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The importance of being OSCAR or Balance and the analysis of factorial designs
Author(s) -
Macdonald Ranald Roderick
Publication year - 1991
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.2044-8317.1991.tb00956.x
Subject(s) - mathematics , variance (accounting) , factorial experiment , main effect , factorial , analysis of variance , statistics , fractional factorial design , population , balance (ability) , design of experiments , order (exchange) , psychology , mathematical analysis , demography , accounting , finance , neuroscience , sociology , business , economics
It is often assumed that balanced factorial designs are desirable as they result in hypotheses to be tested in an analysis of variance which are independent of each other. It is also a consequence of balance that, with the exception of the highest‐order interaction, significant analysis of variance effects derived from balanced designs generalize only to differences between linear functions of cell means with fixed weights. Such generalizations are therefore restricted to replications of complete studies including all the factors not involved in the significant effects. When dealing with non‐experimental factors, e.g. sex, age, etc., there are distinct advantages to designs in which the Observations are Sampled Completely At Random (OSCAR designs). Though this leads to unbalanced designs, analyses can be performed which treat each observation equally. In this way any significant effect generalizes both to the population sampled and to partial replications of the study which omit factors not involved in the particular significant effect. These unconstrained generalizations require that each effect is tested against its within‐effect variance, thus separate error terms are required for each test. Unweighted (equally weighted) means analyses when applied to OSCAR designs suffer from the same demerits as balanced designs and lower‐order effects do not generalize to differences between means in naturally occurring populations.