[Numpy-discussion] Standard Deviation (std): Suggested change for "ddof" default value
mrbago at gmail.com
Thu Apr 3 14:21:19 EDT 2014
> P.S. Personally I am not convinced "unbiased" is ever a valid argument, as
> the biased estimator has smaller error. This is from experience in
> marksmanship: I'd rather shoot a tight series with small systematic error
> than scatter my bullets wildly but "unbiased" on the target. It is the
> total error that counts. The series with smallest total error gets the best
> score. It is better to shoot two series and calibrate the sight in between
> than use a calibration-free sight that don't allow us to aim. That's why I
> think classical statistics got this one wrong. Unbiased is never a virtue,
> but the smallest error is. Thus, if we are to repeat an experiment, we
> should calibrate our estimator just like a marksman calibrates his sight.
> But the aim should always be calibrated to give the smallest error, not an
> unbiased scatter. Noone in their right mind would claim a shotgun is more
> precise than a rifle because it has smaller bias. But that is what applying
> the Bessel correction implies.
I agree with the point, and what makes it even worse is that ddof=1 does
not even produce an unbiased standard deviation estimate. I produces an
unbiased variance estimate but the sqrt of this variance estimate is a
biased standard deviation estimate,
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