Chi-Square Test in SPSS: Independence Test and Goodness of Fit

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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 Academy → Crosstabs.

1. Place one variable in Row(s) and the other in Column(s).
2. Click Academy: check Chi-square and Phi and Cramer's V.
3. Click Cells: check Observed, Expected, and Row/Column percentages.
4. 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 Academy provides full support for chi-square analysis, crosstab interpretation, and APA-formatted results write-up.

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