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Wu, Shu-Fei; Chen, Hubert J.

Multiple comparisons with the average for normal distributions. (English) Zbl 0913.62061

Am. J. Math. Manage. Sci. 18, No. 1-2, 193-218 (1998).
Summary: We propose some multiple comparison procedures with the average. Simultaneous confidence intervals are considered for normal distributions with common known or unknown variances. These procedures can be used to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, stock market, medical research, and auto models. The percentage points for singular multivariate normal and multivariate \(t\) distributions are investigated. Furthermore, the case of normal distributions under heteroscedasticity is also developed. An example is given.

Cited in 2 Documents

MSC:

62J15 Paired and multiple comparisons; multiple testing
62F25 Parametric tolerance and confidence regions

Keywords:

probability requirement; better-than-the-average; Monte-Carlo techniques; Bonferroni inequality; confidence intervals; tables
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References:

[1] Chen H. J., Journal of American Statistical Association 71 pp 752– (1976) · doi:10.1080/01621459.1976.10481561
[2] Chen H. J., Communications in Statistics - Theory and Methods 18 (10) pp 3703– (1989) · Zbl 0696.62165 · doi:10.1080/03610928908830118
[3] Dudewicz E. J., Sankhya, Ser. B. 37 pp 28– (1975)
[4] Dudewicz E. J., American Journal of Mathematical and Management Sciences 4 (3) pp 335– (1984)
[5] Halperin M., Journal of American Statistical Association 50 pp 185– (1955)
[6] Hochberg Y., Multiple Comparison Procedures. (1987) · Zbl 0731.62125 · doi:10.1002/9780470316672
[7] Lam K., The Frontiers of Modern Statistical Inference Procedures, II pp 307– (1992)
[8] Marsaglia G., A current view of randomnumber generators, Computer Science and Statistics: Proc. 16th Symp. Interface, Atlanta, March 1984 (1986)
[9] Marsaglia G., Statistics and Probability Letters 8 pp 35– (1990) · Zbl 0692.65001 · doi:10.1016/0167-7152(90)90092-L
[10] Nair K. R., Biometrika 35 pp 118– (1948)
[11] Nelson L. S., Journal of Quality Technology 15 pp 40– (1983)
[12] Nelson P. R., Communications in Statistics-Theory and Methods 11 pp 699– (1982) · Zbl 0506.62100 · doi:10.1080/03610928208828263
[13] Nelson P. R., Communications in Statistics - Simulation and Computation 11 (2) pp 239– (1982) · Zbl 0505.62011 · doi:10.1080/03610918208812260
[14] Nelson P. R., Technometrics 35 pp 61– (1993) · doi:10.1080/00401706.1993.10484994
[15] Steck G. P., Biometrika pp 269– (1962)
[16] Stein C. M., Annals of Mathematical Statistics 16 pp 243– (1945) · Zbl 0060.30403 · doi:10.1214/aoms/1177731088
[17] Tong Y. L., Probability Inequalities in Multivariate Distributions. (1980) · Zbl 0455.60003
[18] Wen M. J., American Journal of Mathematical and Management Sciences. 14 (1) pp 1– (1994)
[19] Wu S. F., Multiple comparison procedures with the average, normal means (1994)
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