# Perfoming ANOVA test using orthogonal contrasts

1. Feb 13, 2015

### bonfire09

I have to test treatments B,C,D and E where $H_0:\mu_B=\mu_C=\mu_D=\mu_E$ vs $H_1: not H_0$. Use $\alpha=0.05$ given this problem.

Now $\mu_A$ is not included in the hypothesis so I am trying to figure out how to go about this problem. I was thinking of using orthogonal contrasts and this is what I came up with.

$C_1-C_4$ are my 4 orthogonal contrasts (all pairwise) for the $5$ treatments. The part that confuses me is what to do with $\mu_A$ since it was never included in the null hypothesis? Also i'm guessing that I test C1-C4 to see if I can violate the null hypothesis but what if each of my contrasts support the null hypothesis? There should be a better way of doing this problem I think. I am not sure if I was to ask this question here, but since this deals with statistics I asked it here. Thanks.

Edit- I just noticed that my contrasts are not linear independent. I will have to come up with new ones.

Last edited: Feb 13, 2015
2. Feb 18, 2015