t
Message posted by jodi (via 209.18.30.152) on November 4, 2001 at 5:02 PM (ET)

Could you please demonstrate to me how t squared equals f.

Thanks Alot
Jodi

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: t
Message posted by Tomi (via 154.32.143.181) on November 4, 2001 at 9:14 PM (ET)

Re: t
Message posted by Jack Tomsky (via 208.249.113.130) on November 5, 2001 at 7:25 PM (ET)

F(df1,df2) = [X2(df1)/df1]/[X2(df2)/df2]
and
t(df) = z/sqrt(X2(df)/df).

Here, F(df1,df2)is an F with df1 and df2 degrees of freedom , X2(df) is a chi-square with df degrees of freedom, t(df) is Student's t with df degrees of freedom, and z is a standard normal with mean zero and variance equal to one.

Then t^2 = z^2/[X2(df)/df] = [X2(1)/1]/[X2(df)/df] = F(1,df).

We use the fact that the square of a standard normal is a chi-square with 1 degree of freedom.