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The number of decision sets involving n means. (English) Zbl 0652.90003

A decision set is the result of the multiple comparison of n means. The means are placed in order in a diagram and a line is drawn under those that are not significantly different. In this paper, we show how the number of decision sets involving n means can be calculated.

MSC:

91B06 Decision theory
05A17 Combinatorial aspects of partitions of integers
Full Text: DOI

References:

[1] Carlitz, L., Solution of certain recurrences, S.I.A.M. J. Appl. Math., 17, 251-259 (1969) · Zbl 0177.02101
[2] Dale, M. R.T.; Narayana, T. V., Nonparametric tests for Catalan Sequences, J. Statist. Plann. Inference, 14, 43-47 (1985) · Zbl 0592.62038
[3] MacMahon, P. A., Combinatory Analysis (1960), Chelsea Publishing Company: Chelsea Publishing Company New York, (originally published in 1915 by the Cambridge University Press) · Zbl 0101.25102
[4] Motzkin, T. H., Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance and for non-associat ed products, Bull. Amer. Math. Soc., 54, 352-361 (1948) · Zbl 0032.24607
[5] Wine, R. L.; Freund, J. E., On the enumeration of decision patterns involving \(n\) means, Ann. Math. Statist., 28, 256-259 (1957) · Zbl 0078.00905
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