3 ms·

The first example, "unbiased standard deviation" is mislabeled. The estimator of the variance is unbiased but the square root of an unbiased estimator is not i

by pseut 13y ago

The first example, "unbiased standard deviation" is mislabeled. The estimator of the variance is unbiased but the square root of an unbiased estimator is not itself unbiased. So it's not as nit-picky as it looks; it's either a brain fart or a hole in understanding (especially since the linked Wikipedia page discusses this issue)[1,2] Not to be a dick, but getting the first example wrong like that doesn't inspire confidence in the rest of the post. [1] https://en.wikipedia.org/wiki/Standard_deviation https://en.wikipedia.org/wiki/Standard_deviation [2] https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation https://en.wikipedia.org/wiki/Unbiased_estimation_of_standar...

EvanMiller 13y ago
Thanks! I have relabeled it. (In a previous draft the entry was for unbiased variance and the inaccuracy slipped in during the transition.)
- pseut 13y ago
  Your post said, "draft," so I think you're covered for that sort of error. :)
christopheraden 13y ago
Seems more like a brain fart than an error in understanding, especially because he didn't highlight why it was important to have unbiasedness in the first place. Having to explain the unbiased estimator for standard deviation would probably not have contributed much. It's more of a technicality than anything of philosophical importance--the square root of the unbiased estimator of sample variance is pretty accurate. The usage of n-1 instead of n in the denominator was a question I was always asked when I TA'ed for intro statistics classes in grad school. An explanation of unbiasedness might be warranted if this is to be an introductory primer.
joosters 13y ago
This was the first time I'd ever heard about biased/unbiased sample variances, all inspired by the original web page and seeing the (N-1) in the standard deviation formula. This inspired me to go off and read about Bessel's correction in wikipedia. Thank you, Evan Miller! Your web page is great, it taught me new stuff from the very first formula. Much appreciated.
bjhoops1 13y ago
I always make a point of reading comments that start with "Not to be a dick..." :P

by pseut 13y ago

EvanMiller 13y ago

Thanks! I have relabeled it. (In a previous draft the entry was for unbiased variance and the inaccuracy slipped in during the transition.)

pseut 13y ago
Your post said, "draft," so I think you're covered for that sort of error. :)

christopheraden 13y ago

Seems more like a brain fart than an error in understanding, especially because he didn't highlight why it was important to have unbiasedness in the first place. Having to explain the unbiased estimator for standard deviation would probably not have contributed much. It's more of a technicality than anything of philosophical importance--the square root of the unbiased estimator of sample variance is pretty accurate. The usage of n-1 instead of n in the denominator was a question I was always asked when I TA'ed for intro statistics classes in grad school. An explanation of unbiasedness might be warranted if this is to be an introductory primer.

joosters 13y ago

This was the first time I'd ever heard about biased/unbiased sample variances, all inspired by the original web page and seeing the (N-1) in the standard deviation formula. This inspired me to go off and read about Bessel's correction in wikipedia. Thank you, Evan Miller! Your web page is great, it taught me new stuff from the very first formula. Much appreciated.

bjhoops1 13y ago

I always make a point of reading comments that start with "Not to be a dick..." :P