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cNORM - Generating Continuous Test Norms

Alexandra Lenhard, Wolfgang Lenhard & Sebastian Gary

cNORM (W. Lenhard, Lenhard & Gary) is a package for the R environment for statistical computing that aims at generating continuous test norms in psychometrics and biometrics and to analyze the model fit. It is based on the approach of A. Lenhard, Lenhard, Suggate and Segerer (2016).

The method stems from psychometric test construction and was developed to create continuous norms for age or grade in performance assessment (e. g. vocabulary development, A. Lenhard, Lenhard, Segerer & Suggate, 2015; reading and writing development, W. Lenhard, Lenhard & Schneider, 2017). It can however be applied wherever test data like psychological (e. g. intelligence), physiological (e. g. weight) or other measures are dependent on continuous (e.g., age) or discrete (e.g., sex or test mode) explanatory variables. In addition, it can also be used for conventional norm score generation for individual groups, i.e. without modeling depending on other variables.

The package estimates percentile curves in dependence of the explanatory variable (e. g. schooling duration, age ...) via Taylor polynomials, thus offering several advantages:

For the mathematical background, please have a look at the mathematical derivation of the method.

On the following pages, we demonstrate the necessary steps for the application of the R package with real human performance data, namely, with the standardization sample of the sentence comprehension subtest of ELFE 1-6, a reading comprehension test in German language (W. Lenhard & Schneider, 2006). Essentially, there are five steps to complete:

  1. Installation of the R-Package
  2. Data Preparation
  3. Data Modeling
  4. Model Validation
  5. Generating Norm Tables
  6. Graphical User Interface


Terms of use/Licensing

cNORM is licensed under GNU Affero General Public License v3 (AGPL-3.0). This means that copyrighted parts of cNORM may only be used free of charge in commercial and non-commercial projects that run under this same license, retain the copyright notice, provide their source code and correctly cite cNORM. Copyright protection includes, for example, the reproduction and distribution of source code or parts of the source code of cNORM or of graphics created with cNORM. The integration of the package into a server environment in order to access the functionality of the software (e.g. for online delivery of norm scores) is also subject to this license. However, a regression function determined with cNORM is not subject to copyright protection and may be used freely for commercial or non-commercial projects. If you want to apply cNORM in a way that is not compatible with the terms of the AGPL 3.0 license, please do not hesitate to contact us to negotiate individual conditions.

If you want to use cNORM for scientific publications, we would also ask you to quote the source.


CDC (2012). National Health and Nutrition Examination Survey: Questionaires, Datasets and Related Documentation. available: date of retrieval: 25/08/2018
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), e0222279.
Lenhard, A., Lenhard, W., Segerer, R. & Suggate, S. (2015). Peabody Picture Vocabulary Test - Revision IV (Deutsche Adaption). Frankfurt a. M.: Pearson Assessment.
Lenhard, A., Lenhard, W., Suggate, S. & Segerer, R. (2016). A continuous solution to the norming problem. Assessment, Online first, 1-14. doi: 10.1177/1073191116656437
Lenhard, W., Lenhard, A. & Schneider, W. (2017). ELFE II - Ein Leseverständnistest für Erst- bis Siebtklässler. Göttingen: Hogrefe.
Lenhard, W. & Schneider, W. (2006). ELFE 1-6 - Ein Leseverständnistest für Erst- bis Sechstklässler. Göttingen: Hogrefe.
The World Bank (2018). Mortality rate, infant (per 1,000 live births). Data Source available (date of retrieval: 02/09/2018)
The World Bank (2018). Life expectancy at birth, total (years). Data Source World Development Indicators available (date of retrieval: 01/09/2018)

In case you need a reference to this page in a scientific paper, please use the following citation:

Lenhard, A., Lenhard, W. & Gary, S. (2018). cNORM - Generating Continuous Test Norms. Retrieved from: Dettelbach (Germany): Psychometrica. DOI: 10.13140/RG.2.2.25821.26082