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.
Highlights
One central goal in the study of perceptual decision-making is to understand how an observer makes decisions in the presence of several streams of sensory information
By carefully working through the details of a Bayes-optimal observer model completing a continuous cue combination task, we have shown that researchers are limited in their ability to test for an optimal gain in precision when combining cues if the responses are corrupted by additional sources of noise and/or a central tendency bias is present
We have presented a new method of analysis that accounts for central tendency biases in continuous response data to recover estimates of what we define as sensory rather than behavioral precision
Summary
One central goal in the study of perceptual decision-making is to understand how an observer makes decisions in the presence of several streams of sensory information. As central tendency biases appear to be introduced after the sensory estimate is formed (Crawford et al, 2000; Murai & Yotsumoto, 2018), comparing the variability of behavioral responses across different experimental conditions (e.g., when observers use their best single cue compared to multiple cues) will not reflect the reduction in variance, or gain in precision, that is afforded from taking a reliability-weighted average of sensory information, or the underlying combination effect E (Eq 1). We show that using our proposed analysis method to account for a central tendency bias increases statistical power regardless of additional noise level or sample size when the strength of the bias is greater than 0.3 and the ratio of the reliabilities is less than 5.
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