  We derive expressions for the first three moments of the decision time (DT)
distribution produced via first threshold crossings by sample paths of a
drift-diffusion equation. The "pure" and "extended" diffusion processes are
widely used to model two-alternative forced choice decisions, and, while simple
formulae for accuracy, mean DT and coefficient of variation are readily
available, third and higher moments and conditioned moments are not generally
available. We provide explicit formulae for these, describe their behaviors as
drift rates and starting points approach interesting limits, and, with the
support of numerical simulations, discuss how trial-to-trial variability of
drift rates, starting points, and non-decision times affect these behaviors in
the extended diffusion model. Both unconditioned moments and those conditioned
on correct and erroneous responses are treated. We argue that the results will
assist in exploring mechanisms of evidence accumulation and in fitting
parameters to experimental data.
