**When the visual system analyzes distributed patterns of sensory inputs, what features of those distributions does it use? It has been previously demonstrated that higher-order statistical moments of luminance distributions influence perception of static surfaces and textures. Here, we tested whether the brain also represents higher-order moments of dynamic stimuli. We constructed random dot kinematograms, where dots moved according to probability distributions that selectively differed in terms of their mean, variance, skewness, or kurtosis. When viewing these stimuli, human observers were sensitive to the mean direction of coherent motion and to the variance of dot displacement angles, but they were insensitive to skewness and kurtosis. Observer behavior accorded with a model of directional motion energy, suggesting that information about higher-order moments is discarded early in the visual processing hierarchy. These results demonstrate that use of higher-order moments is not a general property of visual perception.**

^{2}; 3 pixel

^{2}) with an average dot density of 100.2 dots per square degree per second. These parameters are similar to those used in other psychophysical and neurophysiological experiments (Britten, Shadlen, Newsome, & Movshon, 1993; Watamaniuk et al., 1989).

*SD*= 20°). Dot motion within a specific circular aperture (the “odd patch”) was generated from one of several different distributions. The odd patch aperture (3° diameter) was always located in the top half of the display, and it was always centered at 3.5° eccentricity from the fixation point. Its radial position varied between 0° and 180° from trial to trial. To reduce adaptation, we added 180° to the mean of both the background and odd distributions on a random half of the trials.

*N*= 100,000,000) using each set of Pearson distribution parameters and computing the circular mean, standard deviation, skewness, and kurtosis. Next, to evaluate the possibility of recovering moment values from the dot stimuli themselves, we computed circular statistics from the stimuli shown on each trial. That is, we measured the angle of each coherent dot displacement after discretization into pixel coordinates and then calculated the sample statistics of that distribution. This computation excluded the final 300 ms of the stimulus, corresponding to the approximate nondecision time (i.e., the approximate sum of visual latency and saccade latency; Palmer, Huk, & Shadlen, 2005; Resulaj, Kiani, Wolpert, & Shadlen, 2009). We did this so that the statistics would correspond to the dot motion that was most likely used to make the decision on each trial.

_{0}:

_{0}:

*z*= 16.63,

*p*< 1e-8) and standard deviation (

*z*= 22.35,

*p*< 1e-8), but not skewness (

*z*=

*p*= 0.47) or kurtosis (

*z*= 0.88,

*p*= 0.38).

*z*=

*p*= 0.66) or by trial-wise kurtosis on kurtosis-manipulated trials (Equation 1,

*z*= 1.40,

*p*= 0.16).

*t*=

*p*< 1e-8) and standard deviation (

*t*=

*p*< 1e-8) but not skewness (

*t*= 0.77,

*p*= 0.44) or kurtosis (

*t*=

*p*= 0.40). This pattern of behavior was consistent across individual observers (Figure 5B).

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