Modifications of and Revised Critical Values for the Half-Normal Plot

The original version of the half-normal plot C. Daniel, Technometrics, t, (1959), 311–34 is reviewed and two modified versions are introduced. The modified versions incorporate corrections of a major flaw in the original version relating to critical values and a minor flaw relating to plotting positions. The critical values given in this article control the probability error rate, the probability of at least one false positive in the analysis of an experiment, and are considerably different from those given by Daniel. One of the modified versions is more powerful than Daniel's original procedure. Anothe improvement made in the modified versions is that only the smallest 70%, of the contrasts not declared significant, are used to constuct the final estimate of the error variance. This results in an appreciable redaction in the mean square error of this estimate. Examples are plesented to illustrate the use of the various half-normal plot versions.