Continuous norming of psychometric tests: A simulation study of parametric and semi-parametric approaches

Continuous norming methods have seldom been subjected to scientific review. In this simulation study, we compared parametric with semi-parametric continuous norming methods in psychometric tests by constructing a fictitious population model within which a latent ability increases with age across seven age groups. We drew samples of different sizes (n = 50, 75, 100, 150, 250, 500 and 1,000 per age group) and simulated the results of an easy, medium, and difficult test scale based on Item Response Theory (IRT). We subjected the resulting data to different continuous norming methods and compared the data fit under the different test conditions with a representative cross-validation dataset of n = 10,000 per age group. The most significant differences were found in suboptimal (i.e., too easy or too difficult) test scales and in ability levels that were far from the population mean. We discuss the results with regard to the selection of the appropriate modeling techniques in psychometric test construction, the required sample sizes, and the requirement to report appropriate quantitative and qualitative test quality criteria for continuous norming methods in test manuals.