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Ryan Ly, Hee Yeon Im, Robert Eisinger, Justin Halberda; Measuring the Coefficient of Variation with continuously varying arrays. Journal of Vision 2012;12(9):712. doi: 10.1167/12.9.712.
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© ARVO (1962-2015); The Authors (2016-present)
Representation of visual features is subject to internal noise, which is sometimes constant (e.g., color), anisotropic (e.g., orientation) or scalar (e.g., luminance) within a dimension. A common metric of internal noise has been the coefficient of variation (CV=SD/mean), which is equivalent to a Weber fraction. For many features, SD varies linearly with the mean such that larger values are subject to higher internal noise (e.g., luminance, number, filled region, length). In such cases, a traditional approach to estimating CV has required testing an observer on a subset of values across many trials in order to generate sufficient data for determining both SD and mean of estimates. Here we describe an analytic transformation of response data which allows the accurate estimation of CV given sparse and distributed observations. We validate this new approach with data from three paradigms. In Experiment 1, observers were asked to shout out how many yellow dots were presented in a visual array consisting of multiple yellow and blue dots. In Experiment 2, observers were given a number and asked to make key-presses to arrive at the approximate number of presses. In Experiment 3, observers clicked to approximately locate a given number on a continuous number scale labeled with the endpoints 0 and 100. Throughout the 3 experiments, our new method yields stable estimates of CV that correlate with those from the traditional method and generate accurate fits with far fewer observations and no repetitions of particular values. Our alternative approach can be particularly powerful given brief assessments. It allows a less biased estimate of CV because our sparse sampling of many values disables brittle response strategies that arise during the traditional repeated testing. This approach can be applied quite broadly to psychophysical assessments of internal noise and/or estimates of the resolution of visual representations.
Meeting abstract presented at VSS 2012
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