Signal detection theory

A framework separating stimulus discriminability from decision criterion in noisy tasks. Response bias and sensory sensitivity need not change together.

The ability to discriminate stimulus classes, conceptually distinct from the decision criterion determining which response is selected. A higher frequency of fear judgments can reflect a criterion shift without better discrimination.

Under an equal-variance Gaussian evidence model, $d^{\prime }$ is separation of signal and noise means in units of their common standard deviation. A yes/no task gives $d^{\prime }={\Phi }^{-1}(H)-{\Phi }^{-1}(F)$, where $H$ and $F$ are hit and false-alarm probabilities. This formula assumes the model; it does not define every possible sensory-discrimination measure.

Compare independent Gaussian samples $R_s,R_n$ with means ${\mu }_s,{\mu }_n$ and common variance ${\sigma }^2$. Choosing the larger is correct when $R_s-R_n>0$. The difference has mean ${\mu }_s-{\mu }_n$ and variance $2{\sigma }^2$, so standardization proves the displayed relation. Correlated samples, unequal variances or a different response rule need a different calculation.

A rule or boundary converting internal evidence into a response, such as reporting a signal when $R>c$. Changing the criterion can change hits and false alarms without changing the separation of the underlying evidence distributions. A measured response threshold is therefore not automatically a pure measure of sensory sensitivity.