Is a "split plot" ANOVA with two factors identical to two-way ANOVA with repeated measures in one factor? if not, what is the distinction?
ANOVA with one repeated-measures factor and one between-groups factor is identical to ANOVA with 3 factors - the formerly repeated-measures factor, the between-groups factor, and the subjects (respondents' ID) factor nested in the previous one.
In SPSS, for instanse, three following commands are equivalent:
The case with one between factor, and one repeated-measures factor is one particular example that leads to a split-plot design. In this case, each observational unit (e.g., a participant in an experiment) is observed multiple times. One participant is one "whole plot" (or block). There are
Now, each whole block is split into multiple "sub-plots". Within each whole block, these sub-plots are treated according to the levels of a second experimental factor
There are three factors: The blocking factor
Importantly, there is a level of nesting, or confounding: Each level of the blocking factor is observed only in one condition of the between-factor
In agricultural terms (the origin of the design name), one whole plot is actually one area of land that is then subdivided into split-plots. In that case, the between factor
As you can see, one whole plot need not be one person observed multiple times. It's just that each whole plot is a homogeneous entity that can be split into sub-plots that are equivalent in some respect. In the social sciences, it could also be one group of subjects that is roughly homogeneous with respect to a nuisance variable, say socio-economic-status, or severity of the illness. In this case, each person within such a homogeneous group is then a split-plot.