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The test of parallelism of k regression lines against ordered alternatives based on a sequential slope
Journal of the Korean Data & Information Science Society 2018;29:873-84
Published online July 31, 2018
© 2018 Korean Data and Information Science Society.

Hyerim Kim1 · Dongjae Kim2

12Department of Biomedicine · Health Science, The Catholic University of Korea
Correspondence to: Professor, Department of Biomedicine · Health Science, The Catholic University of Korea, 222, Banpo-daero, Seocho-gu, Seoul 137-701, Korea. E-mail:
Received June 22, 2018; Revised July 13, 2018; Accepted July 16, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
When comparing regression lines formed in each population, it may be necessary to test the parallelism of k regression lines against ordered alternatives. In this paper, we propose a parallel test using Williams’ (1972) parametric and nonparametric tests and Jonckheere’s (1954) test to calculate the slope of each straight line. The Monte Carlo simulations were performed to compare the power of the three proposed methods with the previous methods proposed by Adichie (1976). As a result, the proposed methods can be relatively easily tested using the sequential slope. In many cases, the power of the proposed method is similar to that of the previous methods. In particular, when the sample size and the slope is small, The power of proposed parametric method was the highest.
Keywords : Ordered alternatives, parallelism test, regression model, sequential slope.