Central tendency biases must be accounted for to consistently capture Bayesian cue combination in continuous response data

Abstract

Observers in perceptual tasks are often reported to combine multiple sensory cues in a weighted average that improves precision—in some studies, approaching statistically optimal (Bayesian) weighting, but in others departing from optimality, or not benefitting from combined cues at all. To correctly conclude which combination rules observers use, it is crucial to have accurate measures of their sensory precision and cue weighting. Here, we present a new approach for accurately recovering these parameters in perceptual tasks with continuous responses. Continuous responses have many advantages, but are susceptible to a central tendency bias, where responses are biased towards the central stimulus value. We show that such biases lead to inaccuracies in estimating both precision gains and cue weightings, two key measures used to assess sensory cue combination. We introduce a method that estimates sensory precision by regressing continuous responses on targets and dividing the variance of the residuals by the squared slope of the regression line, “correcting-out” the error introduced by the central bias and increasing statistical power. We also suggest a complementary analysis that recovers the sensory cue weights. Using both simulations and empirical data, we show that the proposed methods can accurately estimate sensory precision and cue weightings in the presence of central tendency biases. We conclude that central tendency biases should be (and can easily be) accounted for to consistently capture Bayesian cue combination in continuous response data.

Newly learned novel cues to location are combined with familiar cues but not always with each other.

“…In that paper, we also discussed the effects of additional response noise (e.g., motor noise). We showed that if the additional noise is equivalent across all trial types (single and combined cue trials), then it does not disrupt a researcher's ability to detect a reduction in variability using both cues compared to the best single-what we termed the "combination effect" (see equation 3 in Aston et al, 2022). However, the equivalence between the optimal prediction and measured variability using both cues (where the optimal prediction is calculated from the measured single cue variabilities) is not preserved.…”

Newly learned shape-colour associations show signatures of reliability-weighted averaging without forced fusion or a memory colour effect

“…To calculate matching variability we used a method described fully elsewhere (Aston, Negen, et al, 2021). In brief, the method is designed to account for central biases in continuous responses that may reduce statistical power for detecting a gain in precision using multiple cues.…”

“…The weight placed on the novel cue was calculated for each of the four types of conflict adjustment To calculate the weight placed on the novel cue we again used a method that is described fully elsewhere (Aston, Negen, et al, 2021). In brief, we model matches, 𝑚, as…”

Newly learned novel cues to location are combined with familiar cues but not always with each other

“…Thus, our main measure of interest is precision or, equivalently, variability. We calculate measures of variability according to a method we recently described elsewhere (Aston, Negen, Nardini, & Beierholm, 2021). The method is designed to account for central biases in continuous responses that may reduce statistical power for detecting a gain in precision using multiple cues.…”