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?