When to Use a Chi-Square Test: Explained for Beginners

May 2026·6 min read

When to use a chi-square test depends on one thing: whether both your variables are categorical. It is the go-to test when your hypothesis involves proportions, frequencies, or the relationship between two grouping variables — not means. This guide explains the ≥5 expected frequency rule, when to switch to Fisher’s exact test, and how to report Cramér’s V as your effect size.

What Is a Chi-Square Test? Categorical Data Explained

The chi-square (χ²) test of independence checks whether two categorical variables are related or independent. It compares the frequencies you actually observed in each cell of a cross-table against the frequencies you would expect if there were no relationship at all.

Typical thesis example: Is there a relationship between degree programme (Psychology, Sociology, Biology) and preferred learning format (in-person, online, hybrid)? Both variables are categorical — chi-square is the correct test.

Chi-square does not work with means or metric data. If one of your variables is metric (e.g. a score, a time, or a computed scale), use a different test.

When to Use Chi-Square vs. Fisher’s Exact Test

Chi-square assumes that each cell in your cross-table has an expected frequency of at least 5. This condition is automatically checked by SPSS, which prints a warning below the output table.

• If the assumption is met → chi-square test.
• If the assumption is violated → Fisher’s exact test (for 2×2 tables only).

Fisher’s exact test is more conservative and reliable with small samples or rare categories, but it only works for 2×2 cross-tables. If you have a larger table with small expected frequencies, consult your supervisor — collapsing categories may be an option.

[WARNING] If SPSS shows more than 20% of cells with expected count < 5, chi-square results are unreliable. Switch to Fisher’s exact test or combine categories.

Real Example: Gender × Learning Format in a Student Survey

Research question: Is there a relationship between gender (male/female) and preferred learning format (in-person/online)?

SPSS path: Analyze → Descriptive Statistics → Crosstabs → move gender to Rows, learning format to Columns → Statistics → tick Chi-square and Phi and Cramér’s V → Cells → tick Expected → OK.

• Output interpretation:
• Pearson χ²(1) = 6.84, p = .009 → significant association.
• Cramér’s V = .24 → small to medium effect.

Conclusion: There was a significant association between gender and preferred learning format, χ²(1) = 6.84, p = .009, V = .24.

How to Read the Chi-Square Output in SPSS

The SPSS chi-square output has three key sections:

1. Cross-tabulation table: shows observed counts and (if requested) expected counts per cell. Scan for any expected count below 5.

2. Chi-square tests table: read the Pearson Chi-Square row. Note: χ² value, df (degrees of freedom = (rows−1)×(cols−1)), and Asymptotic Significance (your p-value).

3. Symmetric Measures table: find Cramér’s V. This is your effect size. Report it alongside χ² and p.

Reporting Cramér’s V as Effect Size in APA Format

APA requires an effect size alongside every inferential test result. For chi-square, report Cramér’s V:

• Significant:
• "A chi-square test revealed a significant association between gender and learning format preference, χ²(1, N = 121) = 6.84, p = .009, V = .24."
• Non-significant:
• "No significant association was found between degree programme and learning format, χ²(2, N = 121) = 2.14, p = .343, V = .13."

[INFO] Cramér’s V benchmarks depend on the degrees of freedom. For a 2×2 table (df=1): small = .10, medium = .30, large = .50. For larger tables, benchmarks are lower.

When Chi-Square Is NOT Appropriate

Do not use chi-square when:

• One or both variables are metric (use correlation or t-test instead).
• Expected cell frequencies are below 5 in more than 20% of cells (use Fisher’s exact test).
• You want to examine more than two categorical variables simultaneously (logistic regression required).
• You have matched pairs or repeated-measures categorical data (McNemar’s test applies instead).