Integration of information in a visual discrimination task

Abstract

2The integration of information model ofsignal detection theory (SDT) was tested in a multiple observation tilt-discrimination task. Improvement in discriminability with additional observations was consonant with theory over two observations, but observations beyond the second yielded less improvement than predicted by the integration model. Analyses of operating characteristics lent some support to the applicability of SDr to the tilt-discrimination task.This paper describes two experiments designed to test the integration model of signal detection theory (SOT) in a multiple observation task (cf. Green & Swets, 1966). In opposition to traditional threshold theory which posits an all-or-nothing informing effect of stimuli, SOT states that the informing effects range along a continuum from determinate information favoring one stimulus alternative through no information to determinate information favoring the other alternative. A stimulus is evaluated by comparing its informing effect with an internal standard or criterion. The probability density function of the informing effects yielded by a given stimulus source is assumed to be normal. In a two-alternative discrimination task, the informing effects density functions associated with the alternative stimuli would differ in location, but, for the sake of simplicity, can be assumed to be equal in variance. The difference between the means of the probability density functions, in units of the density function standard deviation, is labeled the index of signal detectability (d') and constitutes the SOT measure of discriminability-sensitivity.In order to derive predictions of discriminability when multiple observations of the stimulus are furnished on each trial, it is assumed that the informing effect associated with a set of independent observations is the mean of the informing effects of the component observations. Thus, the probability density function for a set of n observations should possess the same location on the informing effects continuum as the density function for single observations. However, the standard deviation should be only If./ii (n being the number of observations) of the standard deviation of the single observation density function. Because d' is the ratio of the difference in location to the standard deviation of the density functions, reduction in the standard deviation yields a proportional increase in d'. Thus, the d' based on n observations per trial is predicted by the SOT integration model to be v'n times the d' based on one observation per trial. The v'nprediction requires the assumption that the multiple stimulus observations are mutually independent. If dependence should exist, the predicted improvement would be less than v'n. It may be noted that the same predictions can be derived if one assumes that S bases his judgment on the likelihood ratio of the informing effects, and that the likelihood ratio of a set of stimulus observations is the product of the likelihood ratios of the individual observations (Green & Swets, 1966).In an a...

Information integration and the identification of stimulus noise and criterial noise in absolute judgment.

“…As an example, the model is applied to the results of a study performed by Ulehla, Halpern, and Cerf (1968). These researchers conducted an experiment requiring subjects to identify the direction of tilt of a line (either left or right).…”

“…In Figure 3, diamonds are plotted to represent values of(lld')2 computed from the d' values presented in Experiment 2 of Ulehla et al (1968).7 These values are plotted as a function of IIN, where N is the number of stimulus observations on which each d' value is based. As is evident from the figure, the data are extremely well described by a straight line function (r = .997) with a slope7 of 1.28 and an intercept of .09.…”

“…The Ulehla et al (1968) study (Experiment 2) used five observation intervals, with subjects making a response on each interval. It was correctly concluded that each observation past the second observation yielded successively less mean improvement in d'than predicted in the integration model of signal detection theory.…”

The effect of multiple responses and certainty estimates on the integration of visual information

“…The effect of multiple responses and certainty estimates was evaluated using the index of signal detectability (d'), Within TSD, d' is a basic measure of the discriminability of a pair of alternative stimuli for a given S and is theorized to be independent of response bias. A more complete explanation of d' (and the , , Ulehla et al (1968). Empirical d' values were obtained for each S by referring his hit rates and error rates to tables of d' (Elliott, 1964).…”

“…In two separate experiments, they found that performance on the second observation was close to prediction While performance beyond this second observation fell considerably short of predicted values. The Ulehla et al (1968) study assumed that certainty estimations and multiple responses (i.e., a response and certainty statement following each observation) would provide optimal conditions for the effective utilization of information provided by multiple-stimulus observations. In view of the evidence given by the Swets and Birdsall (1966) and Ulehla et al(l967) experiments, it seemed logical to assume that such multiple responses and certainty estimates would serve to increase attention and vigilance.…”