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October 2021

A Probability Plotting Procedure for General Analysis of Variance

Journal/Book: Reprinted from THE JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B (METHODOLOGICAL) Volume 32 No. 1 1970 (pp. 88-101). 1970;

Abstract: SUMMARY This paper describes a generalization of probability plotting to supplement general analysis of variance procedures. The mean squares in a general orthogonal analysis of variance are ordered and plotted against the corresponding expected values of standardized ordered mean squares. Since the mean squares may have differing degrees of freedom alternate conceptions are possible with respect to association of the ordered mean squares with their patent distributions. In considering the statistical distribution of the ith standardized ordered mean square the view adopted here is that of complete conditioning that is repeated sampling so constrained that the Order relationships of the sample mean squares is such that the ith ordered mean square comes from a 2(vi)/vi distribution for i = 1 ... K where K denotes the total number of mean squares in the collection and v1 v2 ... vK are the respective degrees of freedom of the ordered mean squares as observed. Using this completely conditioned distribution methods are described for computing the required plotting positions viz. the expected values of the standardized ordered mean squares. Some illustrative examples of use of the proposed procedure are given. ___MH


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