Calculating and graphing within-subject confidence intervals for ANOVA

The psychological and statistical literature contains several proposals for calculating and plotting confidence intervals (CIs) for within-subjects (repeated measures) ANOVA designs. A key distinction is between intervals supporting inference about patterns of means (and differences between pairs of means, in particular) and those supporting inferences about individual means. In this report, it is argued that CIs for the former are best accomplished by adapting intervals proposed by Cousineau (Tutorials in Quantitative Methods for Psychology, 1, 42-45, 2005) and Morey (Tutorials in Quantitative Methods for Psychology, 4, 61-64, 2008) so that nonoverlapping CIs for individual means correspond to a confidence for their difference that does not include zero. CIs for the latter can be accomplished by fitting a multilevel model. In situations in which both types of inference are of interest, the use of a two-tiered CI is recommended. Free, open-source, cross-platform software for such interval estimates and plots (and for some common alternatives) is provided in the form of R functions for one-way within-subjects and two-way mixed ANOVA designs. These functions provide an easy-to-use solution to the difficult problem of calculating and displaying within-subjects CIs.