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Title: An extension of within-subject confidence intervals to models with crossed random effects
Authors: Politzer-Ahles, S 
Issue Date: 2017
Source: Quantitative methods for psychology, 2017, v. 13, no. 1, p. 75-94
Abstract: A common problem in displaying within-subject data is that of how to show confidence intervals that accurately re 2 ect the pattern of significant differences between conditions. The Cousineau-Morey method (Cousineau, 2005; Morey, 2008) is a widely used solution to this issue; however, this method only applies to experimental designs with only one repeated-measures factor (e. g., subjects). Many experimental designs in fields such as psycholinguistics and social psychology use crossed random effect designs where, e. g., there are repeated measures both for subjects and stimuli. For such designs, extant methods for showing within-subject intervals would require first aggregating over stimuli, and thus such intervals might be a less accurate re 2 ection of the statistical significance patterns if the data are actually analyzed using a method that takes both random effects into account (e. g., linear mixed-effects models). The present paper proposes an extension of the method described above to address this problem; the proposal is to scale the data using a mixed-effects model, rather than using the means from each subject, and then calculate confidence intervals from the data scaled thusly. Analysis of a sample of crossed random effect datasets reveals that intervals calculated using this method give a slightly more accurate re 2 ection of the pattern of statistical significance in the between-condition differences.
Keywords: Confidence intervals
Repeated measures
Linear mixed effects
Within-subjects confidence intervals
Crossed random effects
Publisher: University of Montreal, Department of Psychology
Journal: Quantitative methods for psychology 
ISSN: 2292-1354
DOI: 10.20982/tqmp.13.1.p075
Rights: All copyrights goes to the authors of the articles published in the Quantitative Methods for Psychology. All articles are open-access articles distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
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The following publication Politzer-Ahles, S. (2017). An extension of within-subject confidence intervals to models with crossed random effects. Quantitative Methods for Psychology, 13(1), 75-94 is available at
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