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Robust Rank-Based and Nonparametric Methods pp 175–187Cite as

A New Scale-Invariant Nonparametric Test for Two-Sample Bivariate Location Problem with Application

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 168))

Abstract

Diagnostic testing in medicine is crucial in determining interventions and treatment plans. It is important to analyze diagnostic tests accurately so that the right decision can be made by clinicians. A scale-invariant test is proposed for when treatment and control samples are available and a change in condition between the treatment and control groups is investigated. The proposed test statistic is shown to have an asymptotically normal distribution. The power of the proposed test is compared with that of several existing tests using Monte Carlo simulation techniques under different bivariate population set-ups. The power study shows that the proposed test statistic performs very well as compared to its competitors for almost all the changes in location and for almost all the distributions considered in this study. The computation of proposed test statistic is shown using a real-life data set.

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Acknowledgements

Authors would like to thank the anonymous referee for his/her useful comments which enhanced the clarity of the paper and led to significant improvements in the paper.

Author information

Authors and Affiliations

  1. Department of Biostatistics and Epidemiology, Medical College of Georgia, Georgia Regents University, Augusta, GA, 30912-4900, USA

    Sunil Mathur & Deepak M. Sakate

  2. Department of Statistics, Buchtel College of Arts and Sciences, University of Akron, Akron, OH, 44325-1901, USA

    Sujay Datta

Authors
  1. Sunil Mathur
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  2. Deepak M. Sakate
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  3. Sujay Datta
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Corresponding author

Correspondence to Sunil Mathur .

Editor information

Editors and Affiliations

  1. Department of Statistics, Rutgers University, New Brunswick, New Jersey, USA

    Regina Y. Liu

  2. Department Statistics, Western Michigan University, Kalamazoo, Michigan, USA

    Joseph W. McKean

Appendix

Appendix

See Tables 10.2 and 10.3.

Table 10.2 Monte Carlo rejection proportion, sample size m = 15, n = 18
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Table 10.3 Monte Carlo rejection proportion, sample size m = 25, n = 28
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Mathur, S., Sakate, D.M., Datta, S. (2016). A New Scale-Invariant Nonparametric Test for Two-Sample Bivariate Location Problem with Application. In: Liu, R., McKean, J. (eds) Robust Rank-Based and Nonparametric Methods. Springer Proceedings in Mathematics & Statistics, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-319-39065-9_10

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