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From: Zootal on 28 Oct 2009 12:48
I am attempting to show that an F-statistic is equal to a t-statistic
squared, or IOW F = t^2. I am working with linear regression and extra sum
of squares tests. How would one go about showing this? Or, can some kind
soul nudge me in the right direction?


From: Andrew Magyar on 28 Oct 2009 09:15
This is true only when the numerator degrees of freedom is equal to 1. The proof is simple, an F-statistic with nu1 and nu2 degrees is defined as the ratio of a chi-squared nu1 divided by nu1 over a chi-squared nu2 divided by nu2. When nu1 is one, you get a chi-squared 1 over a chi-squared nu2 divided by nu2. Taking the square root will give you a standard Normal/sqrt(chi-squared nu2 divided by nu2). This is the definition of a t-statistic with nu2 degrees of freedom.
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