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I have a study design with a repeated measures variable (four time points) and a time-invariant covariate. I am analyzing the data using a repeated measures ANCOVA in SPSS. I am interested in the within-subject effect of time point, as well as the main effect of the covariate and the interaction between the covariate and the within subject factor.

If I enter the covariate "as is" (i.e., raw data), I notice that my main within-subject effect is not significant. However, if I mean center my covariate, my within-subject effect is significant (p < .001) - in fact, the results are basically the same as if I run a repeated measures ANOVA (with no covariate; there's just a small difference in degrees of freedom, for obvious reasons).

I am trying to understand why centering my covariate has such a large impact on my within-subject effect.

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