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F Distribution

The F distribution is behind perhaps only the t distribution as the most popular statistic in tests of statistical significance when using continuous response variables. The F statistic is directly related to the chi-square statistic and the explicit output of all analysis of variance (ANOVA) tests. It is the foundation of modern experimental design and is the most powerful test for comparing two variances when the assumptions of normality are met. The following sections covers the history and derivation and properties of the F distribution, a short review of the noncentral F distribution and an ANOVA example, the resulting F statistic, and relevance to the distribution of F values.

History of the F Distribution

When the objective of an analysis is to compare two variances, the ratio ...

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