Pairwise comparisons of J independent regression lines over a finite interval, simultaneous pairwise comparison of their parameters, and the Johnson-Neyman procedure

Authors


Department of Psychology, University of Southern California, University Park, Los Angeles, CA 90089, USA.

Abstract

Consider J regression lines, each with one predictor, corresponding to J independent treatment groups. The purpose of this paper is to address two related problems when comparing these J lines. Using a proposed ‘bivariate’ analogue of the Studentized range distribution, the paper notes that it is possible to get Tukey-Kramer type simultaneous confidence intervals on both the J(J – 1)/2 pairwise differences of the intercepts and the J(J – 1)/2 pairwise differences of the slopes. That is, simultaneous confidence intervals are obtained for all J(J – 1) differences. The first goal is to provide the percentage points needed to implement the procedure. The second goal is to describe a method for obtaining simultaneous 1 – α confidence intervals for the distance between all pairs of regression lines at the end points of a finite interval. Advantages over the Johnson–Neyman procedure are noted, and certain improvements in the Johnson–Neyman procedure are described as well.

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