🔀 Simpson’s Paradox Calculator
Enter success counts and totals for Group A and Group B across two subgroups to see whether the combined (overall) results reverse the trend seen within each subgroup.
What this calculator does
Simpson’s Paradox occurs when a trend that appears in each of several subgroups of data disappears or reverses when those subgroups are combined into one overall total. This calculator compares two groups (A and B) across two subgroups and checks for that reversal.
How it works
For each subgroup, the calculator finds the success rate (successes divided by total) for Group A and Group B, then compares which group has the higher rate. It then computes the combined, overall rate for each group across both subgroups and compares those. If Group A leads Group B in both subgroups individually, but Group B leads overall (or vice versa), that reversal is flagged as Simpson’s Paradox.
Why it happens
The paradox typically arises when the subgroups have very different sizes (sample sizes) for each group, so a group’s stronger subgroup gets weighted more heavily in one group’s overall total than in the other’s. It is a real statistical phenomenon, not an error in the data, and is a useful reminder to check subgroup patterns before drawing conclusions from combined totals.
Note: this tool is for general educational and planning purposes and does not replace formal statistical analysis.