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help > RE: ANCOVA - contrast / hypothesis testing
Dec 13, 2019 05:12 AM | Andrew Zalesky
RE: ANCOVA - contrast / hypothesis testing
Hi Athina,
The design matrix that you specify with two columns is correct. The corresponding contrast and your interpretation is also correct.
However, the three-column design matrix is incorrect. This will test for a parametric effect among the three groups. The 2nd column will test whether FC is smallest in grp1, biggest in grp 3, with FC in grp 2 sandwiched between grp 1 and 3. I am failry sure that you don't want to do this.
If you simply want to control for the effect of diagnosis, the 2nd column should be replaced with a column of 0/1, where 1 indicates grp 1 individuals. You will then need to add an additional column of 0/1, where 1 indicates grp 2 individuals. So you would have 4 columns in total: intercept; 1's for grp 1, 0's elsewhere; 1's for grp 2, 0's elsewhere; inflammation score. Note that you do not need a column for grp 3, since this is covered by the intercept. The contrast would be [ 0 0 0 -1] and select t-test (NOT one-sample).
Happy to provide feedback on your revised design matrix.
To test for a group by inflammation interaction, you would add two additional columns to your design matrix representing the multiplication of the 2nd column x inflammation and the 3rd column by inflammation. Note that you would need a large sample size to test for such an interaction.
Before moving onto the interaction effect, I suggest that you get the simple case working first.
Andrew
Originally posted by Athina Aruldass:
The design matrix that you specify with two columns is correct. The corresponding contrast and your interpretation is also correct.
However, the three-column design matrix is incorrect. This will test for a parametric effect among the three groups. The 2nd column will test whether FC is smallest in grp1, biggest in grp 3, with FC in grp 2 sandwiched between grp 1 and 3. I am failry sure that you don't want to do this.
If you simply want to control for the effect of diagnosis, the 2nd column should be replaced with a column of 0/1, where 1 indicates grp 1 individuals. You will then need to add an additional column of 0/1, where 1 indicates grp 2 individuals. So you would have 4 columns in total: intercept; 1's for grp 1, 0's elsewhere; 1's for grp 2, 0's elsewhere; inflammation score. Note that you do not need a column for grp 3, since this is covered by the intercept. The contrast would be [ 0 0 0 -1] and select t-test (NOT one-sample).
Happy to provide feedback on your revised design matrix.
To test for a group by inflammation interaction, you would add two additional columns to your design matrix representing the multiplication of the 2nd column x inflammation and the 3rd column by inflammation. Note that you would need a large sample size to test for such an interaction.
Before moving onto the interaction effect, I suggest that you get the simple case working first.
Andrew
Originally posted by Athina Aruldass:
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.
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.
Threaded View
| Title | Author | Date |
|---|---|---|
| Athina Aruldass | Dec 6, 2019 | |
| Athina Aruldass | Dec 18, 2019 | |
| Andrew Zalesky | Dec 19, 2019 | |
| Athina Aruldass | Jan 6, 2020 | |
| Andrew Zalesky | Jan 6, 2020 | |
| Athina Aruldass | Dec 10, 2019 | |
| Andrew Zalesky | Dec 13, 2019 | |
| Athina Aruldass | Dec 9, 2019 | |
| Andrew Zalesky | Dec 7, 2019 | |