[open] main effects from a mixed ANOVA
I'm wondering what main effects in a mixed ANOVA represent exactly. I've always thought that in a classical ANOVA a main effect is the effect of Factor A across all levels of Factor B, etc.
However, in a couple of data sets I noticed that main effects of a within-subjects factor, that are not significant when tested with a single t-test or a one-way ANOVA, become significant when tested with a factorial ANOVA when a between-subjects factor is included (or vice versa). To me, this is counter intuitive and it makes me wonder what these main effects show exactly. And which one we should interpret (the one from the t-test or the one from the more complex design).
I attached an example.
When not including the between-subjects factor Groupe, the effect of Cue is just not significant. However, when including the factor Groupe, the effect of Cue does become significant.
I see that the F-value increases because the SS Residual decreases, but I don't understand how to interpret it.
One of my students has an example that is even more extreme, where an effect that is not significant with a t-test does become significant in a much complex ANOVA with two within-subjects factors and two between-subjects factors, even though from the graph it looks like the two conditions do not differ.
I hope someone can help us.