Although some previous studies measured the non-decision time as the point in time at which motion fluctuations no longer exert a significant influence on the initial choice, this method is biased because estimates of latency become shorter if non-decision times are more variable across trials, or if more trials are included. We used an alternative approach, which involves fitting a function, f(t), to the psychophysical kernels. (a) The shape of f(t) was derived assuming that the slow decay of the psychophysical kernels when aligned on movement onset is due to: (i) trial-to-trial variability in the non-decision time, and (ii) the smoothing introduced by the impulse response of the motion energy (inset; same as in Figure 4a). Without these influences, the influence of motion fluctuations on choice would step to zero at a fixed latency (μtnd) before movement (black solid line). Inter-trial variability in the non-decision time reduces the number of trials that contribute to the psychophysical kernel for times closer to movement onset. If this variability is assumed Gaussian, the step function is smoothed into a cumulative Gaussian (g[t μtnd, σtnd]; dashed line). To fit the psychophysical kernels, we also need to consider the additional smoothing introduced by the motion filter, which we do by convolving g(t) with the impulse response of the motion filter, IR(t), such that, where is is an arbitrary scaling parameter. The final fit, that is f(t), is shown by the black line. To increase the statistical power, we combined the motion energy residuals from rightward and leftward choices, such that positive residuals indicate an excess of motion in the direction of the initial choice. The green shaded area represents s.e.m. for the average of the motion energy residuals, including trials from all subjects. We fit μtnd, σtnd and to minimize the deviance between f(t) and the average of the motion energy residuals. The best-fitting parameters μtnd and σtnd are indicated in the panel. (b) Same analysis as in (a), but conducted separately for each subject. Latencies are similar to those obtained by fitting a bounded accumulation model (Table 1).