Pooled vs. Total Variance

Suppose data is collected from 100 individuals on a piece of a paper. The piece of paper is consequently torn, and one half of the page contains 40 samples and the other half contains 60 samples.

Now suppose variance from each page is analysed separately. In order to calculate the combined variance, will using the pooled variance formula for the two separate pages give the same result as if the data was analysed as a single sample?

If not, in what situations should I use pooled variance and in what situations should I use combined variance?

 

No!

In general 2-sample:-

1)common population variance:- if you know each datum in data is independent and Random Variable Normally distributed or you can apply CLT, then it is the Best option.

2)Pooled Variance:- Pooled variance is best estimate for population variance(first you'd accept equality of population variance of both separate data or you can use F-test to determine so). if you can accept equality of variance, then use Pooled variance.

3)separate sample variance:- to use this both sample size must be big enough, say, 20 or more/30 or more........ and each datum in data is independent and Random Variable Normally distributed but you can't accept equality of variance then use it.

For your case:-
Pooled Variance might be good if you collected data from same group(so that you can accept equality of variance) of individuals independently.

 

samples from 2 different independent populations