Etymology: Sir Ronald Aylmer Fisher, British statistician, 1890-1962
a statistical test comparing the means of more than two groups simultaneously by comparing two different measures of variance of the observations. One statistic measures the variations between the means of the groups (the between-groups variation), the other the variations within the groups (the within-group variation). If the two measures of variance yield similar results and their ratio, the F-ratio, approximates 1.0, the null hypothesis that all observations came from the same population cannot be rejected, whereas under the alternative hypothesis, the F-ratio is expected to be larger than 1.0. The test is the first step in the analysis of variance.