title: Comparing a single case to a control group - Applying linear mixed effects models to repeated measures data.
abstract: In neuropsychological research, single-cases are often compared with a small control sample. Crawford and colleagues developed inferential methods (i.e., the modified t-test) for such a research design. In the present article, we suggest an extension of the methods of Crawford and colleagues employing linear mixed models (LMM). We first show that a t-test for the significance of a dummy coded predictor variable in a linear regression is equivalent to the modified t-test of Crawford and colleagues. As an extension to this idea, we then generalized the modified t-test to repeated measures data by using LMMs to compare the performance difference in two conditions observed in a single participant to that of a small control group. The performance of LMMs regarding Type I error rates and statistical power were tested based on Monte-Carlo simulations. We found that starting with about 15-20 participants in the control sample Type I error rates were close to the nominal Type I error rate using the Satterthwaite approximation for the degrees of freedom. Moreover, statistical power was acceptable. Therefore, we conclude that LMMs can be applied successfully to statistically evaluate performance differences between a single-case and a control sample.
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany; Eberhardt-Karls University Tuebingen, Germany. Electronic address: s.huber@iwm-kmrc.de.
authors.forename: Stefan
authors.initials: S
authors.lastname: Huber
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany; Section Neuropsychology, Department of Neurology, University Hospital, RWTH Aachen University, Germany.
authors.forename: Elise
authors.initials: E
authors.lastname: Klein
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany; Eberhardt-Karls University Tuebingen, Germany.
authors.forename: Korbinian
authors.initials: K
authors.lastname: Moeller
authors.affiliation: Section Neuropsychology, Department of Neurology, University Hospital, RWTH Aachen University, Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Willmes
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D035061:Control Groups; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D008959:Models, Neurological; D009010:Monte Carlo Method; D009484:Neuropsychology / Q000379:methods*; D015203:Reproducibility of Results; D012107:Research Design
keywords: Linear mixed models; Monte-Carlo simulation; Neuropsychological methods; Single case methods