Designing, understanding and modelling two-phase experiments with human subjects

In a recent paper, Jarrett, Farewell and Herzberg discussed a strategy for developing the analysis of a previously published two-phase experiment that investigated the effect of training on pain rating by occupational and physical therapy students. Here, their example is used to illustrate how a multi-step factor-allocation paradigm can be employed (i) to design an experiment, (ii) to understand the confounding in the design and (iii) to formulate linear mixed models, called prior allocation models, for the design. These models are intended as starting models for the analysis of the data, when it becomes available. An understanding of the confounding intrinsic to a design is achieved through an anatomy of the design presented in an analysis-of-variance-style table that can be obtained using functions from the $$ package $$. The analysis of the pain-rating experiment is re-examined and it is recommended that conclusions be based on a model with heterogeneous residual variances, in addition to the previously proposed block-treatment interactions. The paradigm is also used in producing an alternative design, taking into account the results of the re-analysis.