When should I use Fisher's exact test instead of chi-square?

Use Fisher's exact test for a 2 × 2 table when any expected count is below 5. For larger tables with many small expected counts, merge categories or collect more data.

Can I enter percentages?

No. The chi-square test needs raw counts of people or cases. Convert percentages back to counts using the group sizes.

Is the Yates continuity correction applied?

No. Results match the uncorrected Pearson chi-square reported by most software. For small 2 × 2 tables, Fisher's exact test is shown instead.

CHI-SQUARE CALCULATOR

Chi-square test calculator with expected counts and effect size.

Test whether two categorical variables are related, or whether counts match expected proportions. You get χ², degrees of freedom, the p value, Cramér's V, an expected-count check, and Fisher's exact test for small 2 × 2 tables.

COUNTS

Test of independence

BROWSER-ONLY

One row per group, one column per category. A header row of column names is optional. Paste straight from Excel or SPSS crosstabs.

CONTINGENCY TABLE (COUNTS)

Chi-square test: formula, solved example, and reporting

Formula

χ² = Σ (O − E)² ÷ E, E = (row total × column total) ÷ N, df = (r − 1)(c − 1)

O is each observed count and E the count expected if the two variables were unrelated. A large χ² means the observed table is far from what independence predicts.

Solved example

100 students: 50 online and 50 in-person. 20 online and 30 in-person students passed. Every expected count is 25, so χ² = 4 × (5² ÷ 25) = 4.00 with df = 1, giving p = .046 and Cramér's V = .20: a small but significant association between study mode and passing.

What type of data is the chi-square test used for?

Two categorical variables (nominal or ordinal categories) counted per person
Each participant appears in exactly one cell
Counts, not percentages or means
Expected count of at least 5 in at least 80% of cells; otherwise use Fisher's exact test (2 × 2) or merge categories

Interpreting Cramér's V

≈ .10 small association
≈ .30 medium association
≈ .50 or more large association
For tables larger than 2 × 2, these thresholds shrink as the smaller dimension grows (Cohen, 1988).

How to report it (APA style)

“A chi-square test of independence showed a significant association between study mode and exam outcome, χ²(1, N = 100) = 4.00, p = .046, Cramér's V = .20.” Include N in the brackets and report the effect size. The APA chi-square guide has templates for every case.

References

Pearson, K. (1900). On the criterion that a given system of deviations from the probable… Philosophical Magazine, 50(302), 157–175.
Cochran, W. G. (1954). Some methods for strengthening the common χ² tests. Biometrics, 10(4), 417–451.
Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.

Chi-Square Test Calculator

Test whether two categorical variables are associated, or whether counts match expected proportions, with expected-count checks and a ready-to-use APA write-up.

Test association between two survey questions (crosstab)

Check whether observed category counts match expected proportions

Switch to Fisher's exact test when expected counts are small

KEY FUNCTIONS

Test of independence (any r × c table)Goodness of fit with custom proportionsExpected counts and the 5-count ruleCramér's V effect sizeFisher's exact p for 2 × 2 tables

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