Dear all,
Can I ask,
In a regression with 1 independent variable, the significance of the F
statistic and the t-ratio are indential. These statistics test:
H_0: B=0
H_1: B ne 0
ie a *2 sided test*.
So in an example where n=8, say we had the t-ratio=2.85 with p=0.029 and the
F ratio=8.10 tested against F_1,6 gives p=0.029 (from tables/MTB).
(I know that in the above scenario the F ratio gives rise to a 2 sided test
from a 1 tailed distribution)
My question is:
When testing for "equality of variance":
e.g.
H_0: sigma_1^2 = sigma_2^2
H_1: sigma_1^2 ne sigma_2^2
where n_1=9 s_1^2=50
and n_2=10 s_2^2=10
where s_1^2>s_2^2 and F= s_1^2/s_2^2 = 5
and from tables we had F_8,9(0.025)=4.10
Why would we say that this F ratio is significant at the *5%* level (i.e.
double the level tabulated) when this is also a 2 sided test?
I am confused as to why we double the significance value in the F tables in
the 'equality of variance' 2 sided test yet we do not double the tabulated
significance value in the F tables when doing the 2 sided test in
regression.
Many thanks for your help on this,
All the Best,
Kim
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