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Ranking procedures for matched pairs with missing data — Asymptotic theory and a small sample approximation

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  • Konietschke, F.
  • Harrar, S.W.
  • Lange, K.
  • Brunner, E.
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    Abstract

    Nonparametric methods for matched pairs with data missing completely at random are considered. It is not assumed that the observations are coming from distribution functions belonging to a certain parametric or semi-parametric family. In particular, the distributions can have different shapes under the null hypothesis. Hence, the so-called nonparametric Behrens–Fisher problem for matched pairs with missing data is considered. Moreover, a new approach for confidence intervals for nonparametric effects is presented. In particular, no restriction on the ratio of the number of complete and incomplete cases is required to derive the asymptotic results. Simulations show that for arbitrary settings of complete data and missing values, the resulting confidence intervals maintain the pre-assigned coverage probability quite accurately. Regarding the power, none of the proposed tests is uniformly superior to the other. A real data set illustrates the application.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 5 ()
    Pages: 1090-1102

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:5:p:1090-1102

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Behrens–Fisher problem; Rank test; Nonparametric hypothesis; Ordered categorical data; Ties; Repeated measures design; Missing values;

    References

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    1. Konietschke, Frank & Brunner, Edgar, 2009. "Nonparametric analysis of clustered data in diagnostic trials: Estimation problems in small sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 730-741, January.
    2. Akritas, Michael G. & Antoniou, Efi S. & Kuha, Jouni, 2006. "Nonparametric Analysis of Factorial Designs With Random Missingness: Bivariate Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1513-1526, December.
    3. Yan Lin & Stuart Lipsitz & Debajyoti Sinha & Atul A. Gawande & Scott E. Regenbogen & Caprice C. Greenberg, 2009. "Using Bayesian "p"-values in a 2 × 2 table of matched pairs with incompletely classified data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(2), pages 237-246.
    4. Munzel, Ullrich, 1999. "Linear rank score statistics when ties are present," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 389-395, February.
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