Overview

This documents a set of dialogs (written in Java) intended to facilitate the study of power and sample-size issues for balanced analysis-of-variance (ANOVA) models. (Certain fractional designs, such as Latin square designs, while perhaps not technically ``balanced'' due to empty cells, are also supported.) All calculations are based on the standard assumptions of normality and mutual independence of all random effects in the model. The ``unrestricted'' version of the mixed model is used throughout.

The current implementation focuses on the powers of F tests of model terms. Extensions that support t tests of comparisons or contrasts are under development.

Warnings

 You could get very wrong answers from these dialogs if you incorrectly guess what is needed for inputs. In particular, the design is such that the concept of effect size have a compatible definition for both fixed and random effects. Accordingly, the author chose to quantify effect size as the standard deviation of the effects in the ANOVA model, labeled ``Effect standard deviation'' in the dialog.

Briefly, for a fixed effect, the effect SD is the root mean square of the constrained effects in an ANOVA model, using the degrees of freedom as the denominator. For a random (or mixed) effect, the effect SD is the square root of a variance component. These are described in detail in a later section; but right now, here are some misconceptions to be aware of:

• An effect SD is not a mean square from a pilot study.
• An effect SD is not the square root of a mean square, either, unless you're talking about the residual or within-cell error.
• An effect SD is not the difference between two means.
• An effect SD is not the half-difference between two means.