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I am performing a t-test on n different samples of both $X_1, X_2,...,X_k$ and $Y_1,Y_2,...,Y_k$. To begin with I want to assume that all 2*n samples have the same variance but that they do not have the same mean.

Any advise on how I would best estimate this shared variance? I know that pooled variance works well if I only had one sample of X and Y, is there any way I can expand this to all n samples of X and Y?

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  • $\begingroup$ If they all have the same variance, then just estimate it from the entire set of data. $\endgroup$
    – soakley
    Nov 25, 2014 at 5:32
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    $\begingroup$ Ok but they all have different mean so I can not simply add them together. Or how do you mean? @soakley $\endgroup$
    – simme
    Nov 25, 2014 at 6:01
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    $\begingroup$ Estimate the variance for each of the $2n$ samples. Sum these estimates and divide by $2n.$ $\endgroup$
    – soakley
    Nov 25, 2014 at 13:31

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