Is a major portion of US citizens religious?
Aryes Lahiry
October 19, 2014
Part 1: Introduction:
Though the religion is highly a personal issue, yet it has social aspects and roles to play. In sociological point of view, it explains individual sufferings, enhances self-importance, comes as a social cohesion, encourages social welfare and controls economic life on the regions of the world [1]. Realising these issues, we are interested to get the answer of our research question - is a major portion of US citizens religious? Two variables that play a key role here are a person’s citizenship status and his or her religious preference [2]. We aim to analyse data on contemporary American society in order to monitor and explain trends in religion beliefs in general so that we can further compare the United States to other societies - which we consider an important issue for others like scholars, students and policy makers.
Part 2: Data:
Data Collection
A sociological survey was performed to collect data on demographic characteristics and attitudes of residents of the United States. For our analysis we used the extract of the General Social Survey (GSS) Cumulative File 1972-2012 that provides a sample of selected indicators in the GSS. This survey data was collected by a number of modes - computer-assisted personal interview (CAPI), face-to-face interview, telephone interview [2]. And the GSS dataset for our analysis was downloaded from http://bit.ly/dasi_gss_data on October 19, 2014 using the R programming language [3].
Cases
load(url("http://bit.ly/dasi_gss_data"))
dim(gss)## [1] 57061 114Our cases are the units of observation that is individual US citizens. Total 57,061 cases are recorded.
Variables
Our two variables of interest are USCITZN (Is respondent US citizen) and RELIG (Respondent’s religious preference). And both the two are ordinal categorical variables as both have ordered levels.
summary(gss$uscitzn)## A U.S. Citizen
## 375
## Not A U.S. Citizen
## 378
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands
## 6
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered)
## 11
## NA's
## 56291summary(gss$relig)## Protestant Catholic Jewish
## 33472 13926 1155
## None Other Buddhism
## 6113 998 130
## Hinduism Other Eastern Moslem/Islam
## 63 31 108
## Orthodox-Christian Christian Native American
## 96 588 24
## Inter-Nondenominational NA's
## 124 233Study
We used the data that were collected from past (1972 - 2012). So the performed study here is of retrospective observational type that do not directly interfere with how the data arise.
Scope of inference - generalizability
In this study, our population of interest for USCITZN variable is those people who are US citizens without any doubt. So considering the whole USCITZN is not correct decision, we only are interested in a true US citizen (value 1), A U.S. CITIZEN BORN IN PUERTO RICO, THE U.S. VIRGIN ISLANDS, OR THE NORTHERN MARIANAS ISLANDS (value 3), BORN OUTSIDE OF THE UNITED STATES TO PARENTS WHO WERE U.S CITIZENS AT THAT TIME (IF VOLUNTEERED) (value 4) - these three levels of USCITZN. And we exclude NOT A U.S. CITIZEN (value 2) and DON’T KNOW (value 8) from our analysis. Considering these factors in our USCITZN dataset we generated a new variable - true US citizen (TRUSCITZN)
On the contrary, we are interested here all the people who are either affiliated with any religious views or not. So we consider all levels of RELIG variable.
NOT A U.S. CITIZEN (value 2) and DON’T KNOW (value 8) levels of USCITZN variable are the Non-response source of sampling bias. These are the potential sources of bias that might prevent generalizability.
Scope of inference - causality
As there is random sampling but no random assignment is accounted in dealing with these two variables of interest (USCITZN and RELIG), so these data may not be used to establish causal links between these variables of interest.
Part 3: Exploratory data analysis:
Exploratory analysis was performed by examining tables and plots of the observed data. Exploratory analysis was used to identify missing values, verify the quality of the data relating US citizens to their religious beliefs.
