Abstract
In combining several test statistics, arising, for instance, from econometrical analyses of panel data, often a direct multivariate combination is not possible, but the corresponding p-values have to be combined. Using the inverse normal and inverse chi-square transformations of the p-values, combining methods are considered that allow the statistics to be dependent. The procedures are based on a modified Gauss test for correlated observations which is developed in the present paper. This is done without needing further information about the correlation structure. The performance of the procedures is demonstrated by simulation studies and illustrated by a real-life example from pharmaceutical industry.
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Berk, R. H., & Jones, D. H. (1978). Relatively optimal combinations of test statistics. Scandinavian Journal of Statistics, 5, 158–162.
Demetrescu, M., Hassler, U., & Tarcolea, A.-I. (2006). Combining significance of correlated statistics with application to panel data. Oxford Bulletin of Economics and Statistics, 68, 647–663.
Hartung, J. (1981). Nonnegative minimum biased invariant estimation in variance component models. The Annals of Statistics, 9, 278–292.
Hartung, J. (1999). A note on combining dependent tests of significance. Biometrical Journal, 41, 849–855.
Hartung, J., Elpelt, B.,& Klösener, K.-H. (2009). Chapter XV: Meta-Analyse zur Kombination von Studien. Experimenten und Prognosen. In Statistik Lehr- und Handbuch der angwandten Statistik (15th ed.). München: Oldenbourg.
Hartung, J., Knapp, G., & Sinha, B. K. (2008). Statistical meta-analysis with applications. New York: Wiley.
Hartung, J., & Voet, B. (1986). Best invariant unbiased estimators for the mean squared error of variance component estimators. Journal of the American Statistical Association, 81, 689–691.
Hedges, L.V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando: Academic Press.
Marden, J. I. (1991). Sensitive and sturdy p-values. The Annals of Statistics, 19, 918–934.
Mathai, A. M., & Provost, S. B. (1992). Quadratic forms in random variables. New York: Marcel Dekker.
Seely, J. (1971). Quadratic subspaces and completeness. The Annals of Mathematical Statistics, 42, 710–721.
Weyer, G., Erzigkeit, H., Hadler, D., & Kubicki, S. (1996). Efficacy and safety of idebenone in the longterm treatment of Alzheimer’s disease: A double-blind, placebo controlled multi-centre study. Human Psychopharmacology, 11, 53–65.
Wilson, E. B., & Hilferty, M. M. (1931). The distribution of chi-square. Proceedings of the National Academy of Sciences, 17, 684–688.
Acknowledgements
Thanks are due to Takeda Euro Research and Development Centre for the permission to publish the homogeneity results presented in Sect. 5.
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Hartung, J., Elpelt-Hartung, B., Knapp, G. (2015). A Modified Gauss Test for Correlated Samples with Application to Combining Dependent Tests or P-Values. In: Beran, J., Feng, Y., Hebbel, H. (eds) Empirical Economic and Financial Research. Advanced Studies in Theoretical and Applied Econometrics, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-03122-4_9
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DOI: https://doi.org/10.1007/978-3-319-03122-4_9
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