ABSTRACT
In this chapter we consider the effect of two or more independent or classification variables (e.g., sex, social class, treatments) on a set of dependent variables. Four schematic two-way designs, where just the classification variables are shown, are given here: https://www.niso.org/standards/z39-96/ns/oasis-exchange/table">
Gender
Treatments
Aptitude
Teaching methods
1
2
3
1
2
Male
Low
Female
Average
High
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Drugs
Stimulus complexity
Diagnosis
1
2
3
4
Intelligence
Easy
Average
Hard
Schizop.
Average
Depressives
Super
We first indicate what the advantages of a factorial design are over a one-way design. We also remind you what an interaction means, and distinguish between two types of interactions (ordinal and disordinal). The univariate equal cell size (balanced design) situation is discussed first, after which we tackle the much more difficult disproportional (non-orthogonal or unbalanced) case. Three different ways of handling the unequal n case are considered; it is indicated why we feel one of these methods is generally superior. After this review of univariate ANOVA, we then discuss a multivariate factorial design, provide an analysis guide for factorial MANOVA, and apply these analysis procedures to a fairly large data set (as most of the data sets provided in the chapter serve instructional purposes and have very small sample sizes). We also provide an example results section for factorial MANOVA and briefly discuss three-way MANOVA, focusing on the three-way interaction. We conclude the chapter by showing how discriminant analysis can be used in the context of a multivariate factorial design. Syntax for running various analyses is provided along the way, and selected output from SPSS is discussed.
