Fisher's method

In statistics, Fisher's method, also known as Fisher's combined probability test, developed by and named for Ronald Fisher, is a data fusion or "meta-analysis" (analysis after analysis) technique for combining the results from a variety of independent tests bearing upon the same overall hypothesis ("H"₀) as if in a single large test.

Fisher's method combines extreme value probabilities, P(results at least as extreme, assuming "H"₀ true) from each test, called "p-values", into one test statistic ("X"²) having a chi-square distribution using the formula

:$X^2\_\{2k\}\; =\; -2sum\_\{i=1\}^k\; log\_e(p\_i).$

The p-value for "X"² itself can then be interpolated from a chi-square table using 2"k" "degrees of freedom", where "k" is the number of tests being combined. As in any similar test, "H"₀ is rejected for small p-values, usually < 0.05.

In the case that the tests are not independent, the null distribution of "X"² is more complicated. If the correlations between the $log\_e(p\_i)$ are known, these can be used to form an approximation.

References

* Fisher, R. A. (1948) "Combining independent tests of significance", "American Statistician", vol. 2, issue 5, page 30. (In response to Question 14)

ee also

* data fusion
* meta-analysis
* hypothesis test
* p-value
* chi-square distribution
* degrees of freedom (statistics)
* statistical significance
* R. A. Fisher
* deciles