August 2012
Volume 12, Issue 9
Free
Vision Sciences Society Annual Meeting Abstract  |   August 2012
P[A and B] > P[A]P[B] for independent events A,B: erroneous use of probability in a simple visual task
Author Affiliations
  • James Tee
    Department of Psychology, New York University
  • Hang Zhang
    Department of Psychology, New York University
  • Laurence T. Maloney
    Department of Psychology, New York University
Journal of Vision August 2012, Vol.12, 432. doi:10.1167/12.9.432
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      James Tee, Hang Zhang, Laurence T. Maloney; P[A and B] > P[A]P[B] for independent events A,B: erroneous use of probability in a simple visual task. Journal of Vision 2012;12(9):432. doi: 10.1167/12.9.432.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Statistical models of optimal visuo-motor performance presuppose that visual processing of probability information conforms to standard probability theory (Maloney & Zhang, VisRes, 2010). We test whether observers combine the visually-estimated probabilities of two independent events normatively.

Task: During each trial, a subject chose between a single roulette wheel with probability r of success and a pair of independent roulette wheels with probabilities p and q of success. The observer’s estimates of p, q, and r were based on visual judgments of the fraction of each roulette wheel colored gold. The wheels were spun and the observer won a small monetary prize (i) if he chose the single wheel and it stopped in the gold, or (ii) chose the pair and both stopped in the gold. We used a staircase procedure to estimate the r for which the subject chose the pair as often as the single wheel: r~(p,q).

Conditions: Twelve experiment conditions corresponded to twelve choices of (p,q), with p being greater than or equal to q. They included four homogeneous groups of conditions of three pairs each, where p1q1 = p2q2 = p3q3. Ten naïve subjects participated.

Results: We tested whether observers’ indifference points satisfied r = pq, implying the observer was combining probabilities normatively. All observers had r > pq (Bonferroni-corrected t-tests): they overestimated the conjunction probability. We next tested whether observers assigned the same (erroneous) probability to each of the three pairs in a homogeneous group: did they converge on the same r for each of p1q1 = p2q2 = p3q3? 9/10 observers passed this test of homogeneity.

Conclusions: Observers’ combination of probabilities in a simple visual task showed systematic deviations from normative theory.

Meeting abstract presented at VSS 2012

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