Question

Why is a pooled standard deviation used for a two sample t-test?

Answer 1

Pooled standard deviation is rarely used in hypothesis testing.

Explanation:

Only use a pooled standard deviation if you KNOW that the standard deviations for both populations are equal (`sigma_1=sigma_2`).

Rarely does the statistician know the population standard deviations and even more rare would be that they know that the population standard deviations are equal .

In summary, most two-sample mean tests are done under the assumption that the standard deviations are not equal . Under this scenario, pooled standard deviations are not used.

hope that helps