Standard error of variance
veena
I remember looking up somewhere on a website for standard error of
variance as (variance/number of samples). Is this the right equation?
I tried to find it again but it just disappeared. I have a set of N
samples, and the mean estimate is M and variance estimated from
samples is S^2.
Standard error of mean is sqrt(S^2/N)
variance of mean is S^2/N which is different from standard error of
variance I suppose?
What does the variance of sample mean specify and what is the
difference between that and standard error of variance?
Could someone help me with this?
Thanks
Veena
Jack Tomsky
The variance of the sample mean is the variance of Xbar as it varies among different samples from the same underlying distribution. Supposing that you have samples of size N. For each sample, calculate Xbar. Then theoretically, the variance of Xbar is
Var(Xbar) = sigma/sqrt(N),
where sigma is the true population standard deviation.
Now for the variance of the sample variance s^2. When you calculate s^2 for many samples of size N, based on the same underlying distribution, the theoretical variance of s^2 is
Var(s^2) = (1/N)*(mu4 - (N-3)/(N-1)*sigma^4),
where mu4 is the central fourth moment of the underlying distribution. For the normal family of distributions, since mu4 = 3*sigma^4, this reduces to
Var(s^2) = (2*sigma^4)/(N-1).
The standard error of the sample variance is merely the square root.
Jack
mark.vog...@googlemail.com
where can I find more information on the standard error of the sample
variance and a derivation of your
results.
Thanks!
Mark
Jack Tomsky
Mark, the general expression for the variance of a sample variance is given in S.S. Wilks, Mathematical Statistics, Wiley & Sons, page 199, (8.2.9). In the reduction of the expression to sampling from a normal distribution, I use the well-known result that the population fourth central moment mu4 is related to the population variance by mu4 = 3*sigma^4.
Jack
