0
$\begingroup$

I have a database of 10-star movie ratings (similar to IMDB). For each movie the raw data is a distribution of votes from 0-star all the way to 10-star, and I have also computed the mean and standard deviation of the votes for each movie.

Now consider the set of all the computed standard deviations. Is there a known statistical distribution that this set is expected to follow in the general case? And if so, how do I compute its parameters?

Addendum: We cannot assume anything (namely normality) about the distribution of the movie scores themselves.

$\endgroup$
  • $\begingroup$ I don't think that there is a general analytical form for the distribution of the sd of an unknown distribution, but I could be wrong. Depending on what you need this for, you could try resampling (with replacement), calculating the sd's of your resamples, and plotting that distribution. $\endgroup$ – generic_user Apr 25 '15 at 16:44
0
$\begingroup$

Are the movie scores themselves normally distributed?

Given a set of samples with a normal distribution, the distribution of the standard deviations would be a scaled chi-squared distribution. See the Wolfram Math page on the standard deviation distribution.

Now if the original samples (movie scores) do not follow a normal distribution. it would make more sense to talk about the distribution of variances. And that would depend on what distribution the scores best follow.

$\endgroup$
  • $\begingroup$ Movie ratings can't really be normal. I addition, the chi-squared distribution is more directly connected to the variance than the SD. $\endgroup$ – gung Apr 25 '15 at 14:59
  • 1
    $\begingroup$ Agreed on both points. Seems like the original question is whether the standard deviation follows a known (same) distribution no matter the distribution of the original samples. Clearly it does not. I'm not sure how to answer the question better without it being more detailed. $\endgroup$ – paisanco Apr 25 '15 at 15:04
  • $\begingroup$ I've edited the question to clarify: we cannot assume anything about the distribution of the movie scores. $\endgroup$ – Jon Smark Apr 25 '15 at 16:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.