help > Mixed Factorial Design (3 by 2) and Post-Hoc Tests
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Feb 10, 2021  02:02 AM | Paul Dhami
Mixed Factorial Design (3 by 2) and Post-Hoc Tests
Greetings Forum Users and Dr. Zalesky,

I was hoping for someone to please verify 1) if my design matrix is correct for testing a 3 (three separate groups) by 2 (two time points) interaction effect, and 2) what would be the appropriate post hoc tests.

With regards to the 3 x 2 interaction effect, following previous examples on this forum, i came up with this example posted else where:

1 1 1 0 1 0 (time 1, group A)
1 1 1 0 1 0 (time 1 ,group A)
1 1 0 1 0 1 (time 1, group B)
1 1 0 1 0 1 (time 1, group B)
1 1 0 0 0 0 (time 1, group C)
1 1 0 0 0 0 (time 1, group C)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 0 0 0 (time 2, group C)
1 -1 0 0 0 0 time 2, group C)

With the interaction contrast being [0 0 0 0 1 1]. Are these correct?

I have yet to run my analysis,  but in the case that I do come across an 3 by 2 interaction, what post-hoc tests would I then run? I understand if there is no significant interaction, I would test for the main effects of group and time. However, I do not know what post-hoc tests I would run for this interaction. Any advice would be greatly appreciated.

Best,
Paul
Feb 10, 2021  05:02 AM | Andrew Zalesky
RE: Mixed Factorial Design (3 by 2) and Post-Hoc Tests
Hi Paul,

the design matrix looks ok.

Unless your sample size is large, you may want to simplify the experimental design (e.g. 2 x 2) to ensure adequate power is available to detect any interaction effects.

The choice of post hoc tests depends on your specific hypotheses. For example you could run a separate t-test for each of the interaction effects:

[0 0 0 0 1 0] or [0 0 0 0 -1 0]   - this would test for the specific effect of time on group A, relative to group C

and

[0 0 0 0 0 1] or [0 0 0 0 0 -1] - this would test for the specific effect of time on group B, relative to group C

Andrew

Originally posted by Paul Dhami:
Greetings Forum Users and Dr. Zalesky,

I was hoping for someone to please verify 1) if my design matrix is correct for testing a 3 (three separate groups) by 2 (two time points) interaction effect, and 2) what would be the appropriate post hoc tests.

With regards to the 3 x 2 interaction effect, following previous examples on this forum, i came up with this example posted else where:

1 1 1 0 1 0 (time 1, group A)
1 1 1 0 1 0 (time 1 ,group A)
1 1 0 1 0 1 (time 1, group B)
1 1 0 1 0 1 (time 1, group B)
1 1 0 0 0 0 (time 1, group C)
1 1 0 0 0 0 (time 1, group C)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 0 0 0 (time 2, group C)
1 -1 0 0 0 0 time 2, group C)

With the interaction contrast being [0 0 0 0 1 1]. Are these correct?

I have yet to run my analysis,  but in the case that I do come across an 3 by 2 interaction, what post-hoc tests would I then run? I understand if there is no significant interaction, I would test for the main effects of group and time. However, I do not know what post-hoc tests I would run for this interaction. Any advice would be greatly appreciated.

Best,
Paul
Feb 10, 2021  04:02 PM | Paul Dhami
RE: Mixed Factorial Design (3 by 2) and Post-Hoc Tests
Dear Dr. Zalesky,

Thank you much for your help.

Just a follow up, I conducted my analysis and found no interaction. I now want to assess the main effects of time and group.

What would be the contrasts, given the above design matrix, for assessing the main effects of time and group?

Thank you again,
Paul
Feb 11, 2021  12:02 AM | Andrew Zalesky
RE: Mixed Factorial Design (3 by 2) and Post-Hoc Tests
time: [0 1 0 0 0 0 ] or [0 -1 0 0 0 0]  t-test

group [0 0 1 1 0 0] F-test

For group, you could also do a separate (post-hoc) t-test for each of the two groups.

Originally posted by Paul Dhami:
Dear Dr. Zalesky,

Thank you much for your help.

Just a follow up, I conducted my analysis and found no interaction. I now want to assess the main effects of time and group.

What would be the contrasts, given the above design matrix, for assessing the main effects of time and group?

Thank you again,
Paul
Feb 12, 2021  02:02 AM | Paul Dhami
RE: Mixed Factorial Design (3 by 2) and Post-Hoc Tests
Hi Dr. Zalesky,

just a follow up question to the original design matrix I provided in the first comment.

