Design matrix for 2 factor Anova with 3 levels each

1

Hi All,
I am a graduate student trying to finish my dissertation and rejoin society and I’m trying to set up both a design matrix and contrast matrix for a 2 factor (age and cognition) ANOVA with 3 levels each (age:young, middle aged and old ; cognition: low, average and high).
I’ve used the FSL guidelines and for the design matrix I’ve assigned age to be “A” and cognition to be “B” and grouped the animals as follows:
A1B1 A1B2 A1B3 A2B1 A2B2 A2B3 A3B1 A3B2 A3B3

Can fixelcfestats be used for such an ANOVA design?
If yes then is this the correct set of contrasts for the main effects of A and B as well as the interaction between the 2.

Contrast Matrix:
Main effect of A:
for A1-A2: 1 1 1 -1 -1 -1 0 0 0
for A1-A3: 1 1 1 0 0 0 -1 -1 -1

Main effect of B:
for B1-B2: 1 -1 0 1 -1 0 1 -1 0
for B1-B3: 1 0 -1 1 0 -1 1 0 -1

Interaction effects:
for A1-A2 across B: A1B1-A2B1 = A1B2-A2B2 = A1B3-A2B3 so A1B1-A2B1-A1B3+A2B3 =A1B2-A2B2-A1B3+A2B3=0
1 0 -1 -1 0 1 0 0
0 1 -1 0 -1 1 0 0 0

for A1-A3 across B: A1B1-A3B1=A1B2-A3B2=A1B3-A3B3 so A1B1-A3B1-A1B3+A3B3 = A1B2-A3B2-A1B3+A3B3 =0

1 0 -1 0 0 0 -1 0 1
0 1 -1 0 0 0 0 -1 1

for B1-B2 across A: B1A1 -B2A1 = B1A2-B2A2 = B1A3-B2A3 so B1A1-B2A1 -B1A3+B2A3 = B1A2-B2A2-B1A3+B2A3 = 0

1 -1 0 0 0 0 -1 1 0
0 0 0 1 -1 0 -1 1 0

for B1-B3 across A: B1A1-B3A1=B1A2-B3A2=B1A3-B3A3 so B1A1-B3A1-B1A3+B3A3 = B1A2-B3A2-B1A3+B3A3=0

1 0 -1 0 0 0 -1 0 1
0 1 0 0 0 -1 -1 0 1

Thank you
Loi Do

2

Welcome Loi!

Apologies, I did have a close look through your tables late last year, but wanted to double-check before posting a reply and didn’t get to it.

for B1-B3 across A: B1A1-B3A1=B1A2-B3A2=B1A3-B3A3 so B1A1-B3A1-B1A3+B3A3 = B1A2-B3A2-B1A3+B3A3=0
1 0 -1 0 0 0 -1 0 1
0 1 0 0 0 -1 -1 0 1

I think your reversal of A and B here may have led to an error. If I avoid this reversal:

for B1-B3 across A:

A1B1-A1B3 = A2B1-A2B3 = A3B1-A3B3
A1B1-A1B3-A3B1+A3B3 = 0
A2B1-A2B3-A3B1+A3B3 = 0

1  0 -1  0  0  0 -1  0  1
0  0  0  1  0 -1 -1  0  1

In the second line, I think you erroneously added A1B2 instead of A2B1.

Beyond this, the only thing to do is construct your F-tests; but if you’ve made it this far, I’d generally trust you to be able to do so.

Cheers
Rob