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In linear models and particularly in ANOVA, a contrast is a linear combination of parameters with coefficients summing up to zero. It is used to test the corresponding null hypothesis. Contrasts are especially often used with categorical predictors (factors) to make comparisons among the groups (categories). [See also tag 'categorical-encoding']

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How to perform a 4 by 4 mixed ANOVA with between- and within-subjects contrasts using R?

Compare groups using custom contrasts (as in an LMATRIX command in SPSS). Compare different levels of DV using custom contrasts (as in an MMATRIX command in SPSS). … Run a set of contrasts that do NOT sum to zero. I know I can do this in SPSS without much of a problem, but I can't get a clear idea of how to do this in R. …
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