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Theorie und Methoden multipler statistischer Vergleiche

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  • Christina C. Bartenschlager
  • Michael Krapp

Abstract

As deciding on more than one null hypothesis based upon the same data set can provoke an inflation of the type I error rate, special methods for these multiple testing problems have been developed since Fisher (1935). Although highly relevant for different areas of research, especially for economics and the social sciences, multiple tests are relatively rarely applied. This paper, therefore, reviews and systematizes the evolution of theory and methods concerning multiple comparisons. We particu larly pursue the objective to sensitize users of statistics to the issues related to multiple testing. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Christina C. Bartenschlager & Michael Krapp, 2015. "Theorie und Methoden multipler statistischer Vergleiche," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(2), pages 107-129, November.
    • Handle: RePEc:spr:astaws:v:9:y:2015:i:2:p:107-129
    DOI: 10.1007/s11943-015-0166-9
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    1. Yoav Benjamini & Abba M. Krieger & Daniel Yekutieli, 2006. "Adaptive linear step-up procedures that control the false discovery rate," Biometrika, Biometrika Trust, vol. 93(3), pages 491-507, September.
    2. Dudoit Sandrine & van der Laan Mark J. & Pollard Katherine S., 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-71, June.
    3. van der Laan Mark J. & Birkner Merrill D. & Hubbard Alan E., 2005. "Empirical Bayes and Resampling Based Multiple Testing Procedure Controlling Tail Probability of the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, October.
    4. Ajit C. Tamhane & Lingyun Liu, 2008. "On weighted Hochberg procedures," Biometrika, Biometrika Trust, vol. 95(2), pages 279-294.
    5. van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-27, June.
    6. Mark van der Laan & Sandrine Dudoit & Katherine Pollard, 2004. "Multiple Testing. Part III. Procedures for Control of the Generalized Family-Wise Error Rate and Proportion of False Positives," U.C. Berkeley Division of Biostatistics Working Paper Series 1140, Berkeley Electronic Press.
    7. Sandrine Dudoit & Mark van der Laan & Katherine Pollard, 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," U.C. Berkeley Division of Biostatistics Working Paper Series 1137, Berkeley Electronic Press.
    8. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    9. Hochberg, Yosef, 1974. "Some generalizations of the T-method in simultaneous inference," Journal of Multivariate Analysis, Elsevier, vol. 4(2), pages 224-234, June.
    10. Thomas Ryan & William Woodall, 2005. "The most-cited statistical papers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(5), pages 461-474.
    11. Welsch, Roy E., 1977. "Tables for stepwise multiple comparison procedures," Working papers 949-77., Massachusetts Institute of Technology (MIT), Sloan School of Management.
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    1. Ralf Thomas Münnich, 2015. "Vorwort des Herausgebers," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 9(2), pages 79-81, November.

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