Three conditions + one control, measured for IQ pre intervention and post intervention. Is this a two or one way repeated measures ANOVA?
Also... does anybody know if SPSS repeated measures option is a one way or two way ANOVA?
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You have two treatment factors: one is language lessons-or L, the other is music lessons-or M. Some people get one or the other, some get both, and some get to go do something else.
There could be an interaction between language and music, called LM, which is the combined effect of L and M. If the combination is quite strong, then LM could be large. If language lessons and music lessons interfere with each other, then this could actually be negative. If there is no joint effect of L and M then the effect of both should be about the same as the sum of the two separate effects. The effect of L plus the effect of M should about add up to the effect of the combination. (For effect, also read the change from before to after.)
The way to describe this is as a two factor or two treatment experiment, with each factor at two levels, nothing or intervention.
There is a third factor, usually termed Pre-Post or something of the sort that isn't very interesting. This is a repeated measures factor if you do an analysis of the original individual observations. This analysis might not be useful or informative. I take it you are interested primarily in change and this could guide your analysis.
You could calculate the differences between the second measurement and the first measurement of you dependent variable. Then do an analysis of variance of the differences using your two factor design. This should tell you whether groups changed and if the combination (LM) added anything to the components L and M.