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THE EFFECTS OF VARIANCE HETEROGENEITY ON SIMULTANEOUS MULTIPLE‐COMPARISON PROCEDURES WITH EQUAL SAMPLE SIZE
Author(s) -
Howell John F.,
Games Paul A.
Publication year - 1974
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1974.tb00529.x
Subject(s) - statistics , mathematics , standard error , statistic , sample size determination , variance (accounting) , robustness (evolution) , analysis of variance , mean squared error , homogeneous , standard deviation , econometrics , combinatorics , biochemistry , chemistry , accounting , business , gene
The robustness of three multiple‐comparison procedures (multiple t test, Tukey WSD and Scheffé S test) to the violation of the homogeneous population variance assumption was investigated using three different standard error estimates. These estimates were (1) the square root of two mean square within/ n , (2) the standard error of the traditional t test and (3) the standard error of the Behrens‐Fisher t ′ statistic. The procedures were highly robust to variance heterogeneity using the Behrens‐Fisher standard error estimate. The procedures were considerably less robust using MSW. The universal use of the Behrens‐Fisher statistic with the Welch solution for critical values is recommended.