error is equal to alpha, because of this there is a 5% chance there will be a change in the proportion of atheists due to random chance

### Exercise 16: use formula for margin of error + plug in values to calc sample size
Based on the plot of p and margin of error (me) you would need to sample 16 people 
