Observers can voluntarily shift their psychometric functions without losing sensitivity

Abstract

Psychometric sensory discrimination functions are usually modeled by cumulative Gaussian functions with just two parameters, their central tendency (μ) and their slope (1/σ). These correspond to Fechner's "constant" and "variable" errors, respectively. Fechner pointed out that even the constant error could vary over space and time and could masquerade as variable error. We wondered whether observers could deliberately introduce a constant error into their performance without loss of precision. In three-dot vernier and bisection tasks with the method of single stimuli, observers were instructed to favour one of the two responses when unsure of their answer. The slope of the resulting psychometric function was not significantly changed, despite a significant change in central tendency. Similar results were obtained when altered feedback was used to induce bias. We inferred that observers can adopt artificial response criteria without any significant increase in criterion fluctuation. These findings have implications for some studies that have measured perceptual "illusions" by shifts in the psychometric functions of sophisticated observers.

Fig. 1

The first panel (top left) shows data from Winawer et al. (2010). The vertical axis shows the probability of classifying the motion direction left versus right. The remaining panels show psychometric functions from a three-dot vernier alignment task, in which the magnitude of the physical shift of the centre dot (horizontal axis) was sampled from a set of fixed values without replacement. The units of displacement are Weber fractions as percentages (100 * target shift/interpatch distance). Negative shifts are shifts “down.” The vertical axis is the probability with which the observer classifies a shift as “up” versus “down.” Vertical bars are 95% confidence limits based on the binomial distribution. The circles show data taken with the observers’ natural biases; the rectangles with a deliberately feigned bias in the opposite direction. All curves are best-fitting two-parameter (μ, σ) cumulative Gaussian functions. The small horizontal bars at .5 on the ordinate show the 95% confidence intervals for the mean of the psychometric function μ, obtained from 160 simulated runs of the experiment using the maximum-likelihood fits of μ and σ

Fig. 2

The figure shows data from the bisection task, presented with the same conventions as in Fig. 1

Fig. 3

Results of Experiment 2, in which subjects were given feedback when classifying vernier offsets as “up” versus “down” relative to a criterion of zero (red curves), –1.75 (green), or +1.75 (blue). The units of displacement are Weber fractions as percentages (100 * target shift/interpatch distance). The nonzero criteria are marked by vertical lines. For further explanations, see the text and the legend of Fig. 1

Fig. 4

Results of simulating an observer who sets a threshold criterion for the absolute level of the internal signal. If the signal falls below that threshold, the observer always responds on the same button. If the absolute value of the signal is greater than the threshold, the observer responds according to its sign. For further explanations, see the text