Reader Query

Question:

I notice that you have reported Within-Subjects Contrasts, here, rather than Within-Subjects Effects. Is there any reason for this? In my analyses, most times the Contrasts and Effects tables come out the same, but in some of my analyses, these differ. Which is the correct table to use?

Answer:

For a two-level factor, these should be equivalent. For a factor with three or more levels, the main effect considers whether the factor as a whole exerts a reliable influence on the dependent variable. The contrasts analysis compares pairs of levels from the multiple levels, its choice of levels being specified in the options of SPSS. It may for instance give the reliability of the biggest difference between any two levels. You should therefore see that the degrees of freedom differ between the main effects and simple contrasts when the factor has more than two levels.

Where you have a reliable difference in simple contrasts but not in main effect, it tells you that a pair of the levels considered alone would show a difference (which you should probably be able to tell from your trajectory plots), but the multiple levels as a whole do not, either due to greater noise in other levels or carrying out the comparison with greater degrees of freedom.

Reader Query

Question:

I've been working through your worksheet to analyse some data. I notice that you always talk about the main effects of repeated measure factors using the within subjects contrasts table. This is presumably because your repeated measures factor has two levels, and so there is no difference between the within subjects effect table and the within subjects contrast table. However, if the repeated measures factor has more than two levels (mine has 3), I only use the within subjects contrast table if the effect is best described as linear, and if not I use the within subjects effects table and explain the effect using pairwise comparisons.

Yes, a previous reader noticed that the main effects and simple contrasts tables differ when the repeated measures factor has more than two levels :0)

So, in light of this, is it fair to say that when looking at the ANCOVA, then if your main effect of the repeated measures factor was not linear, then any interactions between this variable and group or the covariate should be taken from the within subjects effect table, and but that if my main effect of the repeated measure factor was significantly linear, then I look at these interactions using the within subjects contrast table? Or is more complicated than that, and I should always use the within subjects contrast table (as in your worksheet) for a reason that I'm not aware of?

Answer:

My intuition is that you should look at the trajectories to decide. A non-linear repeated measures factor would imply that the difference in intercepts between the 3 (or more) levels are not evenly spaced (collapsed over any other factors). Interactions with other factors would indicate how this spacing was altered at different levels of other factors. The main effects table is giving you summary of all levels, the simple constrasts a (pre-determined) choice of two out of these levels. Quite often, when interpreting factors with more than 3 levels, you end up doing posthoc pairwise comparisons anyhow to see where the reliable difference is coming from.

The main guideline, I think, is examine the data, and see which comparisons give the honest picture of what you think is going on.

Reader Response:

Thanks, yes, that does all make sense. I'm glad to hear that there wasn't some reason for using the contrasts table that I wasn't aware of. I think I'll extend the rule that I use for ANOVAs then. So, if my main effect of the repeated measure is best explained as linear, then when looking at the ANCOVA, I'll look at interaction with that factor using the contrasts table, as this then explains how the linear main effect interacts with group or the covariate. For the same reason, when the main effect of the repeated measures factor is not linear, then it makes more sense to look at the interactions using the main effect table.

Reader Response:

Having thought a bit more, I think your advice to look at the pattern of the data is the better approach, as it's perfectly possible to have a linear effect in one group, but not the other, and for this to cause an interaction which is therefore not linear, but related to a group difference at a specific level of the repeated measures factor only.

Last edited by MT 21/4/10