Simultaneity judgment

A judgment of whether two events occurred together. Its response curve across onset differences depends on timing noise and acceptance criteria; it need not equal the psychometric function of temporal order.

Let internal timing difference be $D=\delta +b+\epsilon$ with $\epsilon \sim N(0,s^2)$, and report simultaneous when $-h<D<h$. Standardizing the two interval bounds gives $P(\mathrm{same})=\Phi ((h-\delta -b)/s)-\Phi ((-h-\delta -b)/s)$. For positive $h,s$ and symmetric noise, this function peaks at $\delta =-b$. Its width reflects both noise and acceptance bounds, so it cannot identify a sensory window without additional assumptions.

An offset at which events are judged most simultaneous under a specified measurement procedure. A fitted peak in simultaneity reports need not coincide with the equal-response point of an order task or with equal neural onset latencies.