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Richard Murray; ROC curves refute an unequal-variance account of search asymmetry. Journal of Vision 2007;7(9):723. doi: 10.1167/7.9.723.
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One of the most unexpected phenomena of visual search is search asymmetry: the finding that switching the targets and distractors in a search task can drastically change the difficulty of the task. A well-known example is that it is easier to locate a letter C among O's than to locate an O among C's. One proposed explanation for such search asymmetries, based on signal detection theory, is that the internal responses generated by the two targets have different variances. We tested this explanation by measuring ROC curves. Method Three observers detected a C among O's, and vice versa, at contrast threshold, at set sizes one and eight. Observers responded on a six-point confidence rating scale, and we used the rating responses to generate ROC curves. Results At set size one, the slope of the ROC curves indicated approximately equal variances for the internal response distributions of letters C and O. At set size eight, the slope of an ROC curve does not directly indicate the ratio of the standard deviations of the responses evoked by C and O. However, a more careful analysis can still recover this ratio, and indicated that at set size eight, the response distributions for C and O again had approximately equal variances. Conclusions These findings are qualitatively inconsistent with the unequal-variance account of search asymmetry, which requires that the internal response distribution evoked by the easier target, in this case the letter C, has a greater variance. We will consider what alternative theories of visual search are consistent with these results.
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