A fully nonparametric method is developed for comparing samples with partially paired data. Partially-paired (correlated) data naturally arise, for example, as a result of missing values, in incomplete block designs or meta analysis. In the nonparametric setup, treatment effects are characterized in terms of functionals of distribution functions and the only assumption needed is that the marginal distributions are non-degenerate. The setup accommodates binary, ordered categorical, discrete and continuous data in a seamless fashion. The use of nonparametric effects addresses the Behrens–Fisher problem from the nonparametric point of view and allows construction of confidence intervals. Although the nonparametric methods are mainly asymptotic, methods for small sample approximations are also proposed. Size and power simulation results show numerical evidence of favorable performance of the nonparametric methods. The new nonparametric method has overwhelming power advantage when treatment effects are in the shape of the distributions and they perform comparably well with parametric methods for location-type alternatives. Data from randomized trials in public health are used to illustrate the application of the method.
|Journal||Computational Statistics and Data Analysis|
|State||Published - Apr 2020|
Bibliographical noteFunding Information:
The authors are grateful to the associate editor and the three anonymous referees for critically reading the original version of the manuscript and making valuable suggestions that led to substantial improvements. The authors are also thankful to the editor for the orderly handling of the manuscript. The authors would like to express their gratitude to Prof. Derek S. Young for his willingness and time to read through the final version of manuscript and make editorial suggestions. Part of the the research of Merga B. Feyasa was done while holding a visiting student positions at the University of Kentucky (UK). He is thankful to the Department of Statistics at UK and the College of Natural and Computational Sciences of Addis Ababa University for providing support for the visits.
© 2019 Elsevier B.V.
- Missing data
- Paired comparison
- Rank methods
- Relative treatment effect
ASJC Scopus subject areas
- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics