Question

Can anyone explain to me the difference between standard deviation and pooled standard deviation. How do I calculate the second one?

Answer 1

I'm guessing this is asking the difference between Unpooled and Pooled std. deviation. :

Unpoled:\[\large s={ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\]

Pooled: \[\large s={\sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}} \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\]

The unpooled one is when the 2 population standard deviations are not equal. The pooled std. deviation formula is actually mathematically exact and assumes that the 2 population variances are assumed to be equal.