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

Abstract

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.Consider the results shown in Figure 1 where mean results from a 2 × 5 experiment are shown.The error bars show the standard error in each condition, measured on 16 participants per point.If confidence intervals had been shown, the error bars would have been about twice their actual sizes!By looking at this figure, we have no doubt that it is only noise.Yet, have a look at the ANOVA table: the effects and the interaction are all highly significant!How can this be?The present data are simulated.However, we obtained similar results in Paradis and Cousineau (in preparation).This kind of situation was first noted by Loftus and Masson (1994).The cause of the discrepancy between the figure and the analyses is not obvious.It is not a problem with homogeneity of variances (all the variances are homogeneous and spherical, Tabachnik & Fidell, 1996,