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Abgeschlossene multiple Spannweitentests

Closed Multiple Range Tests

  • Conference paper
Multiple Hypothesenprüfung / Multiple Hypotheses Testing

Part of the book series: Medizinische Informatik und Statistik ((MEDINFO,volume 70))

Zusammenfassung

In dieser Arbeit wird ein abgeschlossener multipler Spannweitentest zum paarweisen Vergleich von k Lokationsparametern vorgestellt, der auf einer konsequenten Anwendung des Abschlußprinzips beruht. Im Gegensatz zu dem von Begun/Gabriel (1981) vorgestellten Abschluß des NewmanKeuls Tests im ANOVA-Modell werden für die Partitionshypothesen Maxima von Spannweitenstatistiken verwendet. Durch eine Reihe von theoretischen Ergebnissen wird die Zahl der zu prüfenden Hypothesen so reduziert, daß sich Probleme mit bis zu 20 Lokationsparametern bequem lösen lassen. Speziell für das ANOVA-Modell wurden umfangreiche Tafeln für die verwendeten Verteilungen und ein Programm zur Durchführung der Testprozedur erstellt.

Summary

In this paper a closed multiple range test for comparing k location-parameters is proposed, which is a consequent employment of the closure principle. In contrast to the dosed Newman-Keuls test for the ANOVA-model of Begun/Gabriel (1981), maxima of range statistics are used for the partition hypotheses. With a series of theoretical results it is possible to reduce the number of hypotheses to be tested, such that problems with up to 20 location parameters may be solved. In the special case of the ANOVA-model extensive tables for the used distributions and a program for carrying out the procedure are provided.

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Literaturverzeichnis

  • ABRAMOWITZ, M., STEGUN, I.A. (1968). Handbook of Mathematical Functions. Dover Publications, Inc., New York.

    Google Scholar 

  • BEGUN, J.M., GABRIEL, K.R. (1981). Closure of the Newman-Keuls multiple comparisons procedure. J. Am. Statist. Assoc. 76, 241–245.

    MathSciNet  Google Scholar 

  • FINNER, H. (1988). Multiple Spannweitentests. Dissertation. Universität Trier, FB IV, Mathematik.

    Google Scholar 

  • HARTER, H.L. (1960). Tables of range and studentized range. Ann. Math. Statist. 31, 1122–1147.

    MathSciNet  MATH  Google Scholar 

  • HARTLEY, H.O. (1942). The range in random samples. Biometrika 32, 334–348.

    MathSciNet  Google Scholar 

  • HAYTER, A.J. (1986). The maximum familywise error rate of Fisher’s least significance difference test. J. Am. Statist. Assoc. 81, 1000–1004.

    MathSciNet  MATH  Google Scholar 

  • KERRIDGE, D.F., COOK, G.W. (1976). Yet another series for the normal integral. Biometrika 63, 401–403.

    Article  MATH  Google Scholar 

  • KEULS, M. (1952). The use of the studentized range in connection with an analysis of variance. Euphytica 1, 112–122.

    Article  Google Scholar 

  • LACKRITZ, J.R. (1984). Exact p-values for F and t-tests. Am. Statistician 38, 312–314.

    Google Scholar 

  • LEHM,ANN, E.L., SHAFFER, J.P. (1977). On a fundamental theorem in multiple comparisons. J. Am. Statist. Assoc. 72, 576–578.

    MathSciNet  MATH  Google Scholar 

  • MARCUS, R., PERITZ, E., GABRIEL, K.R. (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika 63, 655–660.

    Article  MathSciNet  MATH  Google Scholar 

  • MILLER, R.G. (1966). Simultaneous Statistical Inference. New York: Mc Graw-Hill.

    MATH  Google Scholar 

  • NEWMAN, D. (1939). The distribution of range in samples from a normal population, expressed in terms of an independent estimate of standard deviation. Biometrika 31, 20–30.

    MathSciNet  MATH  Google Scholar 

  • PEARSON, E.S., HARTLAY, H.O. (1976). Biometrika Tables for Statisticians. Biometrika Trust.

    Google Scholar 

  • PERITZ, E. (1970). A note on multiple comparisons. Unpublished Paper. Hebrew University.

    Google Scholar 

  • ROY, S.N. (1953). On a heuristic method of test construction and its use in a multivariate analysis. Ann. Math. Statist. 24, 220–238.

    MATH  Google Scholar 

  • ROYEN, T. (1987). Eine verschärfte Holm-Prozedur zum Vergleich aller Mittelwertpaare. EDV in Med. u. Biologie 18, 45–49.

    MathSciNet  Google Scholar 

  • RYAN, T.A. (1960). Significance tests for multiple comparison of proportions, variances, and other statistics. Psychological Bulletin 57, 318–328.

    Article  Google Scholar 

  • SHAFFER, J.P. (1984). Issues arising in multiple comparisons among population. Proceedings of the Seventh Conference on Probability Theory, 353–362. Ed. M. Josifescu, Bucharest, Romania: Editoria Acadimiei Republicii Socialiste Romania.

    Google Scholar 

  • SHAFFER, J.P. (1986). Modified sequentially rejective multiple test procedures. J. Am. Statist. Assoc. 81, 826–831.

    MATH  Google Scholar 

  • SONNEMANN, E. (1982). Allgemeine Lösungen multipler Testprobleme. EDV in Med. and Biologie 13, 120–128.

    MathSciNet  Google Scholar 

  • TUKEY, J.W. (1953). The problem of multiple comparisons. Unpublished manuscript.

    Google Scholar 

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Author information

Authors and Affiliations

  1. FB IV — Mathematik/Statistik, Universität Trier, Postfach 38 25, D-5500, Trier, Deutschland

    Helmut Finner

Authors
  1. Helmut Finner
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Editor information

Editors and Affiliations

  1. Institut für Medizinische Dokumentation und Statistik, Universität zu Köln, Joseph-Stelzmann-Straße 9, 5000, Köln 41, Germany

    P. Bauer

  2. Institut für Medizinische Statistik und Dokumentation, Universität Mainz, Langenbeckstraße 1, 6500, Mainz, Germany

    G. Hommel

  3. FB IV — Abteilung Mathematik, Universität Trier, Postfach 3825, 5500, Trier, Germany

    E. Sonnemann

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© 1988 Springer-Verlag Berlin Heidelberg

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Finner, H. (1988). Abgeschlossene multiple Spannweitentests. In: Bauer, P., Hommel, G., Sonnemann, E. (eds) Multiple Hypothesenprüfung / Multiple Hypotheses Testing. Medizinische Informatik und Statistik, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52307-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-52307-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50559-4

  • Online ISBN: 978-3-642-52307-6

  • eBook Packages: Springer Book Archive

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