Are Partially Nested, Repeated Measure and Split-Plot Designs Same/Different?
Table 6 provides a comparison among the most common advanced design of experiments, including nested, repeated measure and split-plot designs. Although some authors have possessed different views on the analysis models for these advanced level designs (Hicks, 1964; Montgomery, 2019), some believe that these designs can be analyzed by utilizing the exact same partially nested design model (Hinkelmann & Kempthorne, 2008; Kutner, 2005; Quinn & Keough, 2002). The example presented for each design in this text, we believe that the partially nested design model is the most appropriate model for each of these designs. However, there could be experimental situations in which different models could be more appropriate than the partially nested design model. Experimental conditions must decide the appropriate statistical analysis models. Perhaps, the disagreement among authors in using appropriate models for these designs have arisen from experimental conditions, and they all are appropriate in their own way. Interested learners could explore more and find their analysis models suitable for their design! Until then, a partially nested design model in Equation 2, Equation 3 and Equation 6 could be okay for the nested, repeated measure and split-plot designs.