We identified 56291 missing values, 378 “Not A U.S. Citizen” and no “DON’T KNOW” values for USCITZN variable. So our new units of observation or cases are 392 (375 + 6 + 11) - too small to make a statistical analysis to determine religious preferences of US citizens.
barplot(table(gss$uscitzn))
For RELIG variable, we identified 233 missing values.
barplot(table(gss$relig))
We divided RELIG variable in two subsets. First one is true US citizens (true citizens are already defined) who have religious attachments and the later one is also true US citizens but who have no religious attachments.
summary((gss$uscitzn == "A U.S. Citizen" | gss$uscitzn == "A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands" | gss$uscitzn == "Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered)") & gss$relig == "None") ## Mode FALSE TRUE NA's
## logical 50771 69 6221So, the number of true US citizens who are not attached with any religion is 69.
summary((gss$uscitzn == "A U.S. Citizen" | gss$uscitzn == "A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands" | gss$uscitzn == "Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered)") & gss$relig != "None")## Mode FALSE TRUE NA's
## logical 6436 322 50303So, the number of true US citizens who are attached with any religion is 322.
We now named true citizens with religious attachment as TRUSCITZN_RELIG and true citizens without religious attachment as TRUSCITZN_NONE.
truscitzn_relig <- table((gss$uscitzn == "A U.S. Citizen" | gss$uscitzn == "A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands" | gss$uscitzn == "Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered)") & gss$relig != "None")
truscitzn_none <- table((gss$uscitzn == "A U.S. Citizen" | gss$uscitzn == "A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands" | gss$uscitzn == "Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered)") & gss$relig == "None")
table(truscitzn_relig, truscitzn_none)## truscitzn_none
## truscitzn_relig 69 50771
## 322 1 0
## 6436 0 1mosaicplot(table(truscitzn_relig, truscitzn_none))
table(truscitzn_relig / 392)##
## 0.821428571428571 16.4183673469388
## 1 1table(truscitzn_none / 392)##
## 0.176020408163265 129.517857142857
## 1 1From the exploratory data analysis, we can conclude that 82.14285% of US citizens are attached with any religions whereas 17.60204% of US citizens are not attached with any religions.
Part 4: Inference:
Now, we would like to test the results obtained from exploratory analysis by Statistical Inference methods, namely proportion estimation and hypothesis testing.
Condition Checking
p = 0.8214285
n = 392
Random sample & <17.85715% of all true US citizens -> independent observation.
392 × 0.8214285 = 322 (> 10) and 392 × 0.1785715 = 70.00003 (> 10), Success - Failure condition is met.
Conclusion: As both the conditions are met, so theoretical method is enough for this statistical inference.
Estimating a proportion
p’ = 0.8214285
n = 392
point estimate ± margin of error = p’ ± Z* × SEp’
Standard error for a proportion, for calculating a confidence interval = SEp = sqrt(p’ × (1 - p’) / n) = 0.01934407.
qnorm((1 - 0.95) / 2)## [1] -1.96Therefore, Z* = 1.96
Therefore, p’ ± Z* × SEp = 0.8214285 ± 1.96 × 0.01934407 = (0.7835141, 0.8593429)
Conclusion: We are 95% confident that 78.35% to 85.93% of all true US citizens are religious.
p’ = 0.1760204
n = 392
point estimate ± margin of error = p’ ± Z* × SEp’
Standard error for a proportion, for calculating a confidence interval = SEp = sqrt(p’ × (1 - p’) / n) = 0.0192352.
Therefore, p’ ± Z* × SE = 0.1760204 ± 1.96 × 0.0192352 = (0.1383194, 0.2137214)
Conclusion: We are 95% confident that 13.83% to 21.37% of all true US citizens are not religious.
Hypothesis testing
We found that 82.14285% of 392 randomly sampled true US citizens are attached with any religious views. Now, we would like to test this hypothesis to get convincing evidence that majority of true US citizens are religious.
- Hypotheses setting:-
H0: p = 0.5
HA: p > 0.5
p’ = 0.8214285
n = 392
- Condition checking:-
Independence: 392 < 10% of true US citizens & random sample (Whether one true religious US citizen is independent of another).
Sample size/skew: 392 × 0.5 = 196 > 10 (Therefore, np >= 10 and n(1 - p) >= 10, i.e., Success - Failure condition is met. So sampling distribution is nearly normal).
