AbstractWhen observers make rapid, difficult sensory decisions, their response time is highly variable from trial to trial. We previously compared humans and rats performing the same visual motion discrimination task. Their response time distributions were similar, but for humans accuracy was negatively correlated with response time, whereas for rats it was positively correlated. This is of interest because different mathematical theories of decision-making differ in their predictions regarding the correlation of accuracy with response time. On the premise that sensory decision-making mechanisms are likely to be conserved in mammals, our objective is to reconcile these results within a common theoretical framework. A bounded drift diffusion model (DDM) with stochastic parameters is a strong candidate, because it is known to be able to produce either late errors like humans, or early errors like rats. We consider here such a model with seven free parameters: the evidence accumulator’s starting point z, drift rate v, non-decision-time t, threshold separation a, and three noise terms σz, σv and σt. We fit the model parameters to data from both rats and humans. Trial data simulated by the model recapitulate quantitative details of the relationship between accuracy and response time in both species. On this model, the species difference can be explained by greater variability in the starting point of the diffusion process (σz) in rats, and greater variability in the drift rate (σv) in humans.