From Wikipedia:

a mixed-design analysis of variance model (also known as a split-plot ANOVA) is used to test for differences between two or more independent groups whilst subjecting participants to repeated measures. Thus, in a mixed-design ANOVA model, one factor (a fixed effects factor) is a between-subjects variable and the other (a random effects factor) is a within-subjects variable. Thus, overall, the model is a type of mixed effect model.

My questions:

  1. What relation is between mixed design and split-plot design? Is a split-plot design a within-subject design, or a between-subject design, or both?
  2. Why is the model of a mixed design a mixed effect model? Which input variable has random effect and which input variable has fixed effect?

I'm sure terminology varies, but I think it's fair to say that a split-plot design (where there are two or more treatments imposed at different hierarchical levels) is a specific example of a mixed design. Mixed effect models (also called multilevel or hierarchical models; repeated measures are another special case) are so-called because they include both random and fixed effect terms.

I would say that split-plot designs are "both" between- and within-subject designs, because (at least) one treatment is between- and (at least) one treatment is within-subject.

In order to answer the other question one would need a more specific example.

  • $\begingroup$ +1 but I think one can answer Q2 as well: both between- and within- factors are treated as fixed, whereas the plot id (aka subject id) is a grouping variable that is treated as random. $\endgroup$
    – amoeba
    May 13 '19 at 15:23

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