Remodeling visual search: How gamma distributions can bring those boring old RTs to
life.

Jeremy M Wolfe, Antonio Torralba, Todd S Horowitz

Subjects in even simple visual search tasks often produce RT distributions with long
positive tails. Typically, these long RTs are treated as noise resulting from vigilance or
motor errors and are discarded. We propose instead that the skewed shape of RT
distributions might tell us about the underlying cognitive architecture. These distributions
turn out to be well modeled by gamma distributions (Schneider and Shiffrin Psych Rev,
1977,84, 1; McElree & Carrasco, JEPHPP, 2000, 25,1517). Gamma distributions are
produced by summing processes whose durations are distributed exponentially. The
distribution has two parameters: One reflects the number of sub-processes being
summed; the other, the time constant of the exponential distribution of those sub-processes.
Many models of visual search assume that attention is deployed from one item
to the next at a relatively constant rate. If we suppose, however, that deployments are
exponentially distributed in time, then we would predict gamma distributed RTs, though
matters are complicated by added components in the measured RT such as motor
response times. We evaluated this supposition using 4000 trials from each of 10 subjects
performing a difficult spatial configuration search task. Target present and absent trials
were gamma distributed. Gamma parameters are most readily interpreted for absent trials
because the number of items selected by attention should be roughly constant across
trials. Here fits of the parameter reflecting the number of deployments of attention
increased linearly with set size while the time constant parameter remained relatively
constant across set size. We describe a revised version of the Guided Search model,
employing exponentially distributed deployment times, which produces a good fit to the
experimental data.