# Thread: Difference between within-subjects effects, and within-subjects contrasts?

1. ## Difference between within-subjects effects, and within-subjects contrasts?

I've run a repeated measures ANOVA of some data, looking at the change in an outcome measure in 10 subjects outcome over time.

SPSS tells me that the within-subjects *effect* of time is statistically INsignificant (p=0.143). Yet it also tells me that the within-subject *contrast* (for quadratic trend) is significant (p=0.001).

What does this mean? How are the two conceptually reconciled?

2. The main effect of time just looks at whether there is significantly more variation between the different levels of time compared to the error term (the interaction between time and participants, i.e., the difference in the effect of time for different participants). It had nothing to do with whether the relationship between the levels is linear, quadratic, cubic, or whatever. It just looks for variations between levels.

The trend analysis is more specific in that it looks for a particular kind of relationship between the levels of time, in your case a quadratic relation (a fitted line that contains a quadratic component). The analysis suggests that your data can be well approximated by a quadratic function, but the question may be 1) if it is the kind of quadratic function you would expect? and 2) if you expected a quadratic function at all? If I strongly expected a quadratic relationship I would be inclined to skip the first analysis of the main effect and head directly for the within-subjects contrasts, but only if I really predicted such a result. It may not make much sense otherwise.

This study actually has another factor which I didn't mention earlier, for the sake of simplicity. That factor is group (i.e. one group of participants had active treatment, the other group had placebo). So to summarise: I was looking for changes over 7 timepoints in two groups of 10 participants each, one group which received an active treatment, the other receiving a placebo treatment.

Moreover, it was a crossover design. So it was actually the *same* 10 individuals who had active, who then (after a suitable washout period) received placebo.

I've been looking at the data using repeated measures ANOVA, with two within-subject factors (group and time). Is this a valid approach?

Thanks again.

4. Statistically, I don´t see any problem. The same people participate in each cell so it´s no doubt a pure repeated measures design.

However, you might get all kinds of methodological problems of course that might complicate the interpretations somewhat, but that is a concern for any repeated measures design, and you alleviate those concerns through a variety of procedures, for example counterbalancing etc. Statistically, I see no problem.

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