Following some other threads here, because my design is mixed (time x group), I am a bit confused as to whether I also need to include additional columns for subject means?

If I need to, would I just append the subject mean columns to the original design matrix?

Or is the design matrix provided in the original message fine for a mixed (time x group) design?

Thank you again for all your help.
Paul

Originally posted by Andrew Zalesky:
Hi Paul,

the design matrix looks ok.

Unless your sample size is large, you may want to simplify the experimental design (e.g. 2 x 2) to ensure adequate power is available to detect any interaction effects.

The choice of post hoc tests depends on your specific hypotheses. For example you could run a separate t-test for each of the interaction effects:

[0 0 0 0 1 0] or [0 0 0 0 -1 0]   - this would test for the specific effect of time on group A, relative to group C

and

[0 0 0 0 0 1] or [0 0 0 0 0 -1] - this would test for the specific effect of time on group B, relative to group C

Andrew

Originally posted by Paul Dhami:
Greetings Forum Users and Dr. Zalesky,

I was hoping for someone to please verify 1) if my design matrix is correct for testing a 3 (three separate groups) by 2 (two time points) interaction effect, and 2) what would be the appropriate post hoc tests.

With regards to the 3 x 2 interaction effect, following previous examples on this forum, i came up with this example posted else where:

1 1 1 0 1 0 (time 1, group A)
1 1 1 0 1 0 (time 1 ,group A)
1 1 0 1 0 1 (time 1, group B)
1 1 0 1 0 1 (time 1, group B)
1 1 0 0 0 0 (time 1, group C)
1 1 0 0 0 0 (time 1, group C)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 0 0 0 (time 2, group C)
1 -1 0 0 0 0 time 2, group C)

With the interaction contrast being [0 0 0 0 1 1]. Are these correct?

I have yet to run my analysis,  but in the case that I do come across an 3 by 2 interaction, what post-hoc tests would I then run? I understand if there is no significant interaction, I would test for the main effects of group and time. However, I do not know what post-hoc tests I would run for this interaction. Any advice would be greatly appreciated.

Best,
Paul
Feb 12, 2021  03:02 AM | Andrew Zalesky
RE: Mixed Factorial Design (3 by 2) and Post-Hoc Tests
yes - in short if repeat measurements are performed, each subject mean should be modelled with a separate column and exchange blocks would be helpful.

Originally posted by Paul Dhami:
Hi Dr. Zalesky,

just a follow up question to the original design matrix I provided in the first comment.

Following some other threads here, because my design is mixed (time x group), I am a bit confused as to whether I also need to include additional columns for subject means?

If I need to, would I just append the subject mean columns to the original design matrix?

Or is the design matrix provided in the original message fine for a mixed (time x group) design?

Thank you again for all your help.
Paul

Originally posted by Andrew Zalesky:
Hi Paul,

the design matrix looks ok.

Unless your sample size is large, you may want to simplify the experimental design (e.g. 2 x 2) to ensure adequate power is available to detect any interaction effects.

The choice of post hoc tests depends on your specific hypotheses. For example you could run a separate t-test for each of the interaction effects:

[0 0 0 0 1 0] or [0 0 0 0 -1 0]   - this would test for the specific effect of time on group A, relative to group C

and

[0 0 0 0 0 1] or [0 0 0 0 0 -1] - this would test for the specific effect of time on group B, relative to group C

Andrew

Originally posted by Paul Dhami:
Greetings Forum Users and Dr. Zalesky,

I was hoping for someone to please verify 1) if my design matrix is correct for testing a 3 (three separate groups) by 2 (two time points) interaction effect, and 2) what would be the appropriate post hoc tests.

With regards to the 3 x 2 interaction effect, following previous examples on this forum, i came up with this example posted else where:

1 1 1 0 1 0 (time 1, group A)
1 1 1 0 1 0 (time 1 ,group A)
1 1 0 1 0 1 (time 1, group B)
1 1 0 1 0 1 (time 1, group B)
1 1 0 0 0 0 (time 1, group C)
1 1 0 0 0 0 (time 1, group C)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 1 0 -1 0 (time 2, group A)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 1 0 -1 (time 2, group B)
1 -1 0 0 0 0 (time 2, group C)
1 -1 0 0 0 0 time 2, group C)

With the interaction contrast being [0 0 0 0 1 1]. Are these correct?

I have yet to run my analysis,  but in the case that I do come across an 3 by 2 interaction, what post-hoc tests would I then run? I understand if there is no significant interaction, I would test for the main effects of group and time. However, I do not know what post-hoc tests I would run for this interaction. Any advice would be greatly appreciated.

Best,
Paul