TY - JOUR

T1 - On integer partitions and the Wilcoxon rank-sum statistic

AU - Sills, Andrew V.

N1 - Publisher Copyright:
© 2024 Taylor & Francis Group, LLC.

PY - 2024

Y1 - 2024

N2 - Abstract.: In the literature, derivations of exact null distributions of rank-sum statistics are often avoided in cases where one or more ties exist in the data. By deriving the null distribution in the no-ties case with the aid of the classical q-series results of Euler and Rothe, we demonstrate how a natural generalization of the method may be employed to derive exact null distributions even when one or more ties are present in the data. It is suggested that this method could be implemented in a computer algebra system, or even a more primitive computer language, so that the normal approximation need not be employed in the case of small sample sizes, when it is less likely to be very accurate. Several algorithms for determining exact distributions of the rank-sum statistic (possibly with ties) have been given in the literature (see Streitberg and Röhmel 1986; Marx et al. 2016), but none seem as simple as the procedure discussed here, which amounts to multiplying out a certain polynomial, extracting coëfficients, and finally dividing by a binomal coëfficient.

AB - Abstract.: In the literature, derivations of exact null distributions of rank-sum statistics are often avoided in cases where one or more ties exist in the data. By deriving the null distribution in the no-ties case with the aid of the classical q-series results of Euler and Rothe, we demonstrate how a natural generalization of the method may be employed to derive exact null distributions even when one or more ties are present in the data. It is suggested that this method could be implemented in a computer algebra system, or even a more primitive computer language, so that the normal approximation need not be employed in the case of small sample sizes, when it is less likely to be very accurate. Several algorithms for determining exact distributions of the rank-sum statistic (possibly with ties) have been given in the literature (see Streitberg and Röhmel 1986; Marx et al. 2016), but none seem as simple as the procedure discussed here, which amounts to multiplying out a certain polynomial, extracting coëfficients, and finally dividing by a binomal coëfficient.

KW - integer partitions

KW - Mann–Whitney test

KW - non parametric statistics

KW - q-binomial theorem

KW - Wilcoxon rank-sum test

UR - http://www.scopus.com/inward/record.url?scp=85185302730&partnerID=8YFLogxK

U2 - 10.1080/03610926.2024.2315297

DO - 10.1080/03610926.2024.2315297

M3 - Article

AN - SCOPUS:85185302730

SN - 0361-0926

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

ER -