Why Fisher Exact Testing Matters
Fisher exact testing is used with a 2x2 contingency table. It is helpful when sample sizes are small. It is also useful when expected counts are low. The method does not depend on a large sample approximation. Instead, it uses the hypergeometric distribution and fixed margins.
When To Prefer It
Use this test when two categorical variables are compared. Each variable should have two levels. Common examples include exposed versus unexposed groups and event versus no event outcomes. The test checks whether the observed table is unusual under the null hypothesis of no association.
Interpreting Results
The p-value shows how surprising the table is, assuming no association. A small p-value suggests the row and column variables may be related. The odds ratio gives the estimated strength of association. A value above one suggests higher odds in the first row. A value below one suggests lower odds.
Tail Choices
A two-sided test looks for association in either direction. A left-tailed test checks whether the first row has lower odds. A right-tailed test checks whether the first row has higher odds. Choose the tail before reading results. Changing the tail after seeing data can bias the decision.
Effect Measures
The calculator also reports risk in each row. Risk difference compares the two proportions directly. Risk ratio compares them by division. Odds ratio compares the odds of the outcome across rows. These estimates help explain practical size, while the p-value addresses statistical evidence.
Good Practice
Report the table, chosen alternative, p-value, and odds ratio together. Mention whether any correction was used for interval estimates. For zero cells, the Haldane-Anscombe correction can stabilize estimated odds ratios and confidence intervals. It should not change the exact Fisher probability calculation.
Limits
Fisher exact testing is exact for fixed margins. In some studies, margins may not be fixed by design. The test is still widely used, but context matters. For larger studies, chi-square methods may also be considered. Use judgment, study design, and subject knowledge together.
Practical Notes
Keep raw counts nonnegative and whole. Do not enter percentages. Check that rows and columns match the research question. Save reports with inputs, because small table conclusions can change when one count changes slightly.