1. Sample size calculation and optimal design for regression-based norming of tests and questionnaires
- Author
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Math J. J. M. Candel, Francesco Innocenti, Gerard J. P. van Breukelen, Frans E. S. Tan, RS: CAPHRI School for Public Health and Primary Care, FHML Methodologie & Statistiek, RS: CAPHRI - R1 - Ageing and Long-Term Care, RS: CAPHRI - R6 - Promoting Health & Personalised Care, FPN Methodologie & Statistiek, and RS: FPN M&S I
- Subjects
Optimal design ,percentile rank score ,Z-score ,Regression analysis ,ESTABLISHING NORMATIVE DATA ,Standard score ,normative data ,Regression ,sample size calculation ,Percentile rank ,Sample size determination ,Statistics ,Psychological testing ,Psychology (miscellaneous) ,optimal design ,Categorical variable ,Mathematics - Abstract
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).
- Published
- 2023
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