Pooled Variance - Unbiased Least Square Estimate Vs. Biased Maximum Likelihood Estimate

Unbiased Least Square Estimate Vs. Biased Maximum Likelihood Estimate

Both

and

are used in different contexts. The former can give an unbiased to estimate when the two groups share an equal population variance. The latter one can give a more efficient to estimate biasedly. Note that the quantities in the right hand sides of both equations are the unbiased estimates.

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