Trellis display for modeling data from designed experiments

Visualizing data by graphing a response against certain factors, and conditioning on other factors, has arisen independently in many contexts. One is the interaction plots used in the analysis of data from designed experiments; these plots show conditional dependence based on the output of methods and models applied to the data. Trellis display, a framework for the visualization of multivariable data, allows conditioning to be readily carried out in a general way. It was developed initially in the context of data sets with a moderate or large number of observations to support the conditioning. This article demonstrates through examples that trellis display is also a highly useful visualization framework for designed experiments with a small number of runs. Trellis allows the visualization of conditional dependence, not only based on the output of models and methods, but also based on the raw data directly, which greatly aids the model building process. Trellis can even succeed for highly fractionated designs. The reason appears to be that for success, such designs require an engineering practice that keeps error variability small, which allows interpretable patterns to emerge on conditioning displays with a limited number of plotted points.  2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 133–145, 2011