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Comparing a single case to a control group - Applying linear mixed effects models to repeated measures data.

Stefan Huber1, Elise Klein2, Korbinian Moeller1

  • 1Leibniz-Institut für Wissensmedien, Tuebingen, Germany; Eberhardt-Karls University Tuebingen, Germany.

Cortex; a Journal Devoted to the Study of the Nervous System and Behavior
|July 29, 2015
PubMed
Summary

Linear mixed models (LMMs) offer a powerful extension to existing methods for comparing single neuropsychological cases with small control groups. This approach provides reliable statistical evaluation for performance differences, even with limited sample sizes.

Keywords:
Linear mixed modelsMonte-Carlo simulationNeuropsychological methodsSingle case methods

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Area of Science:

  • Neuropsychology
  • Statistical Modeling

Background:

  • Single-case studies are common in neuropsychology and often involve comparisons with small control samples.
  • Existing inferential methods, like the modified t-test by Crawford et al., are used for these comparisons.

Purpose of the Study:

  • To extend existing inferential methods for single-case comparisons using linear mixed models (LMMs).
  • To adapt these methods for repeated measures data in single-case research.
  • To evaluate the performance of LMMs in terms of Type I error rates and statistical power.

Main Methods:

  • Demonstrated the equivalence of a t-test for a dummy coded predictor and the modified t-test.
  • Generalized the modified t-test to repeated measures using LMMs.
  • Conducted Monte-Carlo simulations to assess Type I error rates and statistical power of LMMs.

Main Results:

  • Linear mixed models (LMMs) showed Type I error rates close to nominal levels with approximately 15-20 participants in the control sample.
  • The Satterthwaite approximation for degrees of freedom was effective in controlling error rates.
  • Statistical power was found to be acceptable for this research design.

Conclusions:

  • Linear mixed models (LMMs) provide a statistically sound method for evaluating performance differences between single cases and small control groups.
  • LMMs offer a viable extension to existing methods, particularly for repeated measures designs in neuropsychological research.