Step 1: Enter a 2×2 table

Instructions:

  • Think of a categorical comparison: exposure vs outcome, treatment vs response, etc.
  • Enter the observed counts in each cell (non-negative whole numbers).
  • Labels are optional — editing them changes the display but not the math.
Used only for the reject/fail-to-reject verdict.

Results

How to read this

When they agree: in tables with all expected counts ≥ 5 and moderate-to-large N, all three tests typically give very similar p-values. Any of them is fine to report.

When they diverge: for small or sparse tables, the χ2 approximation becomes unreliable (Cochran, 1954), and Fisher's exact test is preferred. The Z-test for proportions shares the χ2 large-sample framing and will also be off; in fact for a 2×2 table, Z2 equals χ2 exactly.

What to report: pick the test that matches your sample size and assumptions, report its p-value with the effect size (odds ratio or Cramer's V), and mention which you chose and why.