Environmental and Ecological Statistics

, Volume 7, Issue 1, pp 43–56 | Cite as

Robust trend tests with application to toxicology

  • Markus Neuha¨user
  • Dirk Seidel
  • Ludwig A. Hothorn
  • Wolfgang Urfer


In most real data situations in the one-way design both the underlying distribution and the shape of the dose-response curve are a priori unknown. The power of a trend test strongly depends on both. However, tests which are routinely used to analyze toxicological assays must be robust. We use nonparametric tests with different scores—powerful for different distributions—and different contrasts—powerful for different shapes—and use the maximum of all test statistics as a new test statistic. Simulation results indicate that this maximum test, which is a nonparametric multiple contrast test, stabilizes the power for various shapes and distributions. The investigated tests are applied to the data of a toxicological assay.

maximum test multiple contrast test nonparametric model toxicological assays unknown dose-response shape 


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  1. Berry, J.J. (1995) A simulation-based approach to some nonparametric statistics problems. Observations, 5, 19-26.Google Scholar
  2. Cox, D.R. (1977) The role of significance tests. Scandinavian Journal of Statistics, 4, 49-70.Google Scholar
  3. Erickson, W.P. and McDonald, L.L. (1995) Tests for bioequivalence of control media and test media in studies of toxicity. Environmental Toxicology and Chemistry, 14, 1247-1256.Google Scholar
  4. Fligner, M.A. and Wolfe, D.A. (1982) Distribution-free tests for comparing several treatments with a control. Statistica Neerlandica, 36, 119-127.Google Scholar
  5. Gad, S. and Weil, C.S. (1986) Statistics and Experimental Design for Toxicologists, Telford Press, Caldwell.Google Scholar
  6. Gastwirth, J.L. (1965) Percentile modifications of two-sample rank tests. Journal of the American Statistical Association, 60, 1127-1140.Google Scholar
  7. Good, P.I. (1994) Permutation Tests, Springer, New York.Google Scholar
  8. Hettmansperger, T.P. and Norton, R.M. (1987) Tests for patterned alternatives in k-sample problems. Journal of the American Statistical Association, 82, 292-299.Google Scholar
  9. Hogg, R.V., Fisher, D.M., and Randles, R.H. (1975) A two-sample adaptive distribution-free test. Journal of the American Statistical Association, 70, 656-661.Google Scholar
  10. Hothorn, L.A. (1994) Biostatistical analysis of the micronucleus mutagenicity assay based on the assumption of a mixing distribution. Environmental Health Perspectives, 102(Supplement 1), 121-125.Google Scholar
  11. Hothorn, L.A., Neuhäuser, M., and Koch, H.-F. (1997) Analysis of randomized dose-finding-studies: Closure test modifications based on multiple contrast tests. Biometrical Journal, 39, 467-479.Google Scholar
  12. Robertson, T., Wright, F.T., and Dykstra, R.L. (1988) Order Restricted Statistical Inference, Wiley, New York.Google Scholar
  13. Ruberg, S.J. (1989) Contrasts for identifying the minimum effective dose. Journal of the American Statistical Association, 84, 816-822.Google Scholar
  14. Tamhane, A.C., Hochberg, Y., and Dunnett, C.W. (1996) Multiple test procedures for dose finding. Biometrics, 52, 21-37.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Markus Neuha¨user
    • 1
  • Dirk Seidel
    • 2
  • Ludwig A. Hothorn
    • 2
  • Wolfgang Urfer
    • 3
  1. 1.Department of BiometryByk Gulden PharmaceuticalsKonstanzGermany
  2. 2.Research Unit BioinformaticsUniversity of HannoverHannoverGermany
  3. 3.Department of StatisticsUniversity of DortmundDortmundGermany

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