Abstract
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.
Highlights
Psychological tests are widely used instruments for measuring a variety of constructs such as intelligence, reading ability or personality
(80%) and a validation set (20%), computes norming models with increasing numbers of predictors starting with one predictor up to a specified number based on the training set, and compares the predicted with the observed scores of the validation set in terms of the root mean squared error (RMSE) of the raw score as well as the adjusted R2 of the norm score
We choose the ‘rawTable’ method to transform a series of raw scores, which can be specified by the user, into a series of norm scores as well as corresponding percentiles:
Summary
Psychological tests are widely used instruments for measuring a variety of constructs such as intelligence, reading ability or personality. Modelling the course of distribution parameters such as mean and standard deviation over age was used already early on in intelligence test construction (see [1,3,4,5,6] for an overview). Using the regression formula for the mean and the standard deviation, it was possible to estimate the norm score at any age. This approach is based on very strong assumptions, e.g., normality, and it produces huge deviations especially at the upper and lower bounds of a scale. Psych 2021, 3 start this article with a short general introduction about norm scores and their relevance for decisions based on psychological tests
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