Sample Size Requirements for Traditional and Regression-Based Norms.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Test norms are essential for interpreting individual scores within a group.
• Traditional norming is widely used, but regression-based norming is emerging as a more efficient alternative.
• Limited understanding exists regarding the technical properties and sample size requirements of regression-based norming.

Purpose of the Study:

• To compare the sample size requirements of traditional norming versus regression-based norming.
• To investigate the influence of various factors (covariate effects, test length, answer categories) on norming efficiency.

Main Methods:

• A simulation study was conducted to evaluate sample size needs for both norming methods.
• Examined the 95% interpercentile ranges for percentile estimates across different conditions.
• Assessed the impact of sample size, norming method, covariate effects, test length, and item characteristics.

Main Results:

• When linear regression model assumptions are met, regression-based norming requires 2.5 to 5.5 times smaller sample sizes than traditional norming for subgroup norming.
• Specific sample size requirements are detailed for various conditions, including test length and number of answer categories.
• The efficiency gains of regression-based norming are contingent on the validity of its underlying assumptions.

Conclusions:

• Regression-based norming offers substantial sample size efficiencies compared to traditional methods under ideal conditions.
• The study provides data to guide sample size selection for regression-based norming.
• Further research is necessary to determine sample size requirements when regression model assumptions are violated.