When to use a chi-square test:
A chi square analysis is used when we have a categorical dependent and independent variable. Basically, we’re going to compute a cross-tabulation to ask if there’s a greater frequency of some kind of outcome event in group A compared to group B.
Assumptions of the chi-square test:
1. The data are obtained from a random sample.
2. The expected frequency of each category must be 5 or more. Generally, it’s not a big deal if this assumption is violated, because we are given other statistical tests in the output that correct for this possibility.
Performing a chi-square test in SPSS:
To demonstrate the analysis, we’ll be using the HSB data file, which is free to download. Suppose we were interested in investigating whether there was a significant difference in the number of male or female minority students in the data set; maybe we have reason to think that there are more female minority students in the data file than male minority students. Because each of these groups have data recorded as a binary (0/1 for male/female and 0/1 for minority/non-minority), we would want to use a chi-square to analyze these categories.
On the main toolbar click Analyze –> Descriptive Statistics –> Cross-tabs
The following window is produced:
Move the two variables you wish to test for a relationship between into the boxes labeled rows and columns. It does not matter whether the IV or the DV go into a particular box. The result will be the same.
Click Statistics
Select Chi-Square
Click Continue
Click Okay
The output for the Chi-square test should be given below:
Interpreting the chi square output:
In the above output, we get a table that tells us the frequency for each category and a table with testing information. The test here indicates that there is no significant effect, p = .236. While this does not tell us the direction, from the table above we could readily infer which direction the frequencies (might be) skewed. We do so simply by looking at the relative counts for each category.
Generally, when looking at these chi-square tests, we’re interested in Pearson’s Chi-Square value. We would be more inclined to use Fisher’s Exact Test, if instead we could not meet the assumption of 5 observations per cell. Notice that many of the statistics are 2-tailed tests.