Wybór najlepszych, ze względu na średnią, populacji normalnych

Joachim Cieślik; Mirosława Sitek

doi:10.18778/1898-6773.53.1-2.03

Authors

Joachim Cieślik Instytut Antropologii UAM, ul. Fredry 10, 61-701 Poznań
Mirosława Sitek Instytut Antropologii UAM, ul. Fredry 10, 61-701 Poznań

DOI:

https://doi.org/10.18778/1898-6773.53.1-2.03

Abstract

The work deals with the problem of choosing the best normal population in terms of the average. Two methods of choice are given depending on whether we are interested in choosing exactly one population or a subset including the best population. In both cases the probability of a correct decision P* depends on the amount of observations and the length of the confidence interval 6 for the highest mean. As regards the first method the length of the confidence interval & is fixed, whereas in the second method it is random. The method depends on whether the variances are known or not and whether they are identical or not. In the case of different and unknown variances only the two-stage method is allowed. The authors provide also an example illustrating the way of using both methods and tables of necessary critical values.

Downloads

Download data is not yet available.

References

BOFINGER E., 1979, Two stage selection problem for normal populations with unequal variances. The Australian Journal of Statistics, 21, 149-156. DOI: https://doi.org/10.1111/j.1467-842X.1979.tb01129.x

DUDEWICZ E. J., 1971, Non existance a single-sample selection procedure whose P(CS) is independent of the variances, South African Statistical Journal 5, 37-39.

DUDEWICZ E. J., S. R. DALAL. 1975, Allocation of observations in ranking and selection with unequal variances, Sankhya B., 37, 28-78.

DUNNETT C. W., 1955. A multiple comparison procedure for comparing several treatment with control, J. A mer. Statist. Assn., 50, 1096-1121. DOI: https://doi.org/10.1080/01621459.1955.10501294

GIBBONS J. D., J. OLKIN, M. SOBEL, 1977, Selecting and Oredring Populations: A New Statistical Methodology, J. Wiley & Sons.

GIBBONS J. D., J. OLKIN, M. SOBEL, 1979, An introduction to ranking and Selection, The American Statistican, 33, 185-195. DOI: https://doi.org/10.1080/00031305.1979.10482690

GUPTA S. S., 1963, Probability integrals of the multivariate normal and multivariate t. Ann. Math. Statist., 34, 792-828. DOI: https://doi.org/10.1214/aoms/1177704004

GUPTA S. S., 1965, On some multiple decision (selection and ranking) rules, Technometrics, 7, 225-245. DOI: https://doi.org/10.1080/00401706.1965.10490251

GUPTA S. S., K. NAGEL, S. PANCHAPAKESAN, 1973, On the order statistics from equally correlated random variables, Biometrika, 60, 403-413. DOI: https://doi.org/10.1093/biomet/60.2.403

GUPTA S. S., S. PANCHAPAKESAN, 1979, Multiple Decision Procedure: Theory and Methodology of Selecting and Ranking Populations, J. Wiley & Sons.

GUPTA S. S., M. SOBEL, 1957, On statistics which rises in selection and ranking problems, Ann. Math. Statist., 28, 957-967. DOI: https://doi.org/10.1214/aoms/1177706796

KRISHNAIAH P. R., 1965, Percentage points of the multivariate t-distributtion, Aerospace Research Laboratories Ohio, 500, 65-199.

OFOSU J. B., 1973, A two – sample procedure for selecting the population with the largest mean from several normal populations with unknown variances, Biometrika, 60, 117-124. DOI: https://doi.org/10.1093/biomet/60.1.117

RINOTT J., 1978, On two-stage selection procedures and related probability-inequalities, Commun. Statist. Theory Meth. A., 78, 799-811. DOI: https://doi.org/10.1080/03610927808827671