I have set up one experiment and I m not sure whether I m doing it right or wrong. I will tell the details of my experiment, and it would be great if someone can comment if I m doing it right.

The experiment consists of 2 populations, one is control and the other is patients. At time T1 each subject received a chemical stimulation in the right paw and at time T2 in the left paw. These are animals subjects. As seen from fMRI, we can visualize the change in the time series activity at T1 and T2 in many of the brain region just by checking the time series, which was very much expected. The "final goal" is to find out, which parts of the brain have a different activation in two groups. In order to achieve that I plan to go through these steps

1) I defined my null hypothesis separately for both populations that: there is no effect when given the chemical stimuli. So contrast would be (1, -1). Is that right ?

2) I test the fixed effect analysis first, by first inputting all the control subjects and applying the above mentioned contrast and analyze the activations. Then I repeat the same with inputting all the patient/diseased subjects with the same contrasts and analyse the activations. The hypothesis would be that these two populations should differ in their activations (because one group is control and one group is patients) Is that right ??

3) In case I do not find any difference in activations; then I should not do the random effect, since with high power of fixed effect if it didnt show any difference there is no expected difference in random effects too !! Is that right ??

4) Can I make a 2x2 design here (healthy+chemical stimulation, healthy without chemical stim., disease+chemical stim., disease without chemical stim.) ???

5) My hypothesis is that during the second chemical stimulation at time T2, it would be a different reaction than the chemical stimulation at T1; because these are different paws, and also because T2 might feel more pain than the first stimulation of T1. How can I check my hypothesis ?

Any comments will be highly appreciated

Thanks a lot