FISHER'S METHOD

In statistics, 'Fisher's method', named after 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.

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References

See also

References

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

See also

★ data fusion

★ meta-analysis

★ hypothesis test

★ p-value

★ chi-square distribution

★ degrees of freedom (statistics)

★ statistical significance

★ R. A. Fisher

★ deciles