A Chi-Square Test of Independence is used to determine whether or not there is a significant association between two categorical variables.
This tutorial explains how to perform a Chi-Square Test of Independence in R.
Example: Chi-Square Test of Independence in R
Suppose we want to know whether or not gender is associated with political party preference. We take a simple random sample of 500 voters and survey them on their political party preference. The following table shows the results of the survey:
Republican | Democrat | Independent | Total | |
Male | 120 | 90 | 40 | 250 |
Female | 110 | 95 | 45 | 250 |
Total | 230 | 185 | 85 | 500 |
Use the following steps to perform a Chi-Square Test of Independence in R to determine if gender is associated with political party preference.
Step 1: Create the data.
First, we will create a table to hold our data:
#create table data <- matrix(c(120, 90, 40, 110, 95, 45), ncol=3, byrow=TRUE) colnames(data) <- c("Rep","Dem","Ind") rownames(data) <- c("Male","Female") data <- as.table(data) #view table data Rep Dem Ind Male 120 90 40 Female 110 95 45
Step 2: Perform the Chi-Square Test of Independence.
Next, we can perform the Chi-Square Test of Independence using the chisq.test() function:
#Perform Chi-Square Test of Independence
chisq.test(data)
Pearson's Chi-squared test
data: data
X-squared = 0.86404, df = 2, p-value = 0.6492
The way to interpret the output is as follows:
- Chi-Square Test Statistic: 0.86404
- Degrees of freedom: 2 (calculated as #rows-1 * #columns-1)
- p-value: 0.6492
Recall that the Chi-Square Test of Independence uses the following null and alternative hypotheses:
- H_{0}: (null hypothesis) The two variables are independent.
- H_{1}: (alternative hypothesis) The two variables are not independent.
Since the p-value (0.6492) of the test is not less than 0.05, we fail to reject the null hypothesis. This means we do not have sufficient evidence to say that there is an association between gender and political party preference.
In other words, gender and political party preference are independent.
Additional Resources
An Introduction to the Chi-Square Test of Independence
Chi-Square Test of Independence Calculator
How to Calculate the P-Value of a Chi-Square Statistic in R
How to Find the Chi-Square Critical Value in R