Chi-Square Independence Calculator

Pearson chi-square independence test from observed counts. No continuity correction or exact test is applied.

Load worked example

Observed counts (one table row per line)

Separate values with commas or spaces. Each row must have the same number of cells. Use whole counts, with at least two rows and two columns.

Significance level (α)0.100.050.01

Run chi-square testClear

Start with independent counts

Enter a rectangular contingency table, one row per line, with commas or spaces separating columns. Each unit should contribute to one cell. Use nonnegative whole-number counts, not percentages or repeated observations treated as independent. Empty row or column totals and structural-zero designs require attention outside this ordinary model.

The calculator runs the uncorrected Pearson independence test, with expected cells Eᵢⱼ = row total × column total / overall total. It calculates χ² = Σ(O−E)²/E, df=(r−1)(c−1), the approximate chi-square upper-tail p-value, and Cramér’s V. It does not run goodness-of-fit, Fisher’s exact test, continuity correction or survey-weighted analysis.

Reproduce the worked example

Load the example, then run the test. Its two rows are 30,20 and 20,30, with 100 observations overall. Every expected cell is 25. Contributions are 25/25=1 per cell, giving χ²=4.0000, df=1, p≈0.0455, and V=0.2000.

At α=0.05, this is evidence against independence under the approximation and design assumptions. The row proportions of the first category are 60% and 40%; the analysis does not show why they differ or that row membership causes the outcome. Report the actual category labels and proportions alongside the test.

Check expected counts and the design

The tool flags any expected cell below 5 as a conservative screening warning. It still shows the approximation so you can inspect it, but sparse tables may need an appropriate exact or simulation method. A large grand total does not guarantee adequate expected counts in every cell.

The p-value concerns the null model, not the probability of that null being true. Cramér’s V is descriptive and its practical meaning depends on the categories and context; avoid universal strength labels.

Continue

Read the chi-square lesson, compare the statistic with the chi-square reference, or practice an entire analysis. NIST explains contingency-table independence testing.