The logic behind the F-test for testing whether two populations have equal variances is to determine whether sample variances computed from random samples selected from the two populations differ due to sampling error, or whether the difference is more than can be attributed to sampling error alone, in which case, we conclude that the populations have different variances.

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The F-test compares the variances of two samples to assess whether they come from populations with equal variances. If the observed variance ratio is significantly greater than what would be expected due to sampling variability alone, it suggests the population variances are different.

The Logic Behind the F-Test for Testing Whether Two Populations