Abstract
As the strength of a stimulus increases, the proportions of correct binary responses increases, which define the psychometric function. Simultaneously, mean reaction times (RT) decrease, which collectively define the chronometric function. However, RTs are traditionally ignored when estimating psychophysical parameters, even though they may provide additional Shannon information. Here, we extend Palmer et al's (2005) proportional-rate diffusion model (PRD) by: (a) fitting individual RTs to an inverse Gaussian distribution, (b) including lapse rate, (c) point-of-subjective-equality (PSE) parameters, and, (d) using a two-alternative forced choice (2AFC) design based on the proportion of times a variable comparison stimulus is chosen. Maximum likelihood estimates of mean RT values (from fitted inverse Gaussians) and binary responses were fitted both separately and in combination to this extended PRD (EPRD) model, to obtain psychophysical parameter values. Values estimated from binary responses alone (i.e., the psychometric function) were found to be similar to those estimated from RTs alone (i.e., the chronometric function), which provides support for the underlying diffusion model. The EPRD model was then used to estimate the mutual information between binary responses and stimulus strength, and between RTs and stimulus strength. These provide conservative bounds for the average amount of Shannon information the observer gains about stimulus strength on each trial. For the human experiment reported here, the observer gains between 2.68 and 3.55 bits/trial. These bounds are monotonically related to a new measure, the Shannon increment, which is the expected value of the smallest change in stimulus strength detectable by an observer.
Highlights
For over a 100 years, it has been known that the ability to discriminate between two stimuli increases as a sigmoidal function of the difference between those stimuli, where this is traditionally measured using binary observer responses
This maximum likelihood estimate implies that an inverted face must be 3.1% wider than an upright face in order for the two faces to be perceived as the same width
We have shown how the proportional-rate diffusion model (PRD) model from Palmer et al (2005) can be extended to make use of individual reaction time (RT), which can be combined with binary observer responses to estimate key psychophysical parameters in a 2AFC design
Summary
For over a 100 years, it has been known that the ability to discriminate between two stimuli increases as a sigmoidal function of the difference between those stimuli, where this is traditionally measured using binary observer responses. When an observer makes a response, there is a trade-off between speed, or reaction time (RT), and accuracy of responses This speedaccuracy trade-off has been the subject of numerous papers, notably (Ratcliff, 1978; Harvey, 1986; Swanson and Birch, 1992; Wichmann and Hill, 2001; Palmer et al, 2005), and more recently in Bonnet et al (2008). We introduce a new parameter, the point-of-subjective-equality (PSE), which takes account of systematic shifts or bias in observer perception. This parameter is incorporated into the chronometric and psychometric functions. Note that the 2AFC experimental procedure is the same whether one chooses to measure the proportion of correct responses or the proportion of times a variable comparison stimulus is chosen
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