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Laurence Maloney, Hang Zhang; Ubiquitous log odds: Distortion of frequency estimates in visual numerosity tasks. Journal of Vision 2010;10(7):1204. doi: https://doi.org/10.1167/10.7.1204.
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© ARVO (1962-2015); The Authors (2016-present)
Background: In decision making, people distort probability information (Kahneman & Tversky, 1979, Econometrica). We show that similar distortions are found in many research areas including visual frequency estimation, memory, and motor decisions. Distortions in all tasks can be accurately modeled as lo(d(p)) = a*lo(p) + b where lo(p) denotes the “logit” or log odds, log(p/(1-p)). The slope coefficient a is roughly .6-.7 in decision making but typically greater than 1 in equivalent motor tasks (Wu Delgado, Maloney, 2008, PNAS). What determines the distortion coefficients a, b in all these tasks? Are they task or observer specific? We tested whether observers would vary a, b across conditions in a visual frequency estimation task where we manipulated experience and sample numerosity. Method: Eleven observers saw black and white dots randomly scattered on a display screen for 1.5 seconds and estimated the relative frequency of black or white dots. No feedback was given. Trials were organized into 100 trial blocks. In each block the relative frequencies 0.01, 0.02, …, 0.99 except 0.50 occurred once in randomized order. Subjects completed two sessions of four blocks. The number of dots in a display could be 200, 300, …, 600. Results: We fitted estimates of frequency distortion in each block. Nine out of 11 observers had slope smaller than 1 with mean slope 0.79. Slope was shallower for later blocks than for earlier blocks by about 16% (F(7,70) = 5.592; p <.0001) and shallower for larger numerosity than for smaller numerosity. by about 18% (F(4,40) = 17.714; p <.0001). Conclusions: Distortion of probability/frequency is ubiquitous in cognitive and visual tasks but degree of distortion varies with task. We show that distortions vary systematically even within a single type of task and discuss normative models for selection of distortion coefficients a,b.
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