Hi Tim,

Please see below:



On 12 February 2016 at 05:29, Timothy W. <[log in to unmask]> wrote:
Hi Anderson,

Thanks again for your reply! Could you explain how A, B, C, and D in your design corresponds to these 4 within-subjects scan conditions: Exp_pre, Exp_post, Control_pre, Control_post?

In the first design that you sent, I understood them as A=Exp_pre, B=Exp_post, C=Control_pre, D=Control_post. However, in the second design, I'm not so sure.

Yes, this is the same for both designs.
 

Our main research question is whether (Exp_post - Exp_pre ) > (Control_post - Control_pre),

This can be tested in the 2nd design directly: as you wrote, this is testing (B-A)-(D-C) > 0. The contrasts marked with * can be used to construct this one, and it will then be, for the for the first group:

B-A: -2 -1 -1 0 0 0 0 0 ...
D-C: 0 1 -1 0 0 0 0 0 ...
(B-A)-(D-C): -2 -2 0 0 0 0 0 0 ...

Repeating for the 2nd group gives:
(B-A)-(D-C): 0 0 0 -2 -2 0 0 0 ...

Since you want the difference between groups, then the final contrast is: -2 -2 0 2 2 0 0 0 ...
The signs can be reversed to test the opposite.

This contrast, however, is already there, in the second design (3-way interaction). It is the same because:

(A+D)-(B+C) = -[(B-A)-(D-C)]

That is, both ways lead to the same three way interactions.
 
and whether there's a 3-way interaction with age group.

The two hypotheses, that is, (Exp_post - Exp_pre ) > (Control_post - Control_pre) and 3-way interaction with age group are actually the same as shown above.
 
Perhaps that's what your design is testing, but I could use some clarification!

Hope this helps.

All the best,

Anderson

 

I appreciate your help,
Tim


On Thu, 11 Feb 2016 09:47:44 +0000, Anderson M. Winkler <[log in to unmask]> wrote:

>Hi Tim,
>
>Then the design is different. Please have a look here:
>https://dl.dropboxusercontent.com/u/2785709/outbox/mailinglist/design_tim2.ods
>
>The A, B, C and D represent the 4 conditions organised in a contingency
>table. The interaction is the cross-difference between rows and columns
>(A+D)-(B+C).
>
>All the best,
>
>Anderson
>
>
>On 10 February 2016 at 20:24, Timothy W. <[log in to unmask]> wrote:
>
>> Hi Anderson,
>>
>> Thanks for the quick reply!
>>
>> In our design, we consider subjects as a random effect and condition as
>> fixed. We fixed the conditions before the experiment, and we're interested
>> in the difference between our fixed levels of pre to post for condition A
>> vs. condition B (i.e., is the pre-to-post change for condition A
>> significantly different than the pre-to-post change for condition B?). And
>> then whether or not that interaction is different for the 2 age groups.
>>
>> How would this change the design that you had sketched where condition was
>> considered as a random effect?
>>
>>
>> Many thanks!
>>
>> Tim
>>
>>
>