help > RE: ANCOVA - contrast / hypothesis testing
Dec 10, 2019  11:12 AM | Athina Aruldass - University of Cambridge
RE: ANCOVA - contrast / hypothesis testing
Hi again Andrew

Pls ignore my first 2 questions from above (I was very confused and my brain just broke...).

For Q3 - this is the design matrix I eventually came up with :
1 0.3
1 2.2
1 0.3
1 4
1 0.9

columns : 1st - intercept, 2nd - inflammation
contrast : [0 -1] , stat test : t-test (not one sample t-test)
Hyp : testing for negative correlation between inflammation score and FC

I went on to perform this over 3 groups with this design matrix (after being warned that my initial design was rank deficient) :

1 0 0.3
1 -1 2.2
1 0 0.3
1 1 4
1 0 0.9

columns : 1st - intercept, 2nd - group with 3 levels (g1 : -1, g2 : 0, g3 : 1), 3rd - inflammation
contrast : [0 0 -1] , stat test : t-test
Hyp : testing for negative correlation between inflammation score and FC whilst controlling for group

++++++++ Questions +++++++++

1) Are the above design matrices correct ?

2) If I were to add a group*inflammation interaction column for the 3-group design would the design matrix then look like this

1 0 0.3 0
1 -1 2.2 -2.2
1 0 0.3 0
1 1 4 4
1 0 0.9 0

columns : 1st - intercept, 2nd - group with 3 levels (g1 : -1, g2 : 0, g3 : 1), 3rd - inflammation , 4th - group*inflammation
contrast : [0 0 0 -1] , stat test : t-test (not one sample)

If this is correct - what could one then infer / hypothesise for ? I quoted your reply to another query on interaction effect (with 2 groups) posted on the forum -

" The contrast [0 0 0 1] whether the the slope of the age-connectivity relationship is steeper in the group coded with 1, whereas [0 0 0 -1] will tester whether the slope is less steep.
In other words it is testing whether the age effect is stronger or weaker in one of the particular groups. "

(i) Would the above translate to my exp. (with age = inflammation) ?
(ii) Could I infer anything more specific for groups coded 0 and -1 ?
(iii) Would I have to perform a post-hoc pairwise ie. with 2 groups, interaction effect analyses ?

Please and many thanks - Athina.