Fisher's Exact Test (2×2)
Computes Fisher's exact test for a 2×2 contingency table, the right choice when the counts are small and the chi-square approximation no longer holds. Instead of approximating, it computes the exact probability of observing the current table — and tables even more extreme — holding the margin totals fixed, via the hypergeometric distribution. The tool returns the one-sided and two-sided p-values (the latter by summing the probabilities of tables as likely or less likely than the observed one). Enter the four cells a, b, c and d.
Resultado
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Fisher's Exact Test (2×2)
Computes Fisher's exact test for a 2×2 contingency table, the right choice when the counts are small and the chi-square approximation no longer holds. Instead of approximating, it computes the exact probability of observing the current table — and tables even more extreme — holding the margin totals fixed, via the hypergeometric distribution. The tool returns the one-sided and two-sided p-values (the latter by summing the probabilities of tables as likely or less likely than the observed one). Enter the four cells a, b, c and d.
The exact probability, no approximation, for small tables
The chi-square test of independence is the standard tool for contingency tables, but it relies on an approximation that only works well with reasonably large counts. When some cell has few cases, the approximation misleads. Fisher's exact test solves this by computing the real probability, with no shortcuts, which is why it's reliable even with tiny samples.
The reasoning fixes the row and column totals and asks: given those margins, what is the probability of landing on exactly the observed table? The answer comes from the hypergeometric distribution. Summing the probability of the observed table with that of the more extreme tables in the same direction gives the one-sided p-value; summing all tables as likely or less likely than the observed one gives the two-sided p-value.
Enter the four cells of the 2×2 table: a and b in the first row, c and d in the second. The tool returns the one-sided and two-sided p-values. The latter follows the sum-of-probabilities convention, the same one adopted by R, which is the most accepted definition of two-sidedness in an exact test without an obvious symmetric tail.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.