Tag Info

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
|             |             |
'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.