Fisher's Exact Test calculates the exact probability of observing a 2x2 contingency table, rather than relying on the approximations used by the Chi-Square test. It is particularly mandatory when sample sizes are small (typically if any cell has less than 5 observations).
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Pro Tips
Mandatory for datasets where Total N < 20 or any cell count is < 5.
The Two-Tailed p-value is generally the most robust measure of significance.
An Odds Ratio greater than 1 suggests a positive association between the groupings.
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Fun Facts
"Ronald Fisher invented this test to prove a colleague's claim that she could tell if milk or tea was poured into the cup first (The Lady Tasting Tea)."
"This test is uniquely stable because it evaluates every possible table permutation that could exist with your given marginal totals."
"While computationally expensive for massive datasets, modern computers handle it instantly for typical research sizes."