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Circularity and multiple comparisons in repeated measure designs
Author(s) -
Mitzel Howard C.,
Games Paul A.
Publication year - 1981
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.2044-8317.1981.tb00635.x
Subject(s) - pairwise comparison , mathematics , variance (accounting) , statistics , measure (data warehouse) , monte carlo method , covariance matrix , covariance , one way analysis of variance , variance components , population , multiple comparisons problem , matrix (chemical analysis) , analysis of variance , computer science , data mining , accounting , materials science , business , composite material , demography , sociology
In an RS × T design, MS T /MS RST is distributed as F with the usual df only if the population variance‐covariance matrix has ε = 1.0. This same condition is needed for the usual multiple comparison procedures to be accurate. When testing K — 1 orthogonal contrasts the conventional estimate of the variance of the contrasts is the mean of the K — 1 different true variance estimates. This condition also is observed when testing all pairwise contrasts. A Monte Carlo study demonstrates that with reasonable ns , little power is lost using a robust general matrix solution. The conventional solution will often be inaccurate when ε < 1.0.