Donald D. Dorfman

Maximum-likelihood estimation of parameters of signal-detection theory and determination of confidence intervals—Rating-method data ☆

Abstract Procedures have been developed for obtaining maximum-likelihood estimates of the parameters of the Thurstonian model for the method of successive intervals. The signal-detection model for rating-method data is a special case of the Thurstonian model with fixed boundaries, in that there are two stimuli rather than an unspecified set. The present paper presents the solution to the two-stimulus case, and in addition, provides procedures for obtaining the variance-covariance matrix and confidence intervals. The expected values of the second partial derivatives are presented in analytic form to ensure accurate computation of the variance-covariance matrix. An application of these methods was employed on some data collected by others.

Maximum likelihood estimation of parameters of signal detection theory—A direct solution

Ogilvie and Creelman have recently attempted to develop maximum likelihood estimates of the parameters of signal-detection theory from the data of yes-no ROC curves. Their method involved the assumption of a logistic distribution rather than the normal distribution in order to make the mathematics more tractable. The present paper presents a method of obtaining maximum likelihood estimates of these parameters using the assumption of underlying normal distributions.

Comparison of magnitude estimation of loudness in children and adults

This study compared children (mean age 10.9 years) and college students on the magnitude estimation of loudness. Both the 20 children and the 20 adults were unpracticed observers. In one condition, the standard tone was assigned the number 10, and in the other condition, the number 20. Under both conditions the power function was found to fit the data of the children quite well, and to give approximately the same exponent. Of particular interest was the similarity between the data of the children and adults.

The classification of individuals into two criterion groups on the basis of a discontinuous payoff function

An analytic method is presented for optimally classifying individuals into two subgroups on the basis of a cutting score on a test or test composite. The development assumes the test and criterion scores to be normally distributed, and the correlation surface to be bivariate normal. It is further assumed that individuals belong to the first or second sub-group depending on whether their criterion score is above or below a specified value. The predictor cutting score is determined so as to maximize the expected value of the decision procedure, taking gains and losses associated with correct and incorrect assignments into account.

Receiver-operating characteristic curves for taboo and neutral words

Some investigators have applied signal-detection theory to the recognition of such emotional stimuli as taboo words (Dorfman, Grossberg, & Kroeker, 1965; Dorfman, 1967). Although the theory was applied to these stimuli, no good evidence exists to support such an application. The present study evaluated signal-detection theory with respect to its application to the recognition of taboo words. The theory was fitted to rating-method data by means of the method of maximum likelihood, and the chi-square test of goodness of fit was used to evaluate the theory. The data were found to be in reasonably good agreement with signal-detection theory.

Some effects of light on sound intensity generalization

This study determined whether a sound intensity generalization gradient would be displaced laterally if extraneous light intensity were changed from training to test. The results showed that (a) when Ss were trained in the absence of a light, introduction of the light on generalization-test trials displaced the generalization gradient toward the weaker sound intensities, and (b) when Ss were trained in the presence of a light, omission of the light on generalization-test trials displaced the gradient toward the larger sound intensities.

The effect of light on sound intensity generalization after two-stimulus discrimination training

This study determined if a sound intensity generalization gradient is displaced laterally if extraneous light intensity is changed from training to test after two-stimulus discrimination training. The results agreed with previous studies on three-stimulus discrimination training in that, (a) when Ss were trained in the absence of a light, introduction of the light on generalization-test trials displaced the generalization gradient toward the weaker sound intensities, and (b) when Ss were trained in the presence of a light, omission of the light on generalization-test trials displaced the gradient toward the larger sound intensities.