Same same but different: Subtle but consequential differences between two measures to linearly integrate speed and accuracy (LISAS vs. BIS)

Condition-specific speed-accuracy trade-offs (SATs) are a pervasive issue in experimental psychology, because they sometimes render impossible an unambiguous interpretation of experimental effects on either mean response times (mean RT) or percentage of correct responses (PC). For between-participants designs, we have recently validated a measure (Balanced Integration Score, BIS) that integrates standardized mean RT and standardized PC and thereby controls for cross-group variation in SAT. Another related measure (Linear Integrated Speed-Accuracy Score, LISAS) did not fulfill this specific purpose in our previous simulation study. Given the widespread and seemingly interchangeable use of the two measures, we here illustrate the crucial differences between LISAS and BIS related to their respective choice of standardization variance. We also disconfirm the recently articulated hypothesis that the differences in the behavior of the two combined performance measures observed in our previous simulation study were due to our choice of a between-participants design and we demonstrate why a previous attempt to validate BIS (and LISAS) for within-participants designs has failed, pointing out several consequential issues in the respective simulations and analyses. In sum, the present study clarifies the differences between LISAS and BIS, demonstrates that the choice of the variance used for standardization is crucial, provides further guidance on the calculation and use of BIS, and refutes the claim that BIS is not useful for attenuating condition-specific SATs in within-participants designs.