Dear Colleagues
Several resources recommended following significant interaction ANOVA with a simple main effect analysis to break down and interpret the interaction. I am wondering if I can follow a significant interaction with One-way ANOVA for each independent factor.? Is this correct? if not why? Is there a difference between one-way ANOVA and a simple main effect following a significant interaction effect? Thank you
Dear Sabry Abd-El-Fattah ,
There are many things that need to be addressed in your comment.
To begin with, the recommendations that you have received are inappropriate. You do not need nor should change your current model to test differences within a a significant interaction.
It is VERY important to compare the means among interaction levels using the complete model in order to maintain the same variance components (just mean squared error in a fully fixed effect model) and the estimates of the effects.
Actually, by definition, if there is interaction, looking at the main effects you not tell you anything about the interaction.
More directly answering to your question: What test should I use after a significant factorial ANOVA? Answer: Well, any you would have used for the main effect.
You could use contrasts or a more appropriate mean separation method, such as Tukey's Method - this is considered "the best" when all possible comparisons are of interest.
For example, in a one-Way ANOVA for a categorical effect with 3 levels (let's call them L1, L2, and L3), let's say that there was a significant effect for it. Then, you can test all possible differences:
a1) L1 vs L2
a2) L1 vs L3
a3) L2 vs L3
Let's move now to a factorial design, using the same effect above in addition to another one with two levels (let's call it C1 and C2). In this 2x3 factorial, you have 2 x 3 = 6 combinations in your interaction: L1C1, L1C2, L2C1, L2C2, L3C1, and L3C2. Likewise, you can have all possible pairwise comparisons:
b1) L1C1 vs L1C2
b2) L1C1 vs L2C1
b3) L1C1 vs L2C2
...
b?) L3C1 vs L3C2
However, one it is common to see that not all comparisons are of interest. In general (this is NOT a rule) researchers are interested in within level comparisons. For example, do we have a difference between C1 and C2 WITHIN L1?? This is the very same question as shown in "b1)". Likewise, one could ask, WITHIN C1, are L1, L2, and L3 different from each other?
So, please, those recommendations are WRONG! Do not follow them.
Please let me know if this makes sense. Thanks, Nick
SURE but that's the hard way to do it. Try standard multiple comparisons assuming you have a usual experimental design for that sort of thing. You will want to do that anyway. Best, David Booth
David, could you please clarify and detail your response to my questions? thanks
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