On 28/02/2013 6:35, Ray Koopman wrote: > On Feb 27, 5:13 am, Cristiano <cristi...@NSgmail.com> wrote: >> On 27/02/2013 9:09, Ray Koopman wrote: >> >>> The variance of the unbiased sample variance in samples of size n >>> from a Uniform(0,1) distribution is (2n+3)/(360n(n-1)). For n = 2 >>> this reduces to 7/720 = .0097222... . >> >> But how can I use that formula to calculate the p-value for >> Var[s^2]? I should know the CDF of Var[s^2], right? > > You can get a p-value when n = 2, in which case sd = range/sqrt(2) > and you can take advantage of the fact that we know the cdf of the > range. Otherwise, unless someone can point you to the cdf of the sd > (or, more likely, the variance), you'll have to get a Monte Carlo > estimate of the p-value.
When one tries to use a Monte Carlo simulation to estimate a CDF, there is the big problem of the tails: for small and big p-values, many samples are needed. I can get a very good estimate for p-values in the range, say, .001 < p < .999, in a reasonable amount of time, but outside that range the simulation starts to demand many numbers.