Signal detection theory (SDT) asserts that sensory analysis is limited only by noise, and not by the number of stimuli analysed. To test this claim, we measured the accuracy of visual search for a single tilted element (the *target*) among 7 horizontal elements (*distractors*) using several different exposure durations, each terminated by a random noise mask. In the uncued condition, each element was a potential target. In the cued condition only 2 were. SDT predicts that location errors should be evenly distributed among all distractors. For long exposures (eg, 5.0 seconds), this prediction was confirmed, and SDT could simultaneously fit uncued and cued accuracies. For short exposures (eg, 0.1 seconds), errors were concentrated among distractors adjacent to the target, and, unless modified to account for this, SDT underestimated the difference between uncued and cued accuracies. Therefore, when the time available for search is brief, odd-men-out (ie, featural discontinuities) can be seen, but their positions can be only roughly estimated.

^{2}; viewing distance: 73 cm). Both observers had normal vision. One observer (A.J.) was naïve to the experiment’s purpose, and the other observer (M.J.M.) is an author.

*P*< .05) worse than the modified version at fitting the data from each condition except A.J., 5.0 seconds (

*P*∼ .08; Figure 5).

*P*(

*I*|

*L*) is higher than its inverse

*P*(

*L*|

*I*). Thus, our results cannot be used as evidence for identification without location (Baldassi & Burr, 2000). Most of the symbols in Figure 8 fall below the solid black and green lines. These symbols actually suggest location without identification. Because observers always reported orientation before location, their relatively poor performance in the identification task cannot be attributed to a greater memory load.

^{1}The maximum-apparent-orientation rule is not ideal. If the noise with which the visual system perturbs the true perceived orientation of each element has a high variance, it is nonetheless possible that, on some trials, all of the elements are perceived as being close to horizontal. On such trials, if the majority of those elements had an apparent clockwise tilt, then it would be more likely that the target had a clockwise tilt than a counterclockwise tilt, even if the element having the greatest apparent tilt appeared to be counterclockwise.

^{2}Our modified SDT requires 2 free parameters for each observer and duration: P(B) and σ (see Appendix). In order to model the strategy described here, at least 3 free parameters are required. Each local orientation estimate will now have a different precision. At least 2 parameters (peak and spread) are required to specify the relationship between precision and distance from focus. In addition, a criterion for selecting the opposite element would need to be established.

*P*(

*L*), and the probability of an adjacent error

*P*(

*D*) given

*A*and

*B*, the independent events that the true target has the greatest apparent tilt and the observer mistakes the source of the maximum sensation adjacent to its true source, respectively. When fitting “modified SDT” to the data,

*P*(

*B*) is allowed to assume any value between 0 and 1. When fitting “unmodified SDT” to the data

*P*(

*B*) is fixed at 0. Below, we specify how to compute

*P*(

*A*) according to SDT.

*u*

_{1}is an outcome of the random variable

*U*

_{1}, quantifying the apparent tilt of the target (negative values can indicate counterclockwise tilts, whereas positive values can indicate clockwise tilts) and each

*u*

_{i}*i*≠ 1 is an outcome of the random variable

*U*, quantifying the apparent tilt of a different distractor. Thus,

_{i}_{i}where where

*m*is the number of possible targets and

*f*(

_{x}*u*) and

*F*(

_{X}*u*) denote the probability density and cumulative distribution functions for any random variable

*X*, respectively. Hence,

*z*) is the standard normal density function. Substituting these values into the previous equation we get where Φ(

*z*) is the standard normal cumulative distribution function. For each fit, the parameter σ was allowed to vary between observers and durations, but not conditions.

*P*(

_{Max}*I*). Let

*E*

_{1}denote the event that the actual target is tilted clockwise of horizontal. Assuming the observer has no response bias,

*E*. Here, the integers

_{i,j}*i*and

*j*represent the tilt and position of the target. On any trial in the uncued condition, the target could assume 1 of 10 possible tilts, thus and, with 8 possible positions,

*i*≤

*j*≤8. Because the ideal observer has no response bias and , the probability of a correct identification is

_{0}:

*E*,

_{i,j}*i*>0 than under the alternative H

_{1}:

*E*,

_{i,j}*i*<0. Thus where

*H*(

*x*) is the (Heaviside) unit-step function:

^{7}points within the 8-dimensional hypercube with sides stretching from −3.5σ to 3.5σ along each dimension) iteratively until we found the θ

_{0}for which

*P*

_{Ideal}(

*I*) = 3/4 when σ = 1.

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