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.
Highlights
Within-subject ANOVAs are a powerful tool to analyze data because the variance associated to differences between the participants is removed from the analysis
The error bars show the standard error in each condition, measured on 16 participants per point
We obtained similar results in Paradis and Cousineau. This kind of situation was first noted by Loftus and Masson (1994)
Summary
Within-subject ANOVAs are a powerful tool to analyze data because the variance associated to differences between the participants is removed from the analysis. Loftus and Masson (1994) noticed this fact and proposed an alternate method to compute the error bars. We obtained similar results in Paradis and Cousineau (in preparation) This kind of situation was first noted by Loftus and Masson (1994). We can safely conclude that the participants differ significantly (this information is provided by most statistical software, F(1, 15) = 710, p < .001). By looking carefully at the second condition of the factor 1 (the right panel of Figure 2), we see that for most of the participants, scores decrease when going from the first level of factor 2 to the fifth
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