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A Multivariate Rank-Based Two-Sample Test Statistic

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A Celebration of the EDGE Program’s Impact on the Mathematics Community and Beyond

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 18))

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Abstract

The problem of testing whether two samples come from the same or different populations is a classical one in statistics. A new distribution-free test based on standardized ranks for the univariate two-sample problem is studied. Providing a distribution-free (nonparametric) method offers a valuable technique for analyzing data that consists of ranks or relative preferences of data, and of data that are small samples from unknown distributions. The proposed test statistic examines the difference between the average of between-group rank distances and the average of within-group rank distances. This test statistic is closely related to the classical two-sample Cramér–von Mises criterion; however, they are different empirical versions of the same quantity for testing the equality of two population distributions. The advantage of the proposed rank-based test over the classical one is its ease to generalize to the multivariate case. In addition, the motivation of the proposed test is its application to microarray analyses in identifying sets of genes that are differentially expressed in various biological states, such as diseased versus non-diseased. A numerical study is conducted to compare the power performance of the rank formulation test with other commonly used nonparametric tests.

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Author information

Authors and Affiliations

  1. Georgia Gwinnett College, Lawrenceville, GA, USA

    Jamye Curry

  2. University of Mississippi, University, MS, USA

    Xin Dang & Hailin Sang

Authors
  1. Jamye Curry
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  2. Xin Dang
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  3. Hailin Sang
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Corresponding author

Correspondence to Jamye Curry .

Editor information

Editors and Affiliations

  1. Science Writing Advanced Academic Program, John Hopkins University, Baltimore, MD, USA

    Susan D'Agostino

  2. Department of Mathematics and Computer Science, Dickinson College, Carlisle, PA, USA

    Sarah Bryant

  3. Department of Mathematics, University of San Diego, San Diego, CA, USA

    Amy Buchmann

  4. Department of Mathematics and Computer Science, Belmont University, Nashville, TN, USA

    Michelle Craddock Guinn

  5. Division of Sciences and Mathematics, University of the District of Columbia, Washington, DC, USA

    Leona Harris

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© 2019 The Author(s) and the Association for Women in Mathematics

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Curry, J., Dang, X., Sang, H. (2019). A Multivariate Rank-Based Two-Sample Test Statistic. In: D'Agostino, S., Bryant, S., Buchmann, A., Guinn, M., Harris, L. (eds) A Celebration of the EDGE Program’s Impact on the Mathematics Community and Beyond . Association for Women in Mathematics Series, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-030-19486-4_16

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