Parallel but not equivalent: challenges and solutions for repeated assessment of cognition over time

J Clin Exp Neuropsychol. 2012;34(7):758-72. doi: 10.1080/13803395.2012.681628. Epub 2012 Apr 30.


Objective: Analyses of individual differences in change may be unintentionally biased when versions of a neuropsychological test used at different follow-ups are not of equivalent difficulty. This study's objective was to compare mean, linear, and equipercentile equating methods and demonstrate their utility in longitudinal research.

Study design and setting: The Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE, N = 1,401) study is a longitudinal randomized trial of cognitive training. The Alzheimer's Disease Neuroimaging Initiative (ADNI, n = 819) is an observational cohort study. Nonequivalent alternate versions of the Auditory Verbal Learning Test (AVLT) were administered in both studies.

Results: Using visual displays, raw and mean-equated AVLT scores in both studies showed obvious nonlinear trajectories in reference groups that should show minimal change and poor equivalence over time (ps ≤ .001), and raw scores demonstrated poor fits in models of within-person change (root mean square errors of approximation, RMSEAs > 0.12). Linear and equipercentile equating produced more similar means in reference groups (ps ≥ .09) and performed better in growth models (RMSEAs < 0.05).

Conclusion: Equipercentile equating is the preferred equating method because it accommodates tests more difficult than a reference test at different percentiles of performance and performs well in models of within-person trajectory. The method has broad applications in both clinical and research settings to enhance the ability to use nonequivalent test forms.

Publication types

  • Randomized Controlled Trial
  • Research Support, N.I.H., Intramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Aged
  • Aged, 80 and over
  • Cognition Disorders / diagnosis*
  • Cognition Disorders / psychology
  • Cognition*
  • Female
  • Humans
  • Individuality
  • Longitudinal Studies
  • Male
  • Neuropsychological Tests*
  • Verbal Learning