cNORMj provides conventional and regression-based continuous norming methods for psychometric test development, biometrics and references scores in medical research in Jamovi. It is based on the cNORM package for R (Lenhard, Lenhard & Gary, 2018).
The continuous norming method produces norm scores by modeling the functional relationship between:
- Raw scores
- Norm scores
- Grouping variables (e.g., age, grade)
This approach:
- Reduces necessary sample size
- Closes gaps between norm groups
- Decreases error variance in norm data
- Smooths sampling errors
For norming within a single group (e.g., all participants of the same age/grade).
For creating continuous norms across multiple groups or ages using Taylor polynomials. This is the most flexible approach, suitable if no further information on the type of distribution is available.
Models beta binomial distribution parameters via polynomial regression. The approach fit ideally for 1PL IRT based test (AKA Rasch).
- Lenhard, A., Lenhard, W., Sebastian, S. & Segerer, R. (2018). A continuous solution to the norming problem. Assessment, 25, 112-125. doi:10.1177/1073191116656437
- Lenhard, A., Lenhard, W. & Gary, S. (2019). Continuous norming of psychometric tests: A simulation study of parametric and semi-parametric approaches. PLoS One, 14(9). doi:10.1371/journal.pone.0222279
- Lenhard, W. & Lenhard, A. (2020). Improvement of Norm Score Quality via Regression-Based Continuous Norming. Educational and Psychological Measurement, Online First, 1-33. doi:10.1177/0013164420928457
- Gary, S., Lenhard, W. & Lenhard, A. (2021). Modelling Norm Scores with the cNORM Package in R. Psych, 3(3), 501-521. https://doi.org/10.3390/psych3030033
- Gary, S., Lenhard, W., Lenhard, A., & Herzberg, D. (2023). A tutorial on automatic post-stratification and weighting in conventional and regression-based norming of psychometric tests. Behavior Research Methods. https://doi.org/10.3758/s13428-023-02207-0
- Gary, S., Lenhard, A., Lenhard, W., & Herzberg, D. S. (2023). Reducing the Bias of Norm Scores in Non-Representative Samples: Weighting as an Adjunct to Continuous Norming Methods. Assessment, 30(8), 2491–2509. https://doi.org/10.1177/10731911231153832
- Laurenz, R., & Lenhard, W. (2025). Comparison of cNORM and LMS methods for estimating reference percentile curves from biometric data. Scientific Reports. https://doi.org/10.1038/s41598-025-29580-4
More details and tutorials are available via Psychometrica.