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Illustrations of Some Scheffe-Type Tests for Some Behrens-Fisher-Type Regression Problems

Potthoff, Richard F.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
NATO Research Grants Programme, United States Air Force, Behrens-Fisher Problem, Regression (Statistics), Scheffe Test, Statistical Significance


It is sometimes required to compare two simple regression lines without assuming that the variances of the two sets of error terms are necessarily equal: one may wish to (A) test whether two parallel regression lines are identical, or (B) test whether two regression lines are parallel. In this paper, a t-test for each of these problems is explained and illustrated numerically. These t-tests bear a certain resemblance to Scheffe's test for the Behrens-Fisher problem, but (unlike the latter) are not randomized tests. This paper is on a practical rather than a theoretical level; the more technical aspects of the tests are covered in Research Bulletin 63-35.

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