Re: Formal test for pooled variance?


<shiling99@xxxxxxxxx> wrote in message
news:1135968786.496993.196110@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> As david suggested the F - test should be good enough.
>
> Suppose that two independent samples (S1, S2) from N1(0, sigma1) and
> N2(0, sigma2) with sample size n and m. The sample variances are of
> chi-square(n) and chi-square(m)

I think you meant that (N1-1) * S^2 / sigma1 has chi-square(n-1)
distribution?

Can someone show me how this is derived? It's buried deep in my textbook
and I'm not finding it in the index. I looked through google and didn't
find a derivation either.


> F(n,m)=[chi-square(n)/n]/[chi-square(m)/m]
>
> Under H0 sigma1=sigma2 (equal variance), you will expect that F value
> is close to 1.
>
> Reject H0 if F value is too big / small according to F table with n and
> m degrees of freedom.

As I recall, this is Snedecor's F-distribution. But was someone saying it
is bad to use this to determine whether to use a pooled t-test?


.