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

Area of Science:

• Psychological Measurement
• Statistical Modeling

Background:

• Accurate psychological assessment relies on precise test norms.
• Regression-based norming with large samples enhances norm precision.

Purpose of the Study:

• To propose a sample size planning procedure for regression-based norming.
• To maximize the precision of Z-score and percentile rank estimations.
• To provide methods for assessing individual positions relative to norms with specified precision.

Main Methods:

• Derived sampling variance formulas for norm statistics.
• Optimized predictor distribution for normative samples under five regression models.
• Developed robust designs for uncertain regression models.
• Provided formulas for computing normative sample size.

Main Results:

• Optimized normative sample designs to maximize estimation precision.
• Formulas enable calculation of sample size for desired power and precision.
• Robust designs offered for situations with model uncertainty.

Conclusions:

• The proposed procedure enhances the precision of psychological test norms.
• Effective sample size planning is key for accurate psychological assessment.
• This method supports reliable interpretation of individual scores within normative frameworks.