Exact unconditional distributions for dichotomous data in many-to-one comparisons

• Published in: Journal of statistical planning and inference Vol. 82; no. 1; pp. 83 - 99
• Main Authors: Koch, Hans-Friedrich, Hothorn, Ludwig A.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 01-12-1999; New York,NY Elsevier Science; Amsterdam
• Subjects: Binary data; Distribution theory; Exact sciences and technology; Exact unconditional test; Many-to-one design; Mathematics; Multivariate analysis; Probability and statistics; Sciences and techniques of general use; Statistics; Step-down procedure; Binary data; Many-to-one design; 62J15; 62E15; Exact unconditional test; Step-down procedure; Conditional distribution; Critical value; Distribution function; Binomial distribution; Probability distribution; P value; Multivariate analysis; Algorithm
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(99)00033-6

The exact conditional distribution of a statistic for the many-to-one design with dichotomous response variables was firstly given by
Williams (1988). His approach is expanded to other maximum statistics, and their exact conditional distributions are compared. As an alternative to the conditional approach, the exact unconditional binomial distribution is presented for two maximum statistics. For these distributions algorithms are described to compute the exact unconditional
p-values and critical values. As an application of the exact unconditional distribution, a new simultaneous step-down procedure is suggested. This procedure is based on the exact unconditional distribution and is compared to the
α-adjustment procedure according to Bonferroni–Holm and Hommel when
p-values result from Fisher's exact test and Barnard's test.