Allocating Observations in the Random Effects Balanced One-Way ANOVA

Article

Pignatiello, Joseph J. Jr.   (1987, ASQC)   University of Arizona

Journal of Quality Technology    Vol. 19    No. 4
QICID: 5572    October 1987    pp. 216-220
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Article Abstract

To design a random effects one-way analysis of variance experiment one needs to determine both a, the number of treatments that are to be included in the experiment, as well as n, the number of times that each treatment is to be replicated needs to be determined since the number of treatments of interest is already fixed. We consider the problem of designing a random effects experiment where the total number of observations, N, is fixed and the power of the F-test is to be maximized. This problem is simple when one knows a priori the value of the error standard deviation. We present a method which allows the experimenter to state a distribution for the error standard deviation. Our objective is then to find the experimental design which maximizes the expected power.

Keywords

Sample size,Statistics,Design of experiments (DOE),Power of tests


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