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Frederick Kingdom, Alex Baldwin, Gunnar Schmidtmann; Modelling probability summation for the detection of multiple stimuli under the assumptions of signal detection theory. Journal of Vision 2015;15(12):473. doi: 10.1167/15.12.473.
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© ARVO (1962-2015); The Authors (2016-present)
In general there are two ways in which multiple stimuli can sum to threshold: by probability summation or by additive summation (of which linear summation is a special case). Probability summation (PS) is still often modelled using the long-refuted High Threshold Theory (HTT), in spite of the fact that most researchers believe that Signal Detection Theory (SDT) is the better model. Studies which do model PS under SDT often use Monte Carlo simulations to perform the calculations, but this method is prohibitively slow when many thousands of calculations are required, as when fitting psychometric functions with PS models and estimating bootstrap errors on the fitted parameters and model goodnesses-of-fit. We provide numerical integration formulae for calculating, on the assumptions of SDT, the proportion correct detections for n independently detected stimuli, each subject to a non-linear transducer τ, while Q channels are being monitored, and for an M-AFC task. We show how the equations can be used to simulate psychometric functions in order to determine how parameters such as the Weibull threshold and slope vary with n, τ and Q. We also show how the equations can be used to fit actual psychometric functions from a binocular summation experiment in order to obtain estimates of τ and to determine whether probability or additive summation is the better model of the data.
Meeting abstract presented at VSS 2015
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