Sample Size Determination for Optimal and Sub-Optimal Designs in Simplified Parametric Test Norming

Norms play a critical role in high-stakes individual assessments (e.g., diagnosing intellectual disabilities), where precision and stability are essential. To reduce fluctuations in norms due to sampling, normative studies must be based on sufficiently large and well-designed samples. This paper provides formulas, applicable to any sample composition, for determining the required sample size for normative studies under the simplified parametric norming framework. In addition to a sufficiently large sample size, precision can be further improved by sampling according to an optimal design, that is, a sample composition that minimizes sampling error in the norms. Optimal designs are, here, derived for 45 (multivariate) multiple linear regression models, assuming normality and homoscedasticity. These models vary in the degree of interaction among three norm-predictors: a continuous variable (e.g., age), a categorical variable (e.g., sex), and a variable (e.g., education) that may be treated as either continuous or categorical. To support practical implementation, three interactive Shiny apps are introduced, enabling users to determine the sample size for their normative studies. Their use is demonstrated through the hypothetical planning of a normative study for the Trail Making Test, accompanied by a review of the most common models for this neuropsychological test in current practice.