# Sensitivity index

(Redirected from D')

The sensitivity index or d' (pronounced 'dee-prime') is a statistic used in signal detection theory. It provides the separation between the means of the signal and the noise distributions, compared against the standard deviation of the signal plus noise distributions. For normally distributed signal and noise with mean and standard deviations ${\displaystyle \mu _{S}}$ and ${\displaystyle \sigma _{S}}$, and ${\displaystyle \mu _{N}}$ and ${\displaystyle \sigma _{N}}$, respectively, d' is defined as:

${\displaystyle d'={\frac {\mu _{S}-\mu _{N}}{\sqrt {{\frac {1}{2}}(\sigma _{S}^{2}+\sigma _{N}^{2})}}}}$[1]

An estimate of d' can be also found from measurements of the hit rate and false-alarm rate. It is calculated as:

d' = Z(hit rate) − Z(false alarm rate),[2]

where function Z(p), p ∈ [0,1], is the inverse of the cumulative distribution function of the Gaussian distribution.

d' is a dimensionless statistic. A higher d' indicates that the signal can be more readily detected.