Visual signal detection in structured backgrounds. IV. Figures of merit for model performance in multiple-alternative forced-choice detection tasks with correlated responses

Many investigators are currently developing models to predict human perform ance in detecting a signal embedded in complex backgrounds. A common figure of merit for model performance is d', an index of detectability that can b e mathematically related to the proportion correct (Pc) when the responses of the model are Gaussian distributed and statistically independent. Howeve r, in many multiple-alternative forced-choice (MAFC) detection tasks, the t arget appears in one of M different locations within an image. If the image contains slow spatially varying luminance changes (low-pass noise), the pi xel luminance values at the possible signal locations are correlated and th erefore the model/human responses to the different locations might also be correlated. We investigate the effect of response correlations on model per formance and compare different figures of merit for these conditions. Our r esults show that use of the standard d' index of detectability assuming sta tistical independence can lead to erroneous underestimates of Pc and mislea ding comparisons of models. We introduce a novel figure of merit d(r)(') th at takes into account response correlations and can be used to accurately e stimate Pc. Furthermore, we show that d(r)(') can be readily related to the standard index of detectability d' by d(r)(') = d'/root 1 - r, where r is the correlation between the responses in any MAFC detection task.. We illus trate the use of the theory by computing figures of merit for two linear mo dels detecting a signal in one of four locations within medical image backg rounds. (C) 2000 Optical Society of America. [S0740-3232(00)02401-7] OCIS c odes: 330.7310, 330.1880, 110.3000, 330.4060.