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The nonparametric Behrens‐Fisher problem with dependent replicates
Author(s) -
Roy Akash,
Harrar Solomon W.,
Konietschke Frank
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8343
Subject(s) - nonparametric statistics , mathematics , categorical variable , estimator , statistics , sample size determination , null hypothesis , metric (unit) , statistical hypothesis testing , sample (material) , asymptotic analysis , econometrics , operations management , chemistry , chromatography , economics
Purely nonparametric methods are developed for general two‐sample problems in which each experimental unit may have an individual number of possibly correlated replicates. In particular, equality of the variances, or higher moments, of the distributions of the data is not assumed, even under the null hypothesis of no treatment effect. Thus, a solution for the so‐called nonparametric Behrens‐Fisher problem is proposed for such models. The methods are valid for metric, count, ordered categorical, and even dichotomous data in a unified way. Point estimators of the treatment effects as well as their asymptotic distributions will be studied in detail. For small sample sizes, the distributions of the proposed test statistics are approximated using Satterthwaite‐Welch‐type t ‐approximations. Extensive simulation studies show favorable performance of the new methods, in particular, in small sample size situations. A real data set illustrates the application of the proposed methods.