What Is the Chi-Square Test?
The chi-square (χ²) test is used to analyze categorical variables. The most common form is the test of independence, which examines whether two categorical variables are associated. Example: Is there a significant relationship between gender and smoking status?
Critical Assumption: Expected Cell Frequencies
The chi-square test requires that no expected cell frequency falls below 5. SPSS will warn you: "X cells have expected count less than 5." If this occurs, consider collapsing categories or using Fisher's Exact Test (available for 2×2 tables).
Running Chi-Square in SPSS
Go to Analyze → Descriptive Statistics → Crosstabs.
- Place one variable in Row(s) and the other in Column(s).
- Click Statistics: check Chi-square and Phi and Cramer's V.
- Click Cells: check Observed, Expected, and Row/Column percentages.
- Click OK.
Reading the Output
In the Chi-Square Tests table, find the Pearson Chi-Square row. The Value is your χ² statistic, df is degrees of freedom, and Asymptotic Significance is your p-value. p<0.05 → a statistically significant association exists between the two variables.
Effect Size: Cramer's V
Chi-square tells you about significance, not strength. Use Cramer's V to quantify the association: V=0.10 is weak, V=0.30 is moderate, V=0.50 is strong.
APA Reporting Example
A chi-square test of independence revealed a statistically significant association between gender and smoking status, χ²(1, N=200)=8.34, p=.004, Cramer's V=.20. Males (42%) were more likely to smoke than females (28%).
Expert Support
Boss Statistics provides full support for chi-square analysis, crosstab interpretation, and APA-formatted results write-up.