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A Test of Whether Two Parallel Regression Lines Are the Same When the Variances May Be Unequal

Potthoff, Richard F.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
United States Air Force Office of Scientific Research, Hypothesis Testing, Regression (Statistics), Statistical Analysis


This paper considers a situation where one has two regression lines which are known to be parallel, with the two sets of error terms assumed to be normally distributed but with (possibly) different variances. The paper presents a test of the hypothesis that the two regression lines are identical (i.e., the two a- coefficients are equal). The test is analogous to the Wilcoxon test. The discussion in this paper is on a rather technical level; for a less technical discussion of the test, see Research Bulletin 62-31.

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