d' (also called sensitivity index) is a measure used in signal detection theory to quantify how well a signal can be distinguished from noise.
$d'$ (also called sensitivity index) is a measure used in signal detection theory to quantify how well a signal can be distinguished from noise.
Given that a signal may be present or not, and the receiver may assert that the signal is present or not, there are four possibilities:
Signal:
Present Not present
Receiver: ---------------------------
| | |
'Present' | Hit | False alarm |
| | |
---------------------------
| | |
'Not present' | Miss | Correct |
| | rejection |
---------------------------
The number of Hits divided by (Hits + Misses) is the hit rate ($h$), and the number of False alarms divided by (False alarms + Correct rejections) is the false alarm rate ($fa$). These can be decomposed into the sensitivity ($d'$) of the receiver:
$$
d' = \Phi^{-1}(h) - \Phi^{-1}(fa)
$$
To completely specify a receiver's behavior, sensitivity is usually paired with bias ($c$):
$$
c = \frac{\Phi^{-1}(h) + \Phi^{-1}(fa)}{2}
$$
Although the conceptual background is slightly different, it is interesting to note that sensitivity / $d'$ here is computed the same as the sensitivity that is used to assess classification performance.
