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F-Ratio (F-Test)

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Definition

Although the F-Ratio test is primarily used to test the equality of two independent Variances from normal Populations, it is also applied in the Analysis of variance (Anova) situation to compare the differences between Means of the levels of an effect with regard to the response being measured.

The test statistic is computed as the ratio of the two Variances, or in the case of Anova, the ratio of the Between-Levels mean sum of squares to the Within-Levels or Error mean sum of squares. The p-value for the test statistic is obtained from Fisher's F-distribution tables with corresponding numerator and denominator degrees of freedom. A small p-value leads to rejection of the null hypothesis that there is no difference between the two Variances, or no differences among the level Means in the Anova case.