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Dear FSL experts,

I am investigating FA differences between 4 groups (group 1, 2, 3 & 4) using tbss and randomise. In my analysis, I encountered some irregularities in the outcome of different models that I used to define group differences.

Group 1 is the control group and group 2, 3 and 4 have the same condition but differ in the severity of the condition. Group 3 and 4 are small (n=7 and n=9, respectively) and therefore I have collapsed the groups to achieve a reasonable sample size (these groups are often combined in the relevant literature). I am mainly interested whether group 3/4 has lower FA than group 1 and whether group 2 has lower FA than group 1. My question concerns the first difference (lower FA in group 3/4 than in 1) and for convenience I will further focus on this comparison.

I tested the difference between group 3/4 and group 1 using three models, specified below. Model 1 used an F-test for the combined effect of the separate t-tests 4<1 and 3<1. Model 2 modeled the combined effect of 3,4<1 in one t-test. Model 3 already collapsed groups 3 and 4 into 1 column in the design.mat file, and the t-test of this combined 3/4 group was calculated using randomise. For power reasons, I kept the amount of contrasts provided in the design.con file equal at 2 in all models.

Model 1:

<design.con>
/NumWaves 6
/NumContrasts 2
/Matrix
[Group	1 2 3 4 age gender] 
[EV1]	1 0 -1 0 0 0
[EV2]	1 0 0 -1 0 0

<design.fts>
/NumWaves 2
/NumContrasts 1
/Matrix
1 1

Model 2:

<design.con>
/NumWaves 6
/NumContrasts 2
/Matrix
[Group	1 2 3 4 age gender] 
[EV1]	1 0 -0.5 -0.5 0 0
[EV2]	-1 0 0.5 0.5 0 0

Model 3:

<design.con>
/NumWaves 5
/NumContrasts 2
/Matrix
[Group	1 2 3&4 age gender] 
[EV1]	1 0 -1 0 0
[EV2]	-1 0 1 0 0

Output from all models are comparable in terms of the pattern of differences, but strongly differ in the the level of significance. P value of the F-test does not exceed P=.70. However, significant lower FA is obtained in the 3/4 group as compared to group 1 in both model 2 and 3. The results from model 2 and 3 are highly similar in pattern, but more differences exceed the statistical threshold P>.95 in model 2. 

This pattern of results suggests that model 2 has more statistical power than model 3 (even while model 3 uses one fewer covariate in the model) and both model 2 and model 3 have far more power than model 1. Why is the difference between the F-test and t-tests so large?

And, what makes the difference in the results from model 2 and model 3? Could it be explained by separate modelling of group 3 and 4 variance in model 2, resulting in a better model fit in model 2 than 3, in turn increasing the amount of explained variance and thereby increasing statistical power? 

Does it then makes more sense to use model 2 than model 1 and 3? The differences between model 2 and 3 seem to increase after increasing the number of permutations from 500 to 5000.

Thank you very much in advance!

Marsh Königs