Hi everyone,
I hope that someone may be able to shed some light on the following. This seems a simple query but literature seems to be quite vague as regards description.
A three way interaction occurs 'whenever a two-way interaction differs depending on the level of a third variable'. This is quite clear...however, my question relates to when we have a non significant three way interaction.
Say we have 3 two level variables A, B and C. A has levels 1 and 2, B has levels 1 and 2 and C has levels 1 and 2. We create a plot for A*B at both levels of C. For argument's sake, we'll say that our measurement is "weight".
SCENARIO A
The pattern for A*B looks the same for C=1 and C=2 i.e. we have
C=1
A=1 B=1 mean weight 8
A=1 B=2 mean weight 3
A=2 B=1 mean weight 7
A=2 B=2 mean weight 6
C=2
A=1 B=1 mean weight 6
A=1 B=2 mean weight 1
A=2 B=1 mean weight 5
A=2 B=2 mean weight 4
For C=1, we find that the difference between the mean weights for (i) A=1 at B=1 and (ii) A=1 at B=2 is 5 ; the difference between means for (i) A=2 at B=1 and (ii) A=2 at B=2 is 1.
For C=2, we find that the difference between the mean weights for (i) A=1 at B=1 and (ii) A=1 at B=2 is *also* 5 ; the difference between means for (i) A=2 at B=1 and (ii) A=2 at B=2 is *also* 1.
Clearly the above is illustrative of a non significant 3 way interaction.
SCENARIO B
Now, what if we had the following scenario where the pattern looks the same for A*B at C=1 and C=2 but:
C=1
A=1 B=1 mean weight 90
A=1 B=2 mean weight 85
A=2 B=1 mean weight 89
A=2 B=2 mean weight 70
C=2
A=1 B=1 mean weight 90
A=1 B=2 mean weight 88
A=2 B=1 mean weight 82
A=2 B=2 mean weight 66
For C=1, we find that the difference between the mean weights for (i) A=1 at B=1 and (ii) A=1 at B=2 is 5 ; the difference between means for (i) A=2 at B=1 and (ii) A=2 at B=2 is 19.
For C=2, we find that the difference between the mean weights for (i) A=1 at B=1 and (ii) A=1 at B=2 is 2 ; the difference between means for (i) A=2 at B=1 and (ii) A=2 at B=2 is 16.
Would this be viewed as a non significant interaction?
i.e. my question is....for a non significant 3 way interaction, does the difference between means for (i)A=1 at B=1 and (ii) A=1 at B=2 have to be same for C=1 and C=2? Similarly, does the difference between means for (i) A=2 at B=1 and (ii) A=2 at B=2 have to be the same for C1=1 and C=2?
I hope this makes sense (sorry - it would have looked better illustrated on plots)
Many thanks for your assistance on this matter in advance.
Best Wishes,
Kim
Dr Kim Pearce PhD, CStat, Fellow HEA
Senior Statistician
Haematological Sciences
Room MG261
Institute of Cellular Medicine
William Leech Building
Medical School
Newcastle University
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