Confidence intervals in within-subject designs: A simpler solution to Loftus and Masson's method

By Denis Cousineau. 2005

1,954 citations recorded by the source corpus.

Within-subject ANOVAs are a powerful tool to analyze data because the variance associated to differences between the participants is removed from the analysis. Hence, small differences, when present for most of the participants, can be significant even when the participants are very different from one another. Yet, graphs showing standard error or confidence interval bars are misleading since these bars include the between-subject variability. Loftus and Masson (1994) noticed this fact and proposed an alternate method to compute the error bars. However, i) their approach requires that the ANOVA be performed first, which is paradoxical since a graph is an aid to decide whether to perform analyses or not; ii) their method provides a single error bar for all the conditions, masking information such as the heterogeneity of variances across conditions; iii) the method proposed is difficult to implement in commonly-used graphing software. Here we propose a simple alternative and sow how it can be implemented in SPSS.

Subfields: Developmental and Educational Psychology, Experimental and Cognitive Psychology

View Paper: https://www.semanticscholar.org/paper/e5857a9a0c09a92624a466a063e03104c1c3a605

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In Developmental and Educational Psychology

In Experimental and Cognitive Psychology

Citations in the corpus

The shifting boxplot. A boxplot based on essential summary statistics around the mean. (2010, background): “Such computation basically removes the between-groups variance since it is of no avail in the statistical analysis of dependent-measures designs (Cousineau, 2005; Jarmasz & Hollands, 2009; Loftus & Masson, 1994; Masson & Loftus, 2003; Morey, 2008).”
Reward has a residual impact on target selection in visual search, but not on the suppression of distractors (2011, background): “Error bars in all figures reflect withinsubject 95% confidence intervals (Cousineau, 2005).”
Retrieval Practice & Bloom’s Taxonomy: Do Students Need Fact Knowledge Before Higher Order Learning? (2019, methodology): “Error bars in figures represent 95% confidence intervals, specifically calculated for withinsubject designs according to methods described by Cousineau (2005) and Morey (2008).”
The ventriloquist in periphery: impact of eccentricity-related reliability on audio-visual localization. (2013, background): “mean corrected for between-subjects variability (Cousineau, 2005).”
Repetition suppression versus enhancement--it's quantity that matters. (2013, methodology): “Note that in all figures, standard error bars are presented that have been corrected for within-subject designs according to the methods proposed by Cousineau (2005) and Morey (2008).”
Confidence Intervals from Normalized Data: A correction to Cousineau (2005) (2008, methodology): “Cousineau (2005) presents an alternative to the Loftus and Masson method, but his method produces confidence intervals that are smaller than those of Loftus and Masson.”
Teleoperation with intelligent and customizable interfaces (2013, methodology): “Error bars here represent the standard error of the mean with repeated-measures corrections as suggested by (Cousineau, 2005)”
Target Amplification and Distractor Inhibition: Theta Oscillatory Dynamics of Selective Attention in a Flanker Task (2020, methodology): “Standard errors of the mean were corrected according to Cousineau (2005) for repeated-measures analyses. White boxes (A), white electrodes (B), and grey-shaded areas (C) indicate significant effects 364 Cogn Affect Behav Neurosci (2021) 21:355–371”