Test independence between two categorical variables with contingency tables, effect sizes, and cell contribution analysis.
Full contingency table with observed vs expected frequencies and chi-square statistic.
Standardized effect size measure with interpretation (negligible, small, medium, large).
Standardized residuals and percentage contribution of each cell to chi-square statistic.
Provide a dataset with two categorical columns. We'll create the contingency table and test for independence between the variables.
We calculate expected frequencies, validate cell counts (warning if any < 5), compute standardized residuals, identify cells with maximum contribution to the chi-square statistic, and provide Cramér's V for effect size interpretation.
From inputs to interpretable results
Cross‑tabulate variables using table() function and calculate expected frequencies.
Chi‑square test, standardized residuals, Cramér's V effect size, and cell contributions.
Find cells with maximum contribution to chi‑square and provide visualization datasets.
Test associations between categorical variables with comprehensive diagnostics—identify which specific combinations drive the relationship.
Beyond just significance testing, we provide standardized residuals showing which cells contribute most to the chi‑square statistic, Cramér's V for effect size interpretation, and multiple visualization datasets including heatmaps, mosaic plots, and stacked bar charts.
Note: Tool validates expected frequencies and warns if any cells have expected count < 5 (affects test validity).