dprime

dprime, often written d', is a sensitivity measure in signal detection theory that quantifies an observer's ability to distinguish signal from noise. In the standard model, the internal responses to noise and to signal plus noise are assumed to be normally distributed with equal variance. d' represents the separation of these distributions in units of the shared standard deviation and is equivalently computed as the difference between the z-scores of the hit rate and the false alarm rate: d' = z(H) − z(F).

Calculation typically uses data from a yes/no detection task. H is the proportion of signal trials correctly identified (hits), and F is the proportion of noise trials incorrectly identified as signal (false alarms). To avoid infinite z-values when H or F is 0 or 1, a common correction is applied (for example, H = (hits + 0.5) / (signal trials + 1) and F = (false alarms + 0.5) / (noise trials + 1)); then z-scores are computed from these adjusted rates and their difference yields d'.

Interpretation: d' measures discriminability independent of response bias. A larger d' signals greater sensitivity to detect the signal. While d' captures perceptual or cognitive sensitivity, the decision criterion or bias—how willing the observer is to say "signal"—is separate. A common bias index is c = −0.5 [z(H) + z(F)], where positive values indicate a conservative bias and negative values indicate a liberal bias.

Extensions and notes: If the equal-variance assumption is violated, alternative methods or nonparametric measures (such as A') can be used. d' is widely applied in psychology, neuroscience, and related fields to compare performance across conditions, tasks, or groups. It is unitless and reflects the separation between the underlying internal distributions.