I have just performed 2x4 mixed factorial anova (one between= treatment and one within= time) and found treatment*time interaction as significant. To see at which point(s) my treatment generated a difference between my groups, I ran simple effect tests and didn't find any significant difference at any point. I read some threads and discussions but couldn't fully comprehend these results and not sure how to report this. Can somebody help?
Hello Cinar,
Ordinarily, if the interaction is observed to be statistically significant (non-chance), then you'd expect one or more of the simple effects tests (6 in all) to be significant as well. It's possible (as your query suggests) that this might not be the case, however.
Why might this occur?
1. You didn't run all of the simple effects tests, and therefore missed the way/s in which differences occurred.
2. For group differences, as you describe, the difference might not be at a single time period, but instead a different profile among two or more time periods. These effects aren't among the usual simple effects evaluated (they can be tested, however).
3. Note that the sampling distributions of the respective tests (group A vs. group B at time #3 = 1df; vs. group x time = 3 df) are different, so the thresholds for statistical significance are not the same, nor is the power of the respective tests. If your sample size is marginal, this can exacerbate the situation.
4. Some combination of the above.
Good luck with your work.
Mathematically (statistically), it is possible to present interaction effect in absence of the primary effects. Using effect size plots (countered plots) is a good assistant n this case.
I have a couple of quick comments.
• The type of sums of squares you use may affect if the main effects or interaction effects are reported as significant or not. (There's a nice little explanation here: http://wight.seg.rmit.edu.au/fscholer/anova.php )
• Often, if there is a (significant) interaction, it is this interaction that is really of interest, and the main effects may be of less interest. If the effect of Factor A differs across levels of Factor B, then we want to explore this interaction... This of course depends on your goals.
A simple example of a significant interaction without significant main effects:
Diet Country Weight
A USA 1
A USA 2
A USA 3
A UK 4
A UK 5
A UK 6
B USA 4
B USA 5
B USA 6
B UK 1
B UK 2
B UK 3
Anova Table (Type II tests)
Response: Weight
Sum Sq Df F value Pr(>F)
Diet 0 1 0 1.0000000
Country 0 1 0 1.0000000
Diet:Country 27 1 27 0.0008263 ***
Residuals 8 8
And the plot.
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