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F-ratio
Explanations > Social Research > Analysis > F-ratio Description | Discussion | See also
DescriptionThe F-ratio is a test statistic for multiple independent variables. It is used in ANOVA calculations and calculated as: F-ratio = MS_{M} / MS_{R} ... where MS = SS / df Subscripted M means 'Model' and indicates the expected systematic variance. This is often measured as between-measures variation, and the subscript B is consequently often used here. Subscripted R means 'Residual' and indicates the random, unsystematic variance. This is measured as within-measures variance, and the subscript W is consequently often used. F can also be calculated with the Pearson correlation coefficient, r: F = r^{2} / (1 - r^{2})(n - 2) DiscussionA Test Statistic is generally calculated as the ratio of intended, systematic variance divided by the undesirable and unexpected unsystematic variance. Test statistic = systematic variance / unsystematic variance This is typically measured as the sum of squares, SS, then this is: Test statistic = SS_{M} / SS_{R} However, with multiple variables, there are multiple sums of squares. Therefore the F-ratio takes the mean of these. See also |
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