Sample size calculation and optimal design for regression-based norming of tests and questionnaires

Francesco Innocenti*, Frans E S Tan, Math J J M Candel, Gerard J P van Breukelen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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To prevent mistakes in psychological assessment, the precision of test norms is important. This can be achieved by drawing a large normative sample and using regression-based norming. Based on that norming method, a procedure for sample size planning to make inference on Z-scores and percentile rank scores is proposed. Sampling variance formulas for these norm statistics are derived and used to obtain the optimal design, that is, the optimal predictor distribution, for the normative sample, thereby maximizing precision of estimation. This is done under five regression models with a quantitative and a categorical predictor, differing in whether they allow for interaction and nonlinearity. Efficient robust designs are given in case of uncertainty about the regression model. Furthermore, formulas are provided to compute the normative sample size such that individuals' positions relative to the derived norms can be assessed with prespecified power and precision. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Original languageEnglish
Pages (from-to)89-106
Number of pages18
JournalPsychological Methods
Issue number1
Early online date12 Aug 2021
Publication statusPublished - Feb 2023


  • Z-score
  • normative data
  • optimal design
  • percentile rank score
  • sample size calculation

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