GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 309 of 500
Test association in a 2 × 2 table exactly — the right test when counts are small and the chi-square approximation fails (Fisher, 1934).
Try sample values — fills the form with the worked example below.
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p-value (two-sided)
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Odds ratio
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Total (n)
Equation: Two-sided p = sum of the hypergeometric probabilities of all tables with the same margins whose probability is no larger than the observed table’s. Odds ratio = (a × d) ÷ (b × c).
Method: Fisher’s exact test (Fisher, 1934; two-sided by the Fisher–Irwin rule of summing probabilities no larger than the observed). Probabilities are computed from the hypergeometric distribution via the log-gamma function.
Assumptions: the margins are treated as fixed and the observations are independent; the table must be 2 × 2 with whole-number counts.
Limitations: the test is conservative (low power) with very small samples; the odds ratio is unstable when any cell is 0 — a zero in the denominator is reported as not available.
Rounding: p to 4 decimal places; odds ratio to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Fisher’s exact test (Fisher, 1934; two-sided by the Fisher–Irwin rule of summing probabilities no larger than the observed). Probabilities are computed from the hypergeometric distribution via the log-gamma function.
Assumptions: the margins are treated as fixed and the observations are independent; the table must be 2 × 2 with whole-number counts.
Limitations: the test is conservative (low power) with very small samples; the odds ratio is unstable when any cell is 0 — a zero in the denominator is reported as not available.
Rounding: p to 4 decimal places; odds ratio to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Table [[8, 2], [1, 5]]: p = 0.0350, odds ratio 20.00 — significant at α = 0.05.
Enter values above to see results.
Use this instead of chi-square whenever any expected count is below 5. Tool 309 of 500 — GIFSQ
