Converting between measures of slope of the psychometric function.

The psychometric function's slope provides information about the reliability of psychophysical threshold estimates. Furthermore, knowing the slope allows one to compare, across studies, thresholds that were obtained at different performance criterion levels. Unfortunately, the empirical validation of psychometric function slope estimates is hindered by the bewildering variety of slope measures that are in use. The present article provides conversion formulas for the most popular cases, including the logistic, Weibull, Quick, cumulative normal, and hyperbolic tangent functions as analytic representations, in both linear and log coordinates and to different log bases, the practical decilog unit, the empirically based interquartile range measure of slope, and slope in a d' representation of performance.