Question

There are two procedures for comparing two means from independent, normally distributed samples. The first step is to test for the equality of the two variances, using the __ __ test. If this test is not significant, then use the __ _ test with equal variances, otherwise, use the __ __ test with unequal variances.

Answer 1

There are two procedures for comparing two means from independent, normally distributed samples. The first step is to test for the equality of the two variances, using the F-Test for Equality of Two Variances test.

f this test is not significant, then use the "Welch's t-test/ Two Sample t Test: unequal variances"  test with equal variances, otherwise, use the Sample t Test: equal variances test with unequal variances.

Here is the brief description of all these 3 above mentioned tests :-

- An F-test is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal. The one-tailed version only tests in one direction, that is the variance from the first population is either greater than or less than (but not both) the second population variance.

- Our prime goal is not to ask whether two populations differ, but to quantify how far apart the two means are. The unequal variance t test reports a confidence interval for the difference between two means that is usable even if the standard deviations differ.

- When the population variances are known, hypothesis testing can be done using a normal distribution, as described in Comparing Two Means when Variances are Known. The approach we use instead is to pool sample variances and use the t distribution. We consider three cases where the t distribution is used: Equal variances.

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