D-prime is an index for the discriminability of a signal from noise.
For signals with quantitative values and assummed that values are normally distributed, d-prime is defined as mean(signal) - mean(noise) divided by the square root of the half the sum of variance(noise) plus variance(signal)
Calculating D-prime based on hit rate
The d-prime index can aslo be derived from hit and false-alarm rates by calculating the inverse of the cumulative distribution function of the Gaussian distribution.
In r this is done like this this:
n = length(observations) hits = length(observations[ observations$hit == TRUE]) hr = hits / n fa = 1 - hr dprime = qnorm (hr) - qnorm(fa)