cNORM — Continuous Norming

This tool generates continuous test norms for psychometric and biometric data using regression-based Taylor polynomials. It is distribution-free and allows you to compute robust norm scores even with moderate sample sizes per age (or grade) group. It is based on the cNORM package of the R plattform. For advanced functionality like weighting and fine-grained setting (descending scores, types of bindings, predicting norm scorses for complete new datasets based on existing models ...), please use the cnorm function on the R console.

This GUI guides you through three short steps:

1. Data – load an example or upload your own file.
2. Modeling – pick the grouping variable (e. g. age groups, grade ...), raw-score variable, norm scale and polynomial degrees, then click Run model. You can inspect the percentile plot, the consistency check and the model-fit curve to choose the right number of terms.
3. Prediction – predict single norm/raw scores or generate and download full norm tables. Diagnostic plots are available in the Visualization tab and a stratified Cross-validation can be run separately.

Required variables

• Grouping variable – e.g. age group, grade, year. Must be numeric and meaningful (group mean is fine). Sidenote: If you have a continuous variable like age, please use the parametric modelling or the additional parameters available on the R console.
• Raw-score variable – the test score to be normed.

Built-in example data sets

• elfe – reading-comprehension scores in primary school (sentence-completion task, 0–28).
• ppvt – Peabody Picture Vocabulary Test IV norming sample, ages 2.5–17.5, raw 0–228.
• CDC – epidemiological growth data (BMI, weight, height), ages 2–18, from the CDC.

Model parameters at a glance

• k – polynomial degree of the location (norm score) term. Higher values give a closer fit but risk overfitting (default 5).
• t – polynomial degree of the explanatory term (typically age). Age trajectories are usually smooth, so 2–3 is enough.
• Number of terms – leave blank to auto-select model. Otherwise specify a fixed value (look for the “elbow” in the model-fit curve).

Privacy

When launched locally via cNORM.GUI(), all data stays on your computer. The hosted version runs on shinyapps.io (security & compliance); cNORM itself does not store any uploaded data.

References

• R package cNORM (CRAN)
• Tutorial & manual
• Lenhard, A., Lenhard, W., Suggate, 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), e0222279.
• Lenhard, W. & Lenhard, A. (2021). Improvement of norm score quality via regression-based continuous norming. Educational and Psychological Measurement, 81(2), 229–261. doi:10.1177/0013164420928457