Calculating Fisher's F-ratio is a key step in a number of statistical procedures involving null hypothesis significance testing. This is particularly so in the case of ANOVA (analysis of variance) in its several forms, but even multiple regression includes a test of significance of the overall model which employs an F-ratio. The present paper aims at making the basic ideas behind this common statistic more comprehensible by providing a visual counterpart to, and justification for, its algebraic definition.
As an example of how the definition works, consider the following very simple set of data comprising an independent variable consisting of three groups, where the values of the dependent variable are 1, 2, 3 for the first group, 4, 5, 6 for the second group and 7, 8, 9 for the third group. The groups could represent three drug treatments, and the numbers, a measure of clinical outcome for each of nine participants. One might represent this set of data as a row vector thus: (1, 2, 3, 4, 5, 6, 7, 8, 9).