Fisher Exact Test Calculator
The Fisher Exact Test Calculator determines the significance of associations between categorical variables in 2x2 contingency tables. It's particularly useful for small sample sizes where chi-square tests are inappropriate. Researchers use it in medicine, biology, and social sciences to analyze experimental results and observational studies when dealing with rare events or limited data.
Formula
Fisher's Exact Test formula: p = ( (a+b)! (c+d)! (a+c)! (b+d)! ) / ( a! b! c! d! n! ) where n = a+b+c+d. The p-value sums probabilities of observed and more extreme tables.
How to Use
1. Enter observed counts in the 2x2 table cells
2. Click Calculate to get p-value
3. Compare p-value with significance level (α = 0.05)
4. p < α indicates significant association
Note: Use for small sample sizes (n < 20)
Development Process
1. Designed interface with HTML table inputs
2. Implemented factorial calculations in JavaScript
3. Added Fisher test probability computation
4. Integrated p-value summation for all extreme tables
5. Added responsive styling with CSS
6. Implemented clear/reset functionality
7. Added FAQ section with dynamic display
Frequently Asked Questions
1. When should I use Fisher's Exact Test?
Use Fisher's test when analyzing 2x2 contingency tables with small sample sizes (total n < 20) or when any cell count is less than 5. It's ideal for exact probability calculations in randomized experiments or observational studies with limited data.
2. How to interpret Fisher test results?
The p-value indicates the probability of observing the table arrangement or more extreme under the null hypothesis. A p-value < 0.05 suggests significant association between variables. Lower p-values indicate stronger evidence against the null hypothesis.
3. Can Fisher's test handle large samples?
While possible, Fisher's test becomes computationally intensive for large samples. For n > 30, consider using Pearson's chi-square test instead. Fisher's exact test is most appropriate and efficient for small sample sizes.
4. What's the difference between one-tailed and two-tailed tests?
One-tailed tests examine deviation in one direction, while two-tailed consider both directions. Our calculator provides two-tailed p-values by default, summing probabilities of all tables as or more extreme than observed in either direction.
5. What are the test assumptions?
Assumes fixed marginal totals, independent observations, and mutually exclusive categories. Data should be from random sampling, and all cell counts must be non-negative integers.
6. How accurate are the results?
Results are exact probabilities calculated using factorials. Accuracy depends on numerical precision limitations in JavaScript. For very large numbers, approximations may occur due to floating-point arithmetic limitations.
7. Can I use decimal values?
No. Fisher's Exact Test requires integer counts representing observed frequencies. Decimal values are invalid as they can't represent actual event counts. Always round to nearest whole numbers before analysis.
8. What's the 'exact' in Fisher's test?
The 'exact' refers to the method of calculating precise p-values using hypergeometric distribution, unlike approximate methods like chi-square. It provides accurate results regardless of sample size.
9. How are extreme tables defined?
Extreme tables are those with cell frequencies that deviate from the observed table in the direction of the alternative hypothesis while maintaining the same marginal totals.
10. What alternatives exist for big data?
For large datasets, consider Pearson's chi-square test or G-test. For tables larger than 2x2, use the Freeman-Halton extension. Logistic regression is another alternative for complex analyses.