The one which uses Sir Ronald Fisher's F-distribution for the test statistic is to compare several population means simultaneously.
The F-distribution was developed by Sir Ronald Fisher to study the behavior of two variances from random samples taken from two independent normal populations. The F-distribution allows us to use a F statistic to compare two populations.
The F-distribution is also known as a right-skewed distribution used commonly in another statistical test called an Analysis of Variance (ANOVA). For ANOVA tests we can use the F-distribution to check whether the variance among the means of two populations significantly differ. The F-distribution can also be used in regression analysis to compare the fit of different models.
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