Therefore, p’ ~ N(mean = 0.5, SE = sqrt((0.5 × 0.5) / 392) = 0.02525381)
Z = (0.8214285 - 0.5) / 0.02525381 = 12.73
p - value = P(Z > 12.73) = 0
As p - value is less than 0.05, so we can reject the null hypothesis (H0: p = 0.5) and get convincing evidence to accept the alternative hypothesis (HA: p > 0.5) as true, i.e., major portion or more than 50% of true US citizens is religious.
Similarly, we found that 17.60204% of 392 randomly sampled true US citizens are not attached with any religious views. Now, we would like to test this hypothesis to get convincing evidence that the minor portion of true US citizens is not-religious.
- Hypotheses setting:-
H0: p = 0.1760204
HA: p < 0.1760204
p’ = 0.5
n = 392
- Condition checking:-
Independence: 392 < 10% of true US citizens & random sample (Whether one true religious US citizen is independent of another).
Sample size/skew: 392 × 0.1760204 = 69 > 10 and 392 × (1 - 0.1760204) = 323 > 10 (Therefore, np >= 10 and n(1 - p) >= 10, i.e., Success - Failure condition is met. So sampling distribution is nearly normal).
Therefore, p’ ~ N(mean = 0.1760204, SE = sqrt((0.1760204 × (1 - 0.1760204)) / 392) = 0.0192352)
Z = (0.5 - 0.1760204) / 0.0192352 = 16.84
p - value = P(Z < 16.84) = 0
As p - value is less than 0.05, so we can reject the null hypothesis (H0: p = 0.1760204) and get convincing evidence to accept the alternative hypothesis (HA: p < 0.1760204) as true, i.e., minor portion or less than 17.60204% of true US citizens is not-religious.
Conclusion: We found that results from proportion estimation (confidence interval) and hypothesis testing agree.
Part 5: Conclusion:
Our analysis suggests that major portion of US citizens is religious. Though the United States of America is one of the most advanced countries in scientific and technological development in this planet, yet there is a significant association between its citizens and religious views. We found many missing values in this General Social Survey dataset; otherwise our result would be more accurate, having a larger sample size. With the larger sample size, we could perform zone wise study that may provide a thorough analysis.
References:
“What is the importance of religion?” page by Ajay Bhatt. URL: http://www.preservearticles.com/201101183516/importance-of-religion.html. Accessed on October 20, 2014.
Smith, Tom W., Michael Hout, and Peter V. Marsden. General Social Survey, 1972-2012 [Cumulative File]. ICPSR34802-v1. Storrs, CT: Roper Center for Public Opinion Research, University of Connecticut /Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributors], 2013-09-11. doi:10.3886/ICPSR34802.v1. Persistent URL: http://doi.org/10.3886/ICPSR34802.v1
R Core Team (2012). “R: A language and environment for statistical computing” URL: http://www.R-project.org
Appendix:
table(gss$uscitzn, gss$relig)##
## Protestant
## A U.S. Citizen 110
## Not A U.S. Citizen 81
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 1
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 5
##
## Catholic
## A U.S. Citizen 134
## Not A U.S. Citizen 193
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 4
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 2
##
## Jewish
## A U.S. Citizen 13
## Not A U.S. Citizen 3
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## None
## A U.S. Citizen 64
## Not A U.S. Citizen 55
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 1
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 4
##
## Other
## A U.S. Citizen 3
## Not A U.S. Citizen 3
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Buddhism
## A U.S. Citizen 6
## Not A U.S. Citizen 2
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Hinduism
## A U.S. Citizen 5
## Not A U.S. Citizen 13
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Other Eastern
## A U.S. Citizen 4
## Not A U.S. Citizen 1
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Moslem/Islam
## A U.S. Citizen 7
## Not A U.S. Citizen 14
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Orthodox-Christian
## A U.S. Citizen 10
## Not A U.S. Citizen 4
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Christian
## A U.S. Citizen 18
## Not A U.S. Citizen 8
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Native American
## A U.S. Citizen 0
## Not A U.S. Citizen 0
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0
##
## Inter-Nondenominational
## A U.S. Citizen 0
## Not A U.S. Citizen 0
## A U.S. Citizen Born In Puerto Rico, The U.S. Virgin Islands, Or The Northern Marianas Islands 0
## Born Outside Of The United States To Parents Who Were U.S Citizens At That Time (If Volunteered) 0