About the 10x2 Fisher Exact Test
A 10x2 Fisher exact test studies ten categories and two outcomes. It is useful when counts are small, uneven, or sparse. It fits clinical, survey, quality, genetics, safety, education, and laboratory tables with many ordered categories. The method keeps row totals and column totals fixed. Then it compares the observed table with every possible table that shares those margins. This gives an exact probability model. It does not rely on large sample approximations.
Why This Calculator Helps
A standard two by two test is not enough for ten rows. This calculator uses the Fisher-Freeman-Halton extension. It also reports row totals, expected counts, row percentages, odds, and row versus rest odds ratios. These details help you see which rows drive the association. They also reveal sparse cells that may weaken an approximate chi-square review.
Interpreting the Result
The observed probability is the hypergeometric probability of your exact table. The two-sided p value sums all feasible tables with probability less than or equal to the observed probability. This is a conservative and common exact approach. One-sided choices use ordered row scores. A greater result means the first outcome increases with higher scores. A less result means it decreases.
Advanced Checks
The calculator also shows Pearson chi-square, likelihood ratio G, and Cramer's V. These measures describe association strength and approximate table distance. They are not a replacement for the exact p value when counts are small. Use them as diagnostics. Review expected counts below five. Check rows with strong odds ratios. Then decide whether the rows should remain separate, be ordered, or be combined before final reporting.
Reporting Advice
A clear report should name the test, the row count, the two outcomes, the p value, and the significance level. It should also explain whether the analysis was exact or simulated. If the state space is too large, the Monte Carlo estimate gives a practical approximation. Use more simulations for a stable result. Always keep raw counts available. Percentages alone cannot reproduce the exact test. When row labels have a natural order, enter meaningful scores. When they do not, use the two-sided exact probability method only. This approach keeps the analysis transparent, reproducible, and suitable for small samples.