ABSTRACT
In Chapter 1 examples of informative hypotheses formulated in the context of the univariate normal linear model were presented and discussed. The univariate normal linear model (Cohen, 1968) is
yi = µ1d1i + ...+ µJdJi + β1x1i + ...+ βKxKi + i, (2.1)
that is, there is one dependent variable y, persons (indexed by i) may belong to one of J groups, and there may be up to K variables x. Note that it is assumed that the residuals have a normal distribution with mean 0 and variance σ2, that is, i ∼ N (0, σ2). Several specifications of (2.1) have been discussed in Chapter 1: the ANOVA model, that is, (2.1) without x variables; the ANCOVA model, that is, (2.1) in which the x variables have the role of covariates; and, multiple regression, that is, (2.1) in which µ1d1i + ...+ µJdJi is replaced by the intercept β0 and the x variables have the role of predictors. Furthermore, Chapter 1 presented and discussed several constraints that can be used to construct informative hypotheses: simple constraints like µ1 > µ2, constraints including the size of an effect like |µ1 − µ2| < d× σ, and constraints on combinations of means like (µ1 − µ2) > (µ3 − µ4).
