![]() ![]() The denominator is an average of the sample variances for each group, which is an estimate of the overall population variance (assuming all groups have equal variances). But if the null hypothesis is false and the means are not all equal, then this measure of variance will be larger. ![]() The numerator is computed by measuring the variance of the means and if the true means of the groups are identical then this is a function of the overall variance of the data. If the null hypothesis is true then these are both estimates of the same thing and the ratio will be around 1. The F statistic is a ratio of 2 different measure of variance for the data.
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