Dear Jan, Darren en listmembers.
While reading the excellent and very helpfull tutorial on "Contrast weights in flexible factorial design with multiple groups of subjects" of Jan Gläscher and Darren Gitelman I found that there are apparently 2 different definitions to calculate the main effect of condition. Specifically, I will consider design 1 on p8 (subjects and group*condition interactions) and design 3 on p10 (subjects, groups, conditions and group*condition interactions).
According to the tutorial the following contrasts are used to assess the main effect of condition:
design 1: zeros(1,n1+n2) MEc MEc (1A)
design 2: zeros(1,n1+n2) zeros(1,ng) MEc MEc*[n1/(n1+n2)] MEc*[n2/(n1+n2)] (2A)
In trying to understand the difference between both contrasts, I noticed that there are two approaches to detemine the main effect of condition. The first approach is to first determine the main effect of condition per group and than average over all groups. This would give the following contasts.
design 1: zeros(1,n1+n2) MEc/2 MEc/2 (1B)
design 2: zeros(1,n1+n2) zeros(1,ng) MEc MEc/2 MEc/2 (2B)
The second approach is to pool all the data, ignoring the fact that there are multiple groups and then calculate the main effect of condition. This would give the following contrasts.
design 1: zeros(1,n1+n2) MEc*[n1/(n1+n2)] MEc*[n2/(n1+n2)] (1C)
design 2: zeros(1,n1+n2) zeros(1,ng) MEc MEc*[n1/(n1+n2)] MEc*[n2/(n1+n2)] (2C)
Note that when n1=n2, contrasts (1C) and (2C) reduce to (1B) and (2B). (That's why the division by 2 in (1B) and (2B) is required.)
Contrast 1B (apart from the division by 2) and 2C are given in the tutorial (cf 1A and 2A) i.e. it appears to me that the tutorial uses both definitions of the main effect of condition. Of course, both versions are valid but they can give quite different results especially when group sizes differ considerably. (For example when comparing a small patient group with a large control group.) In addition how should I read literature when a main effect of condition is reported?
Any comments, suggestions? Would either method be considered to be more appropriate?
Antoon Willemsen
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University Medical Center Gronigen
dept. Nuclear Medicine & Molecular Imaging
Groningen
The Netherlands
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The contents of this message are confidential and only intended for the eyes of the addressee(s). Others than the addressee(s) are not allowed to use this message, to make it public or to distribute or multiply this message in any way. The UMCG cannot be held responsible for incomplete reception or delay of this transferred message.
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