Exact Multiple Comparisons of Three or More Regression Lines: Pairwise Comparisons and Comparisons with a Control

• Published in: Biometrical journal Vol. 44; no. 7; pp. 801 - 812
• Main Author: Spurrier, John D.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.10.2002; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Applications; Confidence bound; Exact sciences and technology; Mathematics; Medical sciences; Multivariate analysis; Multivariate studentized range; Nonparametric inference; Parametric inference; Probability and statistics; Sciences and techniques of general use; Simple linear regression; Simultaneous confidence; Statistics; Union-intersection; Biometrics; Normal variable; Linear regression; Treatment efficiency; Indometacin; Confidence limit; Probability distribution; Union intersection; Multiple comparison; Multivariate analysis; Ketoprofen; Multiple regression; Exact solution; Statistical method; Medical science; Simultaneous confidence; Student distribution; Optimal design(statistics); Random variable
• ISSN: 0323-3847; 1521-4036
• DOI: 10.1002/1521-4036(200210)44:7<801::AID-BIMJ801>3.0.CO;2-M

The problem of finding exact simultaneous confidence bounds for differences in regression models for k groups via the union‐intersection method is considered. The error terms are taken to be iid normal random variables. Under an assumption slightly more general than having identical design matrices for each of the k groups, it is shown that an existing probability point for the multivariate studentized range can be used to find the necessary probability point for pairwise comparisons of regression models. The resulting methods can be used with simple or multiple regression. Under a weaker assumption on the k design matrices that allows more observations to be taken from the control group than from the k‐1 treatment groups, a method is developed for computing exact probability points for comparing the simple linear regression models of the k‐1 groups to that of the control. Within a class of designs, the optimal design for comparisons with a control takes the square root of (k‐1) times as many observations from the control than from each treatment group. The simultaneous confidence bounds for all pairwise differences and for comparisons with a control are much narrower than Spurrier's intervals for all contrasts of k regression lines.