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MULTIPLE CONTRASTS, FACTORS, ERROR RATE AND POWER
Author(s) -
Rodger R. S.
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.tb00539.x
Subject(s) - mathematics
A method is given for choosing ( post hoc ) a set of v 1 mutually orthogonal null contrasts such that the maximum number ( r ) rejectable by a new criterion are rejected and v 1 – r retained. Type I error rate is defined as the expected proportion of the v 1 decisions which will be errors when all nulls are true. Because the new criterion uses F , the expected proportion of rejections can be calculated for the case when all nulls are not true, and this is taken as the definition of power. Theoretical means are deducible from decisions for v 1 mutually orthogonal contrasts and, if rejected null contrasts are given suitable non‐zero values, there is no ambiguity about the theoretical means. The traditional values of FΓ; v 1 , v 2 ‘load the dice’ against finding true interactions ‘significant’ in factorial analyses. The new values (table given) do not have this property and their use is illustrated using a one‐way anova on data from a factorially designed experiment. This procedure permits the analysis of unequal replications in factorially designed experiments.