Confidence intervals in within-subject designs: A simpler solution to Loftus and Masson's method
Denis Cousineau
Within-subject ANOVAs are powerful for analyzing data because they remove between-subject variability. However, standard error or confidence interval bars in graphs are misleading as they include between-subject variability. Loftus and Masson (1994) proposed an alternative method to compute error bars, but it has three limitations: (i) it requires prior analysis, (ii) it provides a single error bar for all conditions, and (iii) it is difficult to implement in common graphing software. Here, a simpler alternative is proposed and implemented in SPSS.
In a 2×5 experiment, the error bars show standard error, but confidence intervals would be twice as large. The graph appears to show noise, but the ANOVA shows significant effects. This discrepancy is due to the repeated-measure design, where participants are measured in all conditions. Figure 2 shows individual results, revealing large differences between participants. This indicates significant between-subject variability, but in psychology, this is expected.
By adjusting each participant's scores to remove individual differences, a clear trend is revealed. This approach, using a new variable Y, allows for accurate error bars that exclude between-subject variability. In SPSS, this can be done by first computing participant means, then creating Y as the difference between participant and group means. This method solves the three limitations of Loftus and Masson's approach, allowing for accurate graphical representation of data. The data and syntax for SPSS 13.0 are available on the journal's website.Confidence intervals in within-subject designs: A simpler solution to Loftus and Masson's method
Denis Cousineau
Within-subject ANOVAs are powerful for analyzing data because they remove between-subject variability. However, standard error or confidence interval bars in graphs are misleading as they include between-subject variability. Loftus and Masson (1994) proposed an alternative method to compute error bars, but it has three limitations: (i) it requires prior analysis, (ii) it provides a single error bar for all conditions, and (iii) it is difficult to implement in common graphing software. Here, a simpler alternative is proposed and implemented in SPSS.
In a 2×5 experiment, the error bars show standard error, but confidence intervals would be twice as large. The graph appears to show noise, but the ANOVA shows significant effects. This discrepancy is due to the repeated-measure design, where participants are measured in all conditions. Figure 2 shows individual results, revealing large differences between participants. This indicates significant between-subject variability, but in psychology, this is expected.
By adjusting each participant's scores to remove individual differences, a clear trend is revealed. This approach, using a new variable Y, allows for accurate error bars that exclude between-subject variability. In SPSS, this can be done by first computing participant means, then creating Y as the difference between participant and group means. This method solves the three limitations of Loftus and Masson's approach, allowing for accurate graphical representation of data. The data and syntax for SPSS 13.0 are available on the journal's website.