When to Use Fisher’s Exact Test Instead of Chi-Square

May 2026·5 min read

When to use Fisher’s exact test instead of chi-square comes down to one diagnostic: whether your cross-table has cells with expected frequencies below 5. Chi-square becomes unreliable with small expected counts — Fisher’s exact test solves this for 2×2 tables. This guide explains the rule, when it applies, how SPSS handles it automatically, and how to report the Odds Ratio as your effect size.

Why Chi-Square Fails With Small Samples

The chi-square test relies on an approximation that is only accurate when expected cell frequencies are large enough. The conventional threshold is that each cell must have an expected frequency of at least 5.

When this assumption is violated — for example, when a category is rare, the overall sample is small, or the table has many cells — the chi-square p-value is not reliable. It can produce false positives or false negatives.

This is especially common in student thesis research where subgroup sizes are unequal or where one response category is rarely chosen.

The ≥5 Expected Frequency Rule Explained

Expected frequency = (row total × column total) ÷ grand total. This is the count you would expect in each cell if there were no relationship between the variables.

SPSS checks this automatically. After running a chi-square test, look below the output table for the footnote: "X cells (X%) have expected count less than 5."

• Decision:
• All cells ≥ 5 → chi-square test (reliable).
• Any cells < 5 (up to 20% of cells) → chi-square is still acceptable for larger tables; inspect carefully.
• More than 20% of cells < 5 → switch to Fisher’s exact test (if 2×2) or collapse categories.

[WARNING] If more than 20% of cells have expected count < 5, SPSS will warn you. Do not ignore this warning — your chi-square result is unreliable.

When to Switch to Fisher’s Exact Test

Fisher’s exact test calculates the exact probability of your observed frequency distribution (or a more extreme one) given the marginal totals — no approximation needed.

• Use Fisher’s exact test when:
• Your table is 2×2 (two rows, two columns).
• One or more cells have an expected frequency below 5.
• The overall sample is small (N < 40 is a common threshold).

Do NOT use Fisher’s exact test for tables larger than 2×2. For a 3×2 or larger table with small expected frequencies, options include: collapsing categories to create a 2×2 table, using a mid-p correction, or consulting your supervisor.

How to Run Fisher’s Exact Test in SPSS (It’s Automatic)

SPSS outputs Fisher’s exact p-value automatically alongside chi-square. You do not need to do anything extra.

SPSS path: Analyze → Descriptive Statistics → Crosstabs → move variables to rows/columns → Statistics → tick Chi-square → Cells → tick Expected → OK.

• In the Chi-Square Tests output table, read:
• Pearson Chi-Square row (if assumptions are met).
• Fisher’s Exact Test row: Exact Sig. (2-sided) = your p-value when the assumption is violated.

If the expected frequency assumption is violated, simply report the Fisher’s exact p-value instead of chi-square.

Odds Ratio as Effect Size and APA Reporting

For Fisher’s exact test, the Odds Ratio (OR) is the appropriate effect size. It describes how much more likely one outcome is in one group compared to the other.

SPSS provides OR in the Risk Estimate table: Analyze → Descriptive Statistics → Crosstabs → Statistics → tick Risk → OK.

• OR = 1: no difference between groups.
• OR > 1: the outcome is more likely in the first group.
• OR < 1: the outcome is less likely in the first group.
• APA reporting:
• Significant: "Fisher’s exact test revealed a significant association between intervention group and recovery, p = .031, OR = 3.67, 95% CI [1.12, 12.04]."
• Non-significant: "No significant association was found between gender and dropout, p = .412, OR = 1.43, 95% CI [0.61, 3.35]."

[INFO] There is no chi-square statistic to report for Fisher’s exact test — report only the exact p-value, OR, and 95% CI.