6 April 2005 Statistical analysis of 2AFC contrast threshold measurements
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Abstract
Most prior 2AFC experiments have been designed using a small number of signal strengths with many scenes for each strength. Percent correct is then computed for each level and fit to the assumed psychometric function. However, this introduces error because the signal strengths of individual responses are shifted. An alternative approach is to compute the statistical likelihood as a function of the threshold and width of the psychometric response curve. The best fit is then determined by finding the threshold and width that maximize the likelihood. In this paper, we discuss a method for analyzing 2AFC observer responses using maximum likelihood estimation (MLE) techniques. The logit model is used to represent the psychometric function and derive the likelihood. A conjugate gradient search algorithm is then used to find the maximum likelihood. The method is illustrated using human observer results from a previous study while statistical characteristics of the method are examined using simulated response data. The human observer results show that the psychometric function varies between observers and from test to test. The simulations show that the variance of the threshold and width exhibit a 1/Nobs relationship (σ=1.5201*Nobs-0.5236), where Nobs is the number of observations made in a 2AFC test ranging from 10 to 30000. The variance of the human observer data was in close agreement with the simulations. These results indicate that the method is robust over a wide range of observations and can be used to predict human responses. The results of the simulations also suggest how to minimize error in future studies.
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Philip Tchou, Philip Tchou, Michael Flynn, Michael Flynn, } "Statistical analysis of 2AFC contrast threshold measurements", Proc. SPIE 5749, Medical Imaging 2005: Image Perception, Observer Performance, and Technology Assessment, (6 April 2005); doi: 10.1117/12.596449; https://doi.org/10.1117/12.596449
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