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.
Read more about this topic: Pooled Variance
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—Blaise Pascal (1623–1662)
“Scientists are human—they’re as biased as any other group. But they do have one great advantage in that science is a self-correcting process.”
—Cyril Ponnamperuma (b. 1923)
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—Samuel Richardson (1689–1761)