An Empirical Study of the Half-Normal Plot
TLDR
Monte Carlo studies of a modification of the original version of the half-normal plot and four new versions are reported, indicating that the proportion of real contrasts declared significant, is larger for one of the new versions than for the original versions.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 2p–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 h...read more
Citations
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Analyzing unreplicated factorial experiments: a review with some new proposals
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Developments in Multiple Comparisons 1966–1976
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References
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Book
Simultaneous Statistical Inference
TL;DR: In this article, the authors presented a case of two means regression method for the family error rate, which was used to estimate the probability of a family having a nonzero family error.
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The design and analysis of industrial experiments
TL;DR: This paper is based on a lecture on the “Design and Analysis of Industrial Experiments” given by Dr O. L. Davies on the 8th of May 1954 and the recent designs developed by Box for the exploration of response surfaces are briefly considered.
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Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments
TL;DR: In this article, the empirical cumulative distribution of the usual set of orthogonal contrasts computed from a 2 p experiment on a special grid may be used to estimate the error standard deviation and to make judgments about the reality of the observed effects.
Journal ArticleDOI
A Convenient Method for Generating Normal Variables
George Marsaglia,T. A. Bray +1 more
TL;DR: In this article, a normal random variable X may be generated in terms of uniform random variables (i.e., X = 2(u_1+ u_2 + u_3 - 1.5) ), in 86 percent of the time.