Katharina Anton-Erxleben provided us with the equality judgment data from Experiment 3 in Anton-Erxleben et al. (
2010), and we fit three different functions to the individual subject data for each of the three experimental conditions (test stimulus cued, neutral cue, and standard stimulus cued). The three fitted functions were given as follows:
the equality judgment function described in Schneider and Komlos (
2008), where Φ(
x) ≡
φ(
u)
du and
φ(
x) ≡
are, respectively, the cumulative normal distribution and normal probability density functions,
τ is the subjective equality criterion (subjects report that the two targets have equal contrast if the absolute difference in perceived contrast is less than
τ), Δ
c is the actual difference in contrast between the two target stimuli,
α is the hypothesized attentional boost in the perceived contrast of the cued target, and
σ 2 is the variance of the perceived contrast difference;
a scaled skew normal function (after Azzalini,
1985), where
h is a scale factor, and
γ is a skew parameter (
Figure 2); and
the equality judgment function (with
α = 0) plus a non-zero asymptote or “guessing rate”
g at low contrast, applied with a threshold
μ g and slope
σ g . In fitting this third function, the
σ, μ g, and
σ g parameters were linked across conditions, so that only the subjective criteria
τ and
g were free to independently vary among the conditions; there were nine free parameters in total to fit the data from the three conditions for each subject.