Question about Mean Squared Error::Why Squared?
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Aug30-09, 10:44 PM
Interestingly enough the use of the divisor (n - 1) is a rather recent development. I've read texts as recent as the 40's where the standard deviation has a devisor of n. As such the expected value of s
is [itex]n^2\cdot \sigma^2 / (n-1)^2[/itex] if I'm not mistaken. Since is was an underestimator of the true variance, statisticians and probabilists switched to the current divisor of (n - 1).
Whether the divisor is n or (n - 1), these expressions are all measures of dispersion; whether they're good measures is another matter.
For large n it doesn't really matter.