Analysis of data from non-orthogonal multistratum designs in industrial experiments

Split-plot and other multistratum structures are widely used in factorial and response surface experiments. Residual maximum likelihood (REML) and generalized least squares (GLS) estimation is seen as the state of the art method of data analysis for non-orthogonal designs. We analyse data from an experiment that was run to study the effects of five process factors on the drying rate for freeze-dried coffee and find that the main plot variance component is estimated to be 0. We show that this is a typical property of REML–GLS estimation in non-orthogonal split-plot designs with few main plots which is highly undesirable and can give misleading conclusions. Instead, we recommend a Bayesian analysis, using an informative prior distribution for the main plot variance component and implement this by using Markov chain Monte Carlo sampling. Paradoxically, the Bayesian analysis is less dependent on prior assumptions than the REML–GLS analysis. Bayesian analyses of the coffee freeze-drying data give more realistic conclusions than REML–GLS analysis, providing support for our recommendation.