Applying a fixed-random continuum in multi-factorial mixed-model inference
Generally, researchers working in applied disciplines consider it extremely important carefully to identify each factor that is present in a multi-factorial mixed-model ANOVA context as being either fixed or random. The choice is an important one for purposes of specifying the parameterisation of the analysis, and also has consequences for things such as: (i) the expectations of mean squares for each term in the model; (ii) the construction of suitable F-ratios for tests of relevant hypotheses and (iii) the nature and extent of the inferences arising from such tests. However, Cornfield & Tukey (1956) long ago described a continuum between a fixed and a random factor, identifiable from the ratio of the number of levels of a factor divided by the number of possible levels from the population of interest. Here, I will describe a generalisation of their original approach to allow extension to higher-way multi-factorial designs. I will give an ecological example of its use, and will demonstrate the concomitant increase in power that this approach can afford.