ABSTRACT

A demonstration is given, based on well-known theory, that measures of effect sizes in a linear (ANOVA-type) model can be reinterpreted as measures of goodness of approximation when the effect is omitted from the model. Specifically, in the linear model the geometric mean of the likelihood ratio reduces to the conventional standardized effect size, and constitutes a measure of goodness of approximation. Discussion focuses on the problem of a statistically significant interaction term that we might wish to regard as negligible. Because it is not yet settled how, or even whether, indices of goodness of approximation can be used in the context of structural equation models where they originate, the cautious conclusion is drawn that their application to linear models may provide support for an investigator's decision to retain a restrictive model-for example, a model without interaction-but cannot be a substitute for judgment.