An independent two-sample t-test can be used with which variance assumptions?

An independent two-sample t-test can be used with which variance assumptions?

• A. Assumes equal variances only.
• B. Assumes unequal variances only.
• C. Assumes equal variances when n is large; otherwise variance not specified.
• D. Can be used with either equal or unequal variances.

Answer: (D)

The main idea here is that comparing two independent group means with a t-test doesn’t lock you into one variance scenario. you can use the independent two-sample t-test whether the variances are the same or different. If you assume equal variances, you pool the two-sample variances to get a common estimate and use the pooled t-test. If you don’t want to assume equal variances, you use Welch's t-test, which keeps the separate variances and adjusts the degrees of freedom accordingly. In both cases you’re still testing whether the group means differ, just with different ways of handling variability. So the test is flexible and can be used with either equal or unequal variances.

The main idea here is that comparing two independent group means with a t-test doesn’t lock you into one variance scenario. you can use the independent two-sample t-test whether the variances are the same or different. If you assume equal variances, you pool the two-sample variances to get a common estimate and use the pooled t-test. If you don’t want to assume equal variances, you use Welch's t-test, which keeps the separate variances and adjusts the degrees of freedom accordingly. In both cases you’re still testing whether the group means differ, just with different ways of handling variability. So the test is flexible and can be used with either equal or unequal variances.