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F-ratio
Explanations > Social Research > Analysis > F-ratio
Description | Discussion | See also
Description
The F-ratio is a test statistic for multiple independent variables. It is used in ANOVA calculations and calculated as:
F-ratio = MSM / MSR
... where MS = SS / df
SS = Sum of the Squares
df = degrees of freedom
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 = r2 / (1 - r2)(n - 2)
Discussion
A 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 = SSM / SSR
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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