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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Approximate unconditional test procedure for comparing two ordered multinomials

Language

English

Abstract

The asymptotic and exact conditional methods are widely used to compare two ordered multinomials. The asymptotic method is well known for its good performance when the sample size is sufficiently large. However, Brown et al. (2001) gave a contrary example in which this method performed liberally even when the sample size was large. In practice, when the sample size is moderate, the exact conditional method is a good alternative, but it is often criticised for its conservativeness. Exact unconditional methods are less conservative, but their computational burden usually renders them infeasible in practical applications. To address these issues, we develop an approximate unconditional method in this paper. Its computational burden is successfully alleviated by using an algorithm that is based on polynomial multiplication. Moreover, the proposed method not only corrects the conservativeness of the exact conditional method, but also produces a satisfactory type I error rate. We demonstrate the practicality and applicability of this proposed procedure with two real examples, and simulation studies are conducted to assess its performance. The results of these simulation studies suggest that the proposed procedure outperforms the existing procedures in terms of the type I error rate and power, and is a reliable and attractive method for comparing two ordered multinomials. © 2010 Elsevier B.V. All rights reserved.

Keywords

Approximate unconditional test, Asymptotic test, Exact conditional test, Exact unconditional test, Two ordered Multinomials, Wilcoxon statistic

Publication Date

2011

Source Publication Title

Computational Statistics and Data Analysis

Volume

55

Issue

2

Start Page

955

End Page

963

Publisher

Elsevier

ISSN (print)

01679473

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