Correction: On the Utility of Integrated Speed-Accuracy Measures when Speed-Accuracy Trade-Off is Present

This article details a correction to: Vandierendonck, A. (2021). On the Utility of Integrated Speed-Accuracy Measures when Speed-Accuracy Trade-off is Present. Journal of Cognition, 4(1), 22. DOI: https://doi.org/10.5334/joc.154

It came to the author's attention that in the simulations presented by Vandierendonck (2021) an incorrect formula was used in the calculations of the integrated speed-accuracy measure BIS (Liesefeld & Janczyk, 2019). The pooled standard deviation over trials, conditions, and subjects was used instead of the standard deviation over subjects after aggregating trial and condition data per subject and for the speed data only correct instead of all RTs were used. A recalculation shows that in all four simulation studies the correct values tended to differ from the ones in the publication. In the present article, the correct outcomes for the BIS measure in each study are reported. The data and the scripts for these calculations are available at https://doi.org/10.5281/zenodo.5493844.

STUDY 1: BALANCED SPEED AND ACCURACY EFFECTS
The correct BIS means of the cells of the design are shown in Figure 1 as a function of percentage of errors (PE level, the four panels in the figure) and SAT size (the x-axis in each panel); within each panel the means are shown as a function of the 2 (Test condition) × 3 (directions of SAT) on the y-axis.
The Test effect on the corrected BIS measures (henceforth, BIS c ) was significant in all 40 replications (4 PE levels × 10 SAT size steps) and the 2 p h (partial eta-squared) values ranged between 0.613 and 0.740 (compared to 0.652-0.712 for the original values which also attained significance in all 40 cases). The results of BIS c and all the other measures in the study are shown in Figure 2 as a function of SAT size in four panels, one per PE level.  ) of the Test effect as a function of the variation in PE (panels A to D) and in SAT size for RT and PE for the five combined measures in Study 1.

Vandierendonck
Journal of Cognition DOI: 10.5334/joc.192 Similarly, the SAT effect on BIS c was significant in 5 of the 40 replications with 2 p h between 0.014 and 0.131 (originally 0 of 40 replications were significant and 2 p h varied between 0.016 and 0.057. Figure 3 shows these findings for all the measures per PE level and SAT size.

STUDY 2: SAT EFFECTS BASED ON THE DRIFT-DIFFUSION MODEL
Recalculation of BIS c in the second study revealed also small differences compared to the incorrect calculations. The means are displayed in

STUDY 3: REACTIVE SPEED-ACCURACY MODULATIONS
In the third study, the basic design was different and crossed a Test effect with conditions without and conditions with SAT. This design was also replicated over 4 PE levels and 10 SAT sizes. The means for BIS c are displayed in Figure    ) of the Test effect as a function of the variation in PE (panels A to D) and in SAT size for RT and PE for the five combined measures in Study 3.

STUDY 4: DISCONTINUOUS SPEED-ACCURACY TRADE-OFF
In this study a discontinuous model of speed-accuracy trade-off was tested by varying the SAT target levels that had to be achieved. The basic 2 (Test) × 5 (Targets) design was replicated in 2 PE levels × 5 Target size steps. The BIS c means are displayed in Figure

DISCUSSION
In all the studies, the recalculations of BIS yielded outcomes that were in the same range as the original calculations with the incorrect formula. Therefore, the discussion of the original outcomes is equally applicable to the recalculated outcomes and the conclusions formulated by Vandierendonck (2021) remain valid. ) of SAT Settings as a function of PE level and SAT strength for RT and PE and the five combined measures in Study 3. The dashed line (labeled α) represents the significance threshold for these data.

Figure 10
Sample Means in Study 4 as a function of Test × SAT Targets × SAT size (x-axis in each panel) × PE level. The row of panels shows the BIS c means with respect to PE level × Test, such that the two panels on the left show the control and the experimental condition means at PE level 0.05, and the two panels on the right show the control and experimental condition means at PE level 0.10. Legend: open circles for control condition and closed circles for experimental condition; red solid lines for 75%, orange dashed lines for 80%, yellow dotted lines for 85%, green dashed lines for 90%, and dark green solid lines for 95% target.