# Testing simultaneous equality of contrasts

I have a one-way ANOVA model with 3 treatments. I have contrasts $\hat{\theta}_1=\hat{\mu}_1+\hat{\mu}_2$ and $\hat{\theta}_2=\hat{\mu}_3-\frac{1}{2}(\hat{\mu}_1+\hat{\mu}_2)$.

I want to do a simultaneous test $H_0:\theta_1=\theta_2=0$.

The two contrasts are orthogonal. How do I do this test? Is it the same as the global F test $F=\frac{MST}{MSE}$, since there's t-1 pairwise orthogonal contrasts?

• Yes. ... oh it needs more than 3 characters ... okay ... yes that simultaneous test is the same as the global F in exactly the way you suggest. (If you ask a yes/no question - one for which a yes answer is potentially too short to even post as a comment, you probably should probably try to ask a slightly different question, or phrase it in a way that admits a more detailed response.) – Glen_b Nov 9 '16 at 23:57