As long as the other assumptions are plausible, the F test for testing the equality of population means in an ANOVA can be safely used when the largest sample standard deviation is no more than twice the smallest standard deviation.

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This statement is true. The F test assumes that the population variances are equal across all groups (homogeneity of variance assumption). When the largest sample standard deviation is no more than twice the smallest standard deviation, it is reasonable to assume that the population variances are equal, which allows us to use the F test to test for the equality of population means.

As Long as the Other Assumptions Are Plausible, the F