Evaluate small sample associations with exact table probabilities. Review odds ratios, tails, and expected counts. Download neat reports for audits, research, and presentations today.
| Group | Response | No Response | Total |
|---|---|---|---|
| New Treatment | 12 | 3 | 15 |
| Standard Care | 5 | 10 | 15 |
| Total | 17 | 13 | 30 |
This sample highlights a small study where exact testing is preferred over large sample approximations.
Fisher Exact Test evaluates whether two categorical variables are associated in a 2x2 contingency table. It is ideal when sample sizes are small, margins are fixed, or expected counts are low. Many medical, laboratory, marketing, and quality studies depend on this exact approach.
This calculator produces exact left tailed, right tailed, and two tailed p values. It also reports the observed table probability, odds ratio, confidence interval, relative risk, expected counts, chi square statistics, and the phi coefficient. These outputs support interpretation and documentation.
Use Fisher Exact Test when at least one expected cell count is small, when data are sparse, or when precision matters more than approximation speed. It is especially useful for pilot studies, randomized trials, A/B tests with low events, and safety signal reviews.
A small p value suggests that the observed pattern is unlikely under the null hypothesis of no association. The odds ratio and relative risk explain effect direction and strength. Expected counts and graph views help verify whether the table is balanced or skewed.
For clear reporting, include the exact p value, the tail used, the 2x2 counts, and the odds ratio with its interval. If a cell contains zero, mention whether a continuity style correction was applied for ratio estimation. Keep the original counts visible in your report.
For a 2x2 table with cells a, b, c, and d, Fisher Exact Test conditions on fixed row and column totals.
Exact table probability:
P = ((a+b)! (c+d)! (a+c)! (b+d)!) / (a! b! c! d! n!)
where n = a + b + c + d.
Odds ratio: OR = (a × d) / (b × c)
Expected count: Eij = (row total × column total) / n
Two tailed exact p value: sum the probabilities of all valid tables with probability less than or equal to the observed table probability.
Choose it for 2x2 tables with small samples, low expected counts, or sparse outcomes. It gives exact probabilities instead of relying on approximate large sample assumptions.
It measures how unusual the observed table is under no association. It includes all valid tables that are at least as extreme as the observed one, based on exact probability.
Each one tests a directional hypothesis. Left tailed favors smaller top left counts than expected. Right tailed favors larger top left counts than expected.
The exact p value remains valid. Ratio measures can become unstable or infinite, so the calculator can apply a small correction for more interpretable interval estimates.
It is usually better for very small samples or sparse tables. Chi square is faster for larger samples, but Fisher is more exact when counts are limited.
It compares the odds of the column one event between row one and row two. Values above one suggest higher odds in row one.
Expected counts show what the table would look like under independence. They help you judge sparsity, imbalance, and whether approximate methods might be questionable.
Yes. It works for marketing lift checks, response studies, small conversion tests, quality reviews, and any 2x2 categorical comparison with modest sample sizes.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.