2×2 Chi-Square Test Calculator
Enter observed counts for a 2×2 contingency table. This tool calculates Pearson's chi-square, Yates' correction, p-values, expected counts, and a quick interpretation.
| Outcome Yes | Outcome No | |
|---|---|---|
| Group 1 | ||
| Group 2 |
Tip: Values must be non-negative whole numbers (counts).
What this 2×2 chi-square calculator does
A 2×2 chi-square test checks whether two categorical variables are associated. In practical terms, you compare two groups (rows) against two outcomes (columns), and ask: are these differences likely due to chance, or is there evidence of a real relationship?
This calculator is designed for quick, transparent analysis of a 2×2 contingency table. It returns:
- Pearson's chi-square statistic (the classic test)
- Yates' continuity-corrected chi-square (often reported for small 2×2 tables)
- p-values for both methods with 1 degree of freedom
- Expected counts to help verify test assumptions
- A plain-language significance interpretation using your chosen alpha
How to use the calculator
Step 1: Enter observed counts
Put your real observed frequencies into the four cells:
- a = Group 1 and Outcome Yes
- b = Group 1 and Outcome No
- c = Group 2 and Outcome Yes
- d = Group 2 and Outcome No
Step 2: Choose alpha
Alpha is your significance threshold (commonly 0.05). If p < alpha, results are considered statistically significant.
Step 3: Click calculate
Review the chi-square statistics, p-values, and expected counts. If expected counts are very small, the chi-square approximation can be less reliable.
Formula used (2×2 Pearson chi-square)
For each cell, compute expected count:
Then compute the test statistic:
For a 2×2 table, degrees of freedom:
This page also reports Yates' continuity correction, which adjusts each absolute difference by 0.5 before squaring:
Interpreting the output correctly
- Large chi-square usually means stronger evidence of association.
- Small p-value (below alpha) suggests data are unlikely under the null hypothesis of independence.
- Expected counts help check if chi-square assumptions are reasonable.
Remember: statistical significance does not automatically mean practical importance. Always pair p-values with context, effect size, and study design quality.
Assumptions and when to use Fisher's exact test
The chi-square test is an approximation. In small samples, especially when expected counts are below 5, Fisher's exact test is often preferred because it does not rely on the same large-sample approximation.
- Use chi-square confidently when expected counts are adequately large.
- Consider Fisher's exact test for sparse tables or very small studies.
- Independence of observations is essential in either case.
Worked example
Suppose Group 1 has 20 "Yes" and 15 "No", while Group 2 has 10 "Yes" and 25 "No". Entering these values gives a significant result under Pearson's chi-square at alpha 0.05, suggesting outcome proportions differ between groups.
If Yates' correction is less significant (or non-significant), that's not unusual in modest sample sizes: it is intentionally conservative.
Quick FAQ
Can I enter percentages instead of counts?
No. This test requires observed frequencies (counts), not percentages.
Is this the same as a t-test?
No. A chi-square test analyzes categorical data; a t-test compares means of continuous data.
What if a cell is zero?
Zero cells can occur. The calculator handles them, but if expected counts become very small, interpretation should be cautious and Fisher's exact test may be better.