Assessing the distortions introduced when calculating d': A simulation approach

The discriminability measure $$ is widely used in psychology to estimate sensitivity independently of response bias. The conventional approach to estimate $$ involves a transformation from the hit rate and the false-alarm rate. When performance is perfect, correction methods must be applied to calculate $$ , but these corrections distort the estimate. In three simulation studies, we show that distortion in $$ estimation can arise from other properties of the experimental design (number of trials, sample size, sample variance, task difficulty) that, when combined with application of the correction method, make $$ distortion in any specific experiment design complex and can mislead statistical inference in the worst cases (Type I and Type II errors). To address this problem, we propose that researchers simulate $$ estimation to explore the impact of design choices, given anticipated or observed data. An R Shiny application is introduced that estimates $$ distortion, providing researchers the means to identify distortion and take steps to minimize its impact.