“Fisher's Exact Test”的概念、定义、习题解题方法及翻译-数学辞典

单词

Fisher's Exact Test

释义

Fisher's Exact Test

A Statistical Test used to determine if there are nonrandom associations between two CategoricalVariables. Let there exist two such variables and , with and observed states,respectively. Now form an Matrix in which the entries represent the number of observations inwhich and . Calculate the row and column sums and , respectively, and the total sum

of the Matrix. Then calculate the conditional Likelihood (P-Value) of getting the actual matrixgiven the particular row and column sums, given by

(which is a Hypergeometric Distribution). Now find all possible Matrices of NonnegativeIntegers consistent with the row and column sums

and

. For each one, calculate the associatedP-Value using (0) (where the sum of these probabilities must be 1). Then theP-Value of the test is given by the sum of all P-Value which are

The test is most commonly applied to a Matrices, and is computationally unwieldy for large or .

For an example application of the test, let be a journal, say either Mathematics Magazine or Science, andlet be the number of articles on the topics of mathematics and biology appearing in a given issue of one of thesejournals. If Mathematics Magazine has five articles on math and one on biology, and Science has none on mathand four on biology, then the relevant matrix would be

Computing

gives

and the other possible matrices and their

s are

which indeed sum to 1, as required. The sum of

-values less than or equal to

is then 0.0476which, because it is less than 0.05, is Significant. Therefore, in this case, there would be astatistically significant association between the journal and type of article appearing.

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