Regression-Based Normative Data in Neuropsychology: Using Raw Scores as Observed Response Variable Outperforms Transforming for Normality

Abstract

Regression-based normative data for neuropsychological variables are increasing in popularity over the last years. However, some use raw data while others use transformation when the observed response variable is skewed. This work analyzes how well the linear models fit for each type of variable. We used real data from a sample of n = 163 cognitively healthy individuals and compared the fit of linear regression models for raw scores and for corrected scaled scores. We then simulated a population of 1,000,000 individuals and drew 1,000 random samples of different sizes (n = 100, 200, 5,000, 1,000, 10,000) for seven different scenarios, analyzed the percentage of individuals scoring in the lowest 5%, and analyzed the agreement between models with the Cohen’s κ statistic. Linear models for raw scores and for scaled scores were similar when the model included all the covariates, but barely identified low scores when scaled scores were corrected with covariates taken from different regressions (κ = 0.58). Models with raw scores showed that the expected number of individuals scoring low was close to the expected 5%, whereas models with scaled scores with covariates taken from different regressions were close to 0%. The two models agreed only when the response variable was random symmetrical and uncorrelated with the covariates. When calculating normative data using linear regressions, raw scores should be the preferred choice. If residuals analysis shows that the model does not fit the data well, researchers should consider using nonlinear models. Transforming data for normality of the observed response is discouraged