# Relationship between t-test and Chi-squared

• Feb 13th 2008, 08:42 AM
Relationship between t-test and Chi-squared
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 $t_{0.025}(10) = 2.228$, $F_{0.05}(1,10) = 4.965 = (2.228)^2$.
• Feb 13th 2008, 11:02 PM
CaptainBlack
Quote:

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.