Fitted Weibull function parameters for 2AFC contrast discrimination.

This table shows Weibull parameters fitted to 2AFC contrast discrimination data from six studies. The data from Meese et al. [4] are for their Binocular condition (plotted as squares in their Figure 5); these data were kindly provided by Tim Meese. For the other five papers, we read off the data points from digital scans of the figures (Bird et al. [34], Figure 1; Foley and Legge [1], Figure 1; Henning et al. [47], Figure 4 (sine wave stimuli only); Henning & Wichmann [40], Figure 4; Nachmias & Sansbury [6], Figure 2). In most cases, these figures plotted the proportion correct, P, for several different contrast differences, Δc, and we fitted the Weibull function using a maximum-likelihood method; specifically, we fitted the Weibull function by maximizing the expression , where is the Weibull function whose parameters were being fitted. In Henning & Wichmann's [40] paper, the figures plotted the Δc values corresponding to 60%, 75%, and 90% correct on the fitted psychometric functions, so we had to fit Weibull functions to points sampled from Henning & Wichmann's own fitted psychometric functions, rather than to the raw data. Where possible, we fitted both the lapse-free Weibull function of Equation (1), and the Weibull function of Equation (2), which includes a fitted lapse rate parameter, λ. Parameters for the former fit appear under the heading “′′, and those for the latter appear under the heading “λ fitted”. In many cases, the data did not sufficiently constrain λ because there were no data points on the saturating portion of the psychometric function; in addition, Meese et al. 's Weibull fits did not include a lapse rate parameter. The Weber fraction, W, is given by , where is the pedestal value. The means and medians at the bottom of the table are calculated from those studies for which the pedestal level exceeds the detection threshold, so that both stimuli were clearly visible. The cases where the pedestal is below detection threshold are stared in the table, and these were excluded from the means and medians.