The variance in the numerator of the F-ratio provides a single number that measures the differences among all of the sample means (Gravetter, 2021). The variance in the denominator of the F-ratio, like the standard error in the denominator of the t statistic, measures the mean differences that would be expected if there is no treatment effect (Gravetter, 2021). The t statistic and the F-ratio provide the same basic information and in each case, a large value for the test statistic provides evidence that the sample mean differences are larger than would be expected if there were no treatment effects (Gravetter, 2021).
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