What is the difference between using the pooled variance and the unpooled variance in a two-sample t test for means?

I have found a nice example for you to check out on the Penn State web page.

With the final notice saying:

"Comparing two proportions – For proportions there consideration to using "pooled" or "unpooled" is based on the hypothesis: if testing "no difference" between the two proportions then we will pool the variance, however, if testing for a specific difference (e.g. the difference between two proportions is 0.1, 0.02, etc --- i.e. the value in Ho is a number other than 0) then unpooled will be used."

as a quick sum up.

here is a link to a detailed description, if you would like some more detail as to why this is.

https://onlinecourses.science.psu.edu/stat200/node/60