I have a data set containing three groups (A, B, C). Group A and Group B have undergone two different types of training designed to improve the same thing. Group C is my control group with no training. I have specific hypotheses stating that:
- Group A will be better than group C
- Group B will be better than group C and
- Group B will be better than group group A.
This is because the training used in group A has already been shown to improve over control (so I am trying to replicate that effect), while group B is a new training method which I expect to exceed both groups A and C.
How would I go about conducting this analysis? I have conducted a one-way ANOVA with planned comparisons, but I realized that my comparisons would have to be non-orthogonal since comparing B to A and C in one contrast would be pooling variance from an experimental and control condition together. Optimally, I want these comparisons:
A B C 1 0 -1 0 1 -1 -1 1 0
What is the proper way to conduct such comparisons?