A comparison of methods to combine speed and accuracy measures of performance: A rejoinder on the binning procedure

In cognitive research, speed and accuracy are two important aspects of performance. When analyzed separately, these performance variables sometimes lead to contradictory conclusions about the effect of a manipulation. To avoid such conflicts, several measures that integrate speed and accuracy have been proposed, but the added value of using such measures remains unclear. The present paper compares the relative utility of seven integrated performance measures, namely four variations on a binning procedure that weights response times of correct and incorrect trials differently, and three measures that combine averaged speed and accuracy scores. The properties of these integrated measures were explored in three simulation studies. The first study compared three binning measures and showed that one measure failed to grasp the performance difference between two conditions. The second study showed that the sampling distributions of the measures were symmetric, except for a strong skewness on the rate correct score. The third study varied the trade-off and the effect sizes of speed and accuracy in four different combinations of size and direction of speed and accuracy effects. These studies highlighted some further shortcomings of the binning measures. The combination measures performed well, but linear integration of speed and accuracy and rate correct score were most efficient in detecting effects and accounting for a larger proportion of the variance. The paper concludes that these combination measures are useful provided that the speed and accuracy data are also inspected.