The F-statistic is a test on ratio of the sum of squares regression and the sum of squares error (divided by their degrees of freedom). If this ratio is large, then the regression dominates and the model fits well. If it is small, the regression model is poorly fitting.
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F is the test statistic and H0 is the means are equal. A small test statistic such as 1 would mean you would fail to reject the null hypothesis that the means are equal.
Mean, variance, t-statistic, z-score, chi-squared statistic, F-statistic, Mann-Whitney U, Wilcoxon W, Pearson's correlation and so on.
If X and Y have Gaussian (Normal) distributions, then the ratio ofthe mean of m variables distributed as X2 andthe mean of n variables distributed as Y2 hasan F distribution with m and n degrees of freedom.
Usually the F-statistic.
The parent probability distribution from which the statistic was calculated is referred to as f(x) and cumulative distribution function as F(x). The sampling distribution and cumulative distribution of a statistic is commonly referred to as g(y) and G(y) where Y is the random variable representing the statistic. There are numerous other notations.