Psychometric functions.

*Top row*: time-independent cumulative Weibull function (), fit to data binned by viewing time.

*Middle row*: time-dependent cumulative Weibull function (), fit to data as a function of both motion strength and viewing time.

*Bottom row*: decision model (

*Eq. 3*), fit to data as a function of both motion strength and viewing time.

*Left column*: percentage correct plotted vs. stimulus strength.

*Middle column*: discriminability (

*d*′) plotted vs. signal strength on log–log coordinates.

*Right column*: relationship between psychometric slope and threshold for changes in the values of key parameters of each model, as indicated (arrows point to larger values for each parameter). The dash–dotted line in

*A* indicates psychometric slope, defined as the steepness of the function plotted on a logarithmic abscissa at threshold. The dashed lines in

*left* and

*middle columns* indicate threshold, defined as the stimulus strength corresponding to

*d*′ = 1. The grayscale in

*D*,

*E*,

*G*, and

*H* depicts viewing time (darker lines correspond to longer times). The

*inset* in

*B* depicts the relationship between percentage correct and

*d*′ according to signal-detection theory: for a 2-alternative task, percentage correct is the proportion of a normally distributed random variable >0 (gray) (; ; ). In this case, the random variable is assumed to reflect the net accumulated evidence in favor of the correct (positive values) vs. the incorrect (negative values) choice.

*d*′ is the mean divided by the SD of this random variable (scaled by

because it is assumed to represent a difference between signals representing the 2 choices). Parameters of the cumulative Weibull functions correspond directly to threshold and slope and are therefore useful for describing the data. Parameters of the decision model are more complicated and are thought to more closely reflect the underlying neural mechanisms.

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