An Empirical Study of the Half-Normal Plot

Abstract

Monte Carlo studies of a modification of the original version of the half-normal plot (Daniel, Technometrics, 1 (1959), 311–341) and four new versions are reported. Data representative of the 15 contrasts from a 2^p–q , p – q = 4, factorial experirnenl. are generated. Design parameters in the Main Simiulation Study are the probability error rate, the number of real contrasts, and the size of the real contrasts.

The critical values used by the various versions control the probability error rate. These critical values are considerably different, than those given by Daniel.

The Monte Carlo strtdies indicate that the detection rate, i.e., the proportion of real contrasts declared significant, is larger for one of the new versions than for the original version. The detection rate of all versions decreases drastically when the number of real contrasts present increases from one to two to four.

Nomination procedures for analyzing single replication 2⁴ factorial experiments have a smaller detection rate than the half-normal plot with an eqrlivalent probability error rate, unless the experimenter can accuately nominate ten error contrasts in the 2⁴ experiment.

KEY WORDS:

• Critical Vahles
• Detection Rate
• Graphical Statistical Procedure
• Half-Normal Plot
• Monte Carlo
• Nomination
• Probability Error Rate
• Variance Estimation