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Stefano Baldassi, David C. Burr, Nicola Megna; Confidence grows with uncertainty in visual search.. Journal of Vision 2004;4(8):166. doi: https://doi.org/10.1167/4.8.166.
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A target tilted right or left of vertical is harder to discriminate when presented together with vertical distractors. The set-size effect is well explained by a Signed-Max model in which the subjects monitor two sets of noisy filters tuned clockwise (CW) and counter-clockwise (CCW), and choose the maximum (signed) response. An interesting corollary of this model is that, for large set sizes, the distribution of maxima is bimodal, with two distinct non-zero peaks for errors and correct responses, implying that observers should make “high confidence errors”. We tested this prediction using a magnitude estimation task: a target was tilted CW or CCW by a variable angle (between ±16 ), and subjects indicated both the direction and magnitude of the tilt (by clicking an appropriate icon). The target was intermingled with a variable number of vertical distractors equi-spaced around a circular array of 5° eccentricity. After collecting a total of over 1000 trials, we plotted histograms of magnitude estimation separately for correct responses and errors (for the tilt angle yielding d'=1) for each subject and set-size. For set-size of 1, the distribution was unimodal and symmetric. For large set-sizes it was bimodal, with the two peaks becoming sharper and more separated with increasing set size. At set-size 16 the peak response for errors was ∼3 tilt, suggesting that subjects saw the responses clearly in the wrong direction. The results do not simply reflect the higher thresholds with large set-size, as adding noise to the set-size 1 condition (to equate thresholds with the set-size 16 condition) did not change the shape of the distribution. The pattern of data confirm the prediction of the SDT based Signed-Max model, that under conditions of high stimulus uncertainty, where a distractor may be mistaken for the target by chance, subjects make many “high-confidence errors”, and “see” the stimulus oriented in the wrong direction. By a large amount.
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