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

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Summary

Accurate norms are vital for assessments. This study offers formulas and tools to calculate the necessary sample size and optimal design for norming studies, ensuring precise and stable assessment results.

Keywords:
Accuracy in parameter estimation (AIPE)Z-scorecontinuous normingmahalanobis distanceoptimal designpercentile rank scorerelative efficiencysample compositionsample size calculationsub-optimal designstest norming

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Neuropsychological Assessment

Background:

  • Norms are crucial for accurate interpretation in high-stakes assessments like diagnosing intellectual disabilities.
  • Sampling fluctuations can compromise the precision and stability of assessment norms.
  • Current methods for determining sample size and design in normative studies require refinement.

Purpose of the Study:

  • To provide formulas for calculating required sample sizes in normative studies within the simplified parametric norming framework.
  • To derive optimal sampling designs that minimize error in norm estimation.
  • To facilitate practical implementation through interactive tools for sample size determination.

Main Methods:

  • Development of formulas for sample size calculation applicable to any sample composition.
  • Derivation of optimal designs for 45 multivariate multiple linear regression models under normality and homoscedasticity assumptions.
  • Creation of three interactive Shiny applications for practical use in planning normative studies.

Main Results:

  • Formulas are presented for determining sample size based on desired precision.
  • Optimal designs are derived for regression models incorporating continuous, categorical, and mixed norm-predictors.
  • Interactive applications are provided to aid researchers in sample size and design selection.

Conclusions:

  • Sufficiently large and optimally designed samples are essential for precise and stable norms in assessments.
  • The provided formulas and tools support evidence-based planning of normative studies.
  • Practical implementation is enhanced, aiding researchers in conducting robust norming studies, exemplified by the Trail Making Test.