Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments

Abstract

Plotting the empirical cumulative distribution of the usual set of orthogonal contrasts computed from a 2 p experiment on a special grid may aid in its criticism and interpretation. Bad values, heteroscedasticity, dependence of variance on mean, and some types of defective randomization, all leave characteristic stigmata. The halfnormal plot can be used to estimate the error standard deviation and to make judgments about the reality of the observed effects. An accompanying paper by A. Birnbaum gives some operating characteristics of these judgments. Examples are given of the use of half-normal plots in each of these ways.