Dive into diagnostics for DOE model discrepancies

Abstract

The purpose of running a statistically designed experiment (DOE) is to take a strategically selected small sample of data from a larger system, and then extract a prediction equation that appropriately models the overall system. The statistical tool used to relate the independent factors to the dependent responses is analysis of variance (ANOVA). This article will lay out the key assumptions for ANOVA and how to verify them using graphical diagnostic plots. The first assumption (and one that is often overlooked) is that the chosen model is correct. This means that the terms in the model explain the relationship between the factors and the response, and there are not too many terms (over-fitting), or too few terms (underfitting). One should not use the raw R-squared statistic as it is misleading. Please see Journal of Plastic Film& Sheeting Volume 37, Number 4, page 405, “R-squared mysteries solved” which explains how to interpret raw versus adjusted versus predicted R-squared.