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Covariance appears along the off-diagonal elements of the variance-covariance matrix, while variance appears along the diagonal. The first assumption is compound symmetry, which means that in addition to homogeneity of variance, the covariances are similar. rmANOVAs require two additional assumptions (for example, see Maxwell and Delaney, 2004 Nimon, 2012). This phenomenon, which is known as pseudoreplication, is common in neuroscience experiments and leads to the use of repeated-measures (rm) ANOVAs. These measurements cannot be considered as independent because three measurements (“repeated measures”) were collected per listener. If the measurements came from a single group of multilingual listeners who all performed the task in each language, then language would be described as a “within-participants” factor. Now it may be that the measurements were obtained in a very different manner.
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This method assumes that the response variable comes from a normally distributed population and shows homogeneity of variance.
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In this case, language can also be described as a “between-participants” factor, and the data may be analyzed with a standard analysis of variance (ANOVA). Such data is grouped by listener and by language, and since each listener can only belong to one language group, the grouping factors of listener and language are said to be nested. Importantly, each measurement would be from a different listener. RTs may have been measured from three different groups of monolingual listeners. Measurements of RT are available for concurrent speech in French, German, and English, and thus language can be described as a categorical factor with three levels. The response variable collected is the average reaction time (RT), and at first, only one explanatory variable is available: language. Let us consider a hypothetical experiment where a researcher is interested in how quickly human listeners can detect a telephone ringing in the presence of concurrent speech. Why Would One use LMMs to Analyse Within-Participant Data? The current article briefly reviews the use of LMMs for within-participant studies typical in in experimental psychology, before describing a free, graphical user interface (LMMgui ) to carry out LMM analyses. Linear mixed-effects models (LMMs) provide a versatile approach to data analysis and have been shown to be very useful in a several branches of neuroscience ( Gueorguieva and Krystal, 2004 Kristensen and Hansen, 2004 Quené and van den Bergh, 2004 Baayen et al., 2008 Lazic, 2010 Judd et al., 2012 Aarts et al., 2014).