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Implications of random cut‐points theory for the Mann‐Whitney and binomial tests
Author(s) -
Edwardes Michael D.Deb.
Publication year - 2000
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315989
Subject(s) - mathematics , mann–whitney u test , categorical variable , binomial (polynomial) , statistics , cut point , inference , binomial distribution , binomial test , combinatorics , negative binomial distribution , poisson distribution , artificial intelligence , computer science
Through random cut‐points theory, the author extends inference for ordered categorical data to the unspecified continuum underlying the ordered categories. He shows that a random cut‐point Mann‐Whitney test yields slightly smaller p ‐values than the conventional test for most data. However, when at least P % of the data lie in one of the k categories (with P = 80 for k = 2, P = 67 for k = 3,…, P = 18 for k = 30), he also shows that the conventional test can yield much smaller p ‐values, and hence misleadingly liberal inference for the underlying continuum. The author derives formulas for exact tests; for k = 2, the Mann‐Whitney test is but a binomial test.