TY  - JOUR
A1  - Gary, Sebastian
A1  - Lenhard, Wolfgang
A1  - Lenhard, Alexandra
T1  - Modelling norm scores with the cNORM package in R
JF  - Psych
N2  - In this article, we explain and demonstrate how to model norm scores with the cNORM package in R. This package is designed specifically to determine norm scores when the latent ability to be measured covaries with age or other explanatory variables such as grade level. The mathematical method used in this package draws on polynomial regression to model a three-dimensional hyperplane that smoothly and continuously captures the relation between raw scores, norm scores and the explanatory variable. By doing so, it overcomes the typical problems of classical norming methods, such as overly large age intervals, missing norm scores, large amounts of sampling error in the subsamples or huge requirements with regard to the sample size. After a brief introduction to the mathematics of the model, we describe the individual methods of the package. We close the article with a practical example using data from a real reading comprehension test.
KW  - regression-based norming
KW  - continuous norming
KW  - inferential norming
KW  - data smoothing
KW  - curve fitting
KW  - percentile estimation
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-284143
SN  - 2624-8611
VL  - 3
IS  - 3
SP  - 501
EP  - 521
ER  - 
TY  - JOUR
A1  - Lenhard, Alexandra
A1  - Lenhard, Wolfgang
A1  - Gary, Sebastian
T1  - Continuous norming of psychometric tests: A simulation study of parametric and semi-parametric approaches
JF  - PLoS ONE
N2  - 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.
KW  - statistical models
KW  - simulation and modeling
KW  - psychometrics
KW  - age groups
KW  - skewness
KW  - normal distribution
KW  - polynomials
KW  - statistical distributions
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-200480
VL  - 14
IS  - 9
ER  -