Sample size computing for factorial designs: An extension of the Athenian representative method

摘要

The paper considers sample size computing as a problem of representation. It clarifies the notion of representation and concentrates on the simultaneous representation of: i) a finite population divided into r × c cells provided by the crossing of levels of two factors, and ii) the respective set of values that a variable of interest takes upon the population subjects. Through a probabilistic approach, the sample size formula for the full factorial design, with non-zero mean differences among cells and interaction among factors, was derived. The formula verifies, that the statistical sample size n_(st) is the product of population representation n_p and variance (SD) representation n_s multiplied by the factor R (sum of cell percentages). This law is an extension of the Athenian law of representation. It applies both for balanced and unbalanced factorial designs and operates as the representation standard in sample size computing for a multi-way (n-way) ANOVA.