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Fisher's exact test (also Fisher-Irwin test) is a statistical significance test used in the analysis of contingency tables. [ 1 ] [ 2 ] [ 3 ] Although in practice it is employed when sample sizes are small, it is valid for all sample sizes.
Fisher's method is typically applied to a collection of independent test statistics, usually from separate studies having the same null hypothesis. The meta-analysis null hypothesis is that all of the separate null hypotheses are true. The meta-analysis alternative hypothesis is that at least one of the separate alternative hypotheses is true.
The explicit null hypothesis of Fisher's Lady tasting tea example was that the Lady had no such ability, which led to a symmetric probability distribution. The one-tailed nature of the test resulted from the one-tailed alternate hypothesis (a term not used by Fisher). The null hypothesis became implicitly one-tailed.
Fisher introduced the null hypothesis by an example, the now famous Lady tasting tea experiment, as a casual wager. She claimed the ability to determine the means of tea preparation by taste. Fisher proposed an experiment and an analysis to test her claim. She was to be offered 8 cups of tea, 4 prepared by each method, for determination.
The null hypothesis is that the subject has no ability to distinguish the teas. In Fisher's approach, there was no alternative hypothesis , [ 2 ] unlike in the Neyman–Pearson approach . The test statistic is a simple count of the number of successful attempts to select the four cups prepared by a given method.
[50] [61] In this book Fisher also outlined the Lady tasting tea, now a famous design of a statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis. [62] [63]
The F table serves as a reference guide containing critical F values for the distribution of the F-statistic under the assumption of a true null hypothesis. It is designed to help determine the threshold beyond which the F statistic is expected to exceed a controlled percentage of the time (e.g., 5%) when the null hypothesis is accurate.
This is why the hypothesis under test is often called the null hypothesis (most likely, coined by Fisher (1935, p. 19)), because it is this hypothesis that is to be either nullified or not nullified by the test. When the null hypothesis is nullified, it is possible to conclude that data support the "alternative hypothesis" (which is the ...