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This mixed model should give you the same results as the repeated measures ANOVA MIXED accuracy BY training section format /CRITERIA = CIN(95) MXITER(100) MXSTEP(5) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE) /FIXED = training section format section*training format*training ...

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SPSS usually provides univariate tests of such a main effect on each variable all the way down in the output (“Tests of Between-Subjects Effects”), even for doubly multivariate designs. So, barring any particular problem in the way you specified the model, they should be there. There are also multivariate tests of between-subject factors (why are you ...

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First of all given you are using a standard LMM you definitely look to have normally distributed residuals. ie. $\epsilon \sim N(0, \sigma^2 I)$. When you are using a LMM you are practically saying that you data have a distribution as : $y \sim N( X\beta, \sigma^2 I + ZDZ^T)$. So in relation with what we wrote above : \$y|u \sim N( X\beta + Zu, \sigma^2 ...

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@GaelLaurans makes a good point that you are thinking of this as a repeated-measures analysis, but you are actually fitting a regular ANOVA. Thus, this isn't the problem of how to correctly determine the denominator's degrees of freedom (which is what I had linked to in my comment above). I think the issue here is simpler. You have four data points, ...

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