# Statistical significance of sample variance

Suppose that I have a vector X of 50 numbers between 1 and 10. Then I calculate the variance of X. Let us say it turns out to be 8, that is, VAR(X) is equal to 8.

Is it meaningful to ask the statistical significance of this result? If yes, how can I calculate it?

Note: Although Matlab calculates statistical significance of correlation coefficient, it does not calculate the statistical significance of variance. This led me to think that may be it is not meaningful to ask the statistical significance of variance. However, it seems to me a meaningful question because for a list of uniformly distributed random numbers with a certain range some variances are quite unlikely.

Thanks. Ahmet

• I think that rather than a hypothesis testing problem, this is an estimation problem, unless you have an explicit hypothesis about the variance of the random variable (not to be confounded with the sample variance). – user10525 May 12 '12 at 11:36

In this case, you can talk about significance if you have a hypothesis (eg $Var(X)$>5). Note that the hypothesis is a statement about the underlying population (a random variable) and not about the sample.