Abstract
The paper is mainly concerned with multiple testing procedures which control a given multiple level α. General concepts for this purpose are the closure test and a modification which is independent of the special structure of hypotheses and tests. We consider improvements of this modification using information about the logical dependences (redundancies) within the system of hypotheses and present an efficient algorithm. Finally, we discuss some problems which are specific for hierarchical systems of hypotheses, e.g. in model search.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akaike H., A new look at the statistical model identification, IEEE Transactions on Automation and Control 19 (1974), 716–723.
Alt R., Hierarchical test problems and the closure principle, Multiple Hypothesenprüfung — Multiple Hypotheses Testing (Bauer P., Hommel G. and Sonnemann E., eds.), Springer, Berlin/Heidelberg/New York, 1988, pp. 162–176.
Bauer P. and Hackl P., Multiple testing in a set of nested hypotheses, Statistics 18 (1987), 345–349.
Bauer P., Pötscher B. M. and Hackl P., Model selection by multiple test procedures, Statistics 19 (1988), 39–44.
Bergmann B. and Hommel G., Improvements of general multiple test procedures for redundant systems of hypotheses, Multiple Hypothesenprüfung — Multiple Hypotheses Testing (Bauer P., Hommel G. and Sonnemann E., eds.), Springer, Berlin/Heidelberg/New York, 1988, pp. 100–115.
Bernhard G., Computergestützte Durchführung von multiplen Testprozeduren — Algorithmen und Powervergleich, Universität Mainz, Mainz, 1992. (Doctoral thesis.)
Box G.E. P. and Hill W. J., Discriminating among mechanistic models, Technometrics 9 (1967), 57–71.
Cox, D. R. and Spjøtvoll E., On partitioning means into groups, Scandinavian Journal of Statistics 9 (1982), 147–152.
Dunnett C.W., A multiple comparison procedure for comparing several treatments with a control, Journal of American Statistical Association 50 (1955), 1096–1121.
Dunn O. J., Multiple comparisons among means, Journal of American Statistical Association 56 (1961), 52–64.
Fisher R. A., Statistical Methods for Research Workers, Oliver & Boyd, Edinburgh, 1925.
Fisher R. A., The Design of Experiments, Oliver & Boyd, Edinburgh, 1935.
Gabbert H. E., Meier S., Gerharz C. D. and Hommel G., Tumor cell dissociation at the invasion front: a new progostic parameter in gastric cancer patients, International Journal of Cancer 50 (1992), 202–207.
Hartung J., Statistik, Lehr- und Handbuch der angewandten Statistik, Oldenbourg, München/Wien, 1987. (6th ed.)
Hochberg Y. and Tamhane A.C., Multiple Comparison Procedures, J. Wiley, New York, 1987.
Holm S., A simple sequentially rejective multiple test procedure, Scandinavian Journal of Statistics 6 (1979), 65–70.
Hommel G., Tests of the overall hypothesis for arbitrary dependence structures, Biometrical Journal 25 (1983), 423–430.
Hommel G., Multiple test procedures for arbitrary dependence structures, Metrika 33 (1986), 321–336.
Hommel G., A stagewise rejective multiple test procedure based on a modified Bonferroni test, Biometrika 75 (1988), 383–386.
Hunter D., An upper bound for the probability of a union, Journal of Applied Probability 13 (1976), 597–603.
Kalbfleisch J.D. and Prentice R. L., The Statistical Analysis of Failure Time Data, J. Wiley, New York, 1980.
Keuls M., The use of the“Studentized range” in connection with an analysis of variance, Euphytica 1 (1952), 112–122.
Mallows C.L., Some comments on C p , Technometrics 15 (1973), 661–675.
Marcus R., Peritz E. and Gabriel K.R., On closed testing procedures with special reference to ordered analysis of variance, Biometrika 63 (1976), 655–660.
Maurer W. and Mellein B., On new multiple tests based on independent p-values and the assessment of their power, Multiple Hypothesenprüfung — Multiple Hypotheses Testing (Bauer P., Hommel G. and Sonnemann E., eds.), Springer, Berlin/Heidelberg/New York, 1988, pp. 48–66.
Miller R. G., Simultaneous Statistical Inference, Springer, New York, 1981. (2nd ed.)
Newman D., The distribution of the range in samples from a normal population, expressed in terms of an independent estimate of standard deviation, Biometrika 31 (1939), 20–30.
Rüger B., Das maximale Signifikanzniveau des Tests:“Lehne Ho ab, wenn k unter n gegebenen Tests zur Ablehnung führen”, Metrika 25 (1978), 171–178.
Ryan T.A., Significance tests for multiple comparison of proportions, variances, and other statistics, Psychological Bulletin 57 (1960), 318–328.
Scheffé H., A method for judging all contrasts in the analysis of variance, Biometrika 40 (1953), 87–104.
Schiller K., Der Abschlu„stest zur Unterst“ utzung bei der Modellauswahl loglinearer Modelle, Multiple Hypothesenprüfung — Multiple Hypotheses Testing (Bauer P., Hommel G. and Sonnemann E., eds.), Springer, Berlin/Heidelberg/New York, 1988, pp. 177–189.
Shaffer J. P., Modified sequentially rejective multiple test procedures, Journal of American Statistical Association 81 (1986), 826–831.
Šidák Z., Rectangular confidence regions for the means of multivariate normal distributions, Journal of American Statistical Association 62 (1967), 626–633.
Simes R. J., An improved Bonferroni procedure for multiple tests of significance, Biometrika 73 (1986), 751–754.
Sonnemann E., Allgemeine Lösungen multipler Testprobleme, EDV in Medicine and Biologie 13 (1982), 120–128.
Tippett L. M. C., The Methods of Statistics, Williams & Norgate, London, 1931.
Tukey J. W., The Problem of Multiple Comparisons, 1953. (Unpublished manuscript.)
Westfall P. H. and Young S.S., P value adjustments for multiple tests in multivariate binomial models, Journal of American Statistical Association 84 (1989), 780–786.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Physica-Verlag Heidelberg
About this paper
Cite this paper
Hommel, G., Bernhard, G. (1993). Multiple Hypotheses Testing. In: Antoch, J. (eds) Computational Aspects of Model Choice. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-99766-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-99766-2_10
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0652-6
Online ISBN: 978-3-642-99766-2
eBook Packages: Springer Book Archive