This article presents an overview of procedures for calculating power of the F test under all three models of analysis of variance. A comparison of power of tests on faxed and random factors shows the latter to have substantially lower power. Consequences for designing experiments and for interpreting experimental results are discussed. Throughout, the simplicity with which power calculations are done is emphasized.For determining the power of the F test in analysis of variance (ANOVA) there exists a relative abundance of tables (for instance, Cohen, 1977; Rotton & Schonemann, 1978;Tiku, 1967). These tables, however, apply only to the fixed-effects model of ANOVA, and of course they cannot cover all possible tests under this model. It is therefore desirable to have procedures for calculating power according to one's own specifications under any ANOVA model. As a matter of fact, these procedures are already given by Scheffe (1959), and this article consequently offers nothing really new as far as the theory of the power of the F test is concerned. The purpose of this article is primarily to elucidate the application of power-calculating procedures. To this effect I present parameters that determine the power of the -F test in a general and convenient form and illustrate how approximations to F distributions are executed.A few lines about the notation that is used are necessary. The dependent variable is denoted by X, the independent variables (factors) are denoted by capital letters A, B, and so forth. In a given design each factor has a definite number of scaling points or levels. Factor A has a levels, Factor B has b levels, and so forth. Interactions of factors are denoted by AB, AC, and so forth. Interaction AB has ab levels. Whenever an argument holds for factors as well as for interactions, the word treatment will be used. TreatmentThe author is indebted to Johan Hoogstraten for his stimulating comments.

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Background: In the complex domain of medical decision making, reasoning under uncertainty can benefit from supporting tools. Automated decision support tools often build upon mathematical models, such as Bayesian networks. These networks require probabilities which often have to be assessed by experts in the domain of application. Probability response scales can be used to support the assessment process. We compare assessments obtained with different types of response scale.Methods: General practitioners (GPs) gave assessments on and preferences for three different probability response scales: a numerical scale, a scale with only verbal labels, and a combined verbalnumerical scale we had designed ourselves. Standard analyses of variance were performed.Results: No differences in assessments over the three response scales were found. Preferences for type of scale differed: the less experienced GPs preferred the verbal scale, the most experienced preferred the numerical scale, with the groups in between having a preference for the combined verbal-numerical scale. Conclusion:We conclude that all three response scales are equally suitable for supporting probability assessment. The combined verbal-numerical scale is a good choice for aiding the process, since it offers numerical labels to those who prefer numbers and verbal labels to those who prefer words, and accommodates both more and less experienced professionals.

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