How chi-square power analysis works
This calculator uses Cohen's w as the effect size — a standardized measure of the discrepancy between observed and expected proportions, analogous to d for means and f for ANOVA. Power is computed from the exact noncentral chi-square distribution, with degrees of freedom set by the test type: k − 1 categories for a goodness-of-fit test, or (rows − 1) × (columns − 1) for a contingency table.
Cohen's (1988) benchmarks are w = .10 (small), .30 (medium), and .50 (large). For a 2×2 table, w is closely related to other familiar association measures — including the phi coefficient, which equals w exactly in that case. Larger tables need a bigger effect or larger sample to reach the same power as a 2×2 table, because the same w is spread across more degrees of freedom.
Worked example
Detecting a medium effect (w = .30) in a 2×2 table (df = 1) at α = .05 with target power of .80 calls for 88 total observations — matching Cohen's (1988) published tables.
Required N = 88, achieved power = 80.4%, χ² critical (df = 1) = 3.841.