Research Question
Does there appear to be a relationship between gun possession and political ideology?
This question aims to explore whether there is any relation between having a gun in home (gun here refers to any guns or revolvers) and the respondent’s political ideology (i.e. Liberal, Moderate, or conservative with various levels). We find interest in this question because gun ownership laws and regulation has always been a political debate. With this study we can confirm if the act of owning a firearm is associated with the political ideology.
About The Data
Data Collection Method :
The General Social Survey has been monitoring societal change and studying the growing complexity of American society since 1972. Block quota sampling was used in 1972, 1973, and 1974 surveys and for half of the 1975 and 1976 surveys.Full probability sampling was employed in half of the 1975 and 1976 surveys.The same sampling method was also employed from 1977 to 2018.
Targeted Population:
Surveys from 1972 to 2004 targeted English-speaking adult population, aged 18 years or older, living in non-institutional arrangements within the United States. Starting in 2006 Spanish-speakers were added to the target population.
Sample Used:
The used Sample was collected in the year 2012, and consist of 1216 observations.
Load packages
## Warning: package 'dplyr' was built under R version 4.0.3## Warning: package 'statsr' was built under R version 4.0.3Exploratory data analysis
#select and filter the data with null values
data <- gss %>%
select(polviews, year, owngun) %>%
filter(!is.na(polviews),
!is.na(owngun),
owngun != "Refused",
year == 2012)
data$owngun <- factor(data$owngun)
#print the number of observations
nrow(data)## [1] 1216#print the total proportions for gun owners
data %>%
group_by(owngun) %>%
summarize(total = n()) %>%
mutate(proportion = total/sum(total))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 2 x 3
## owngun total proportion
## <fct> <int> <dbl>
## 1 Yes 420 0.345
## 2 No 796 0.655##
## Yes No
## Extremely Liberal 13 41
## Liberal 33 127
## Slightly Liberal 46 97
## Moderate 156 302
## Slightly Conservative 70 97
## Conservative 89 105
## Extrmly Conservative 13 27#visualize the contingency table with mosaic plot
ggplot(data) +
geom_mosaic(aes(x= product(polviews, owngun), fill = polviews)) +
labs(title = "Gun Ownership And Political Ideology",
x = "Owns Gun?",
y = "Political Ideology") +
theme(plot.title = element_text(hjust = 0.5))
The above mosaic plot visualizes all the summary statistics calculated above, it shows the proportions for political ideology and gun ownership. It appear that generally Moderate respondents comprises the highest count in the sample, and extremely conservative respondents have the highest count.
#show the proportion of gun owners for each political ideology
ggplot(data, aes(x = polviews, fill = owngun)) +
geom_bar(position = "fill") +
labs(title = "Political Ideology by Gun Ownership in Household",
x = "Political Ideology",
y = "Proportion",
fill = "Owns Gun?") +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5),
plot.title = element_text(hjust = 0.5))
The Above bar plot shows the proportion of gun owners for the different political ideologies. It appears that conservatives and slightly conservative have the highest proportions of gun possession, while liberals have the lowest rate of gun possession in household.
Inference
Hypotheses:
H0: Gun possession and political ideology are independent. Gun position rates do not vary by political ideology
HA: Gun possession and political ideology are dependent. Gun possession rates do vary by political ideology
Significance Level:
Significance level of α = 0.05 is used.
- Independence:
- Observations are independent of each other. (this is mentioned data collection section)
- Random sampling was used (this is mentioned data collection section)
- Sample size, n = 1216, n < 10% of the population
- Each case only contributes to one cell
- Sample size:
- Each cell has at least 5 expected cases
Method used:
Since, the variables used are of multiple levels the Chi-square test of independence is used to conduct the inference. Chi-square test of independence find the p-value by using the Chi-square statistic, and degree of freedom. The expected values and degree of freedom are obtained using following formula:
Expected count = (row total) * (column total)/ table total
Degree of freedom = (number of rows – 1) * (number of columns – 1)
Using the expected counts, the chi-square value is calculated which is then used along with the degree of freedom to find the p-value.
chisq.test() function which is part of the stats package is used to carry out the calculation by passing the contingency table as argument.
Inference:
# To make the contingency table a bit readable we change labels of plviews
levels(data$polviews) <- c("Extremely Lib",
"Liberal",
"Slightly Lib",
"Moderate",
"Slightly Con",
"Conservative",
"Extremely Con")
#create a contingency table for the variables
count_tbl <- table(data$owngun, data$polviews)
#perform the test
chi_test <- chisq.test(count_tbl)
chi_test##
## Pearson's Chi-squared test
##
## data: count_tbl
## X-squared = 31.84, df = 6, p-value = 1.751e-05##
## Extremely Lib Liberal Slightly Lib Moderate Slightly Con Conservative
## Yes 13 33 46 156 70 89
## No 41 127 97 302 97 105
##
## Extremely Con
## Yes 13
## No 27##
## Extremely Lib Liberal Slightly Lib Moderate Slightly Con Conservative
## Yes 19 55 49 158 58 67
## No 35 105 94 300 109 127
##
## Extremely Con
## Yes 14
## No 26## [1] 1.751318e-05Interpretation:
At X-squared of 31.84 and 6 degrees of freedom, the chi-square test of independence yields a p-value that is almost zero.
Inference:
At 0.05 significance level and with a p-value ≈ 0, we reject the null hypothesis in favor of the alternative.
The data provide convincing evidence that political ideology and gun possession are associated in the targeted population.
Since this is an observational study, no causality can be concluded.
Remarks on Confidence Interval:
Chi-square test of independence is used to conduct the inference, for which there is no associated confidence interval. No confidence interval has been calculated for the parameter of interest.