Relationship between t-test and Chi-squared

**Deadstar** · February 13th 2008, 08:42 AM

This is something that has been pointed out to me but never explained. Any idea how these are linked? Heres the exact question...

It is no accident that $\Phi (1.96) = 0.975$ , i.e. $z_{0.025} = 1.96,$ and $\chi^2_{0.05}(1) = 3.841 = (1.96)^2$ .

Also

It is no accident that $t_{0.025}(10) = 2.228$ , $F_{0.05}(1,10) = 4.965 = (2.228)^2$ .

**CaptainBlack** · February 13th 2008, 11:02 PM

Originally Posted by Deadstar

This is something that has been pointed out to me but never explained. Any idea how these are linked? Heres the exact question...

It is no accident that $\Phi (1.96) = 0.975$ , i.e. $z_{0.025} = 1.96,$ and $\chi^2_{0.05}(1) = 3.841 = (1.96)^2$ .

The square of a standard normal RV has a $\chi^2$ distribution.

Presumably the same relation holds for t and F distributions (but I do not know that).

RonL

Thread: Relationship between t-test and Chi-squared

LinkBack

Thread Tools

Display

Relationship between t-test and Chi-squared

Similar Math Help Forum Discussions

Chi - squared test

A question about Chi-Squared test

p value on chi squared test??

[Research Statistics] Chi-Squared Test?

Pooling in the Chi-squared test?

Search Tags