A Chi-Square Test of Independence is used to determine whether or not there is a significant association between two categorical variables.
The following example shows how to perform a Chi-Square Test of Independence in SAS.
Example: Chi-Square Test of Independence in SAS
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 SAS to determine if gender is associated with political party preference.
Step 1: Create the data.
First, we will create a dataset in SAS to hold the survey responses:
/*create dataset*/ data my_data; input Gender $ Party $ Count; datalines; Male Rep 120 Male Dem 90 Male Ind 40 Female Rep 110 Female Dem 95 Female Ind 45 ; run; /*print dataset*/ proc print data=my_data;
Step 2: Perform the Chi-Square Test of Independence.
Next, we can use the following code to perform the Chi-Square Test of Independence:
/*perform Chi-Square Test of Independence*/ proc freq data=my_data; tables Gender*Party / chisq; weight Count; run;
There are two values of interest in the output:
- Chi-Square Test Statistic: 0.8640
- Corresponding p-value: 0.6492
Recall that the Chi-Square Test of Independence uses the following null and alternative hypotheses:
- H_{0}: The two variables are independent.
- H_{A}: 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
The following tutorials provide additional information about the Chi-Square test of independence:
Introduction to the Chi-Square Test of Independence
Chi-Square Test of Independence Calculator
How to Perform a Chi-Square Test of Independence in Excel