Why is a pooled standard deviation used for a two sample t-test?
Only use a pooled standard deviation if you KNOW that the standard deviations for both populations are equal (
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