Edward F. Alf

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.

The use of extreme groups in assessing relationships

The relationship between variables in applied and experimental research is often investigated by the use of extreme (i.e., upper and lower) groups. Earlier analytical work has demonstrated that the extreme groups procedure is more powerful than the standard correlational approach for some values of the correlation and extreme group size. The present article provides methods for using the covariance information that is usually discarded in the classical extreme groups approach. Essentially, then, the new procedure combines the extreme groups approach and the correlational approach. Consequently, it includes the advantages of each and is shown to be more powerful than either approach used alone.

Correlations Redux: Asymptotic Confidence Limits for Partial and Squared Multiple Correlations

Olkin & Finn (1995) developed expressions for confidence intervals for functions of simple, partial, and multiple correlations. This paper describes procedures and computer programs for solving these problems using the methods described by Olkin and Finn. The programs extendthe methods for any number of predictors or for partialing out any number of variables.

Relative costs and statistical power in the extreme groups approach

The relationship between variables in applied and experimental research is often investigated by the use of extreme (i.e., upper and lower) groups. Recent analytical work has provided an extreme groups procedure that is more powerful than the standard correlational approach for all values of the correlation and extreme group size. The present article provides procedures to optimize power by determining the relative number of subjects to use in each of two stages of data collection given a fixed testing budget.

A New Maximum Likelihood Estimator for the Population Squared Multiple Correlation

Using maximum likelihood estimation as described by R. A. Fisher (1912), a new estimator for the population squared multiple correlation was developed. This estimator ( ρcirc;2 (ML) ) was derived by examining all possible values of the population squared multiple correlation for a given sample size and number of predictors, and finding the one for which the observed sample value had the highest probability of occurring. The new estimator is shown to have greater accuracy than other estimators and to generate values that always fall within the parameter space. The utility of ρcirc; 2 (ML) in terms of providing the basis for the development of small sample significance tests is demonstrated. A Microsoft Excel workbook for computing ρcirc; 2 (ML) and its regions of nonsignificance and for computing a normal transformation for R2 is offered.

Relationship Between Per Cent Overlap and Measures of Correlation

IN educational and psychological measurement research, a test is often used or empirically constructed to differentiate between two groups. Three common statistics used to estimate the validity of such a test are: (1) A measure of correlation, (2) a measure of the distance, in standard deviation units, between the group means, and (3) a measure of the extent to which the two test score distributions overlap. The purpose of the present paper is to show the analytic relationships between these three types of measures. Symonds (1930) previously attempted such an analysis using &dquo;median overlap&dquo; and biserial r (rb). His measure of overlap was unsatisfactory and his development violated the assumptions of the biserial r. Median overlap was defined as &dquo;the per cent of one distribution reaching or exceeding the median score of another distribution....&dquo; (1930, p. 586). Tilton (1937) criticized this measure because it provided an unrealistic estimate of overlap. For example, when the areas of two normal distributions overlap completely, Symonds’ measure of overlap is 50 per cent; and when the areas overlap 19 per cent, Symonds’ measure is almost zero. Thus, there is little meaningful relation between Symonds’ per cent overlap measure and the extent to which the actual area of the distributions

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.

The Impact of Number of Jobs and Selection Ratio on Classification Efficiency: An Extended Table of Brogden's Allocation Average

This article is an extension of Brodgens table of allocation averages, presented in EPM in 1959. The current table deals with up to 1,000 jobs and rejection rates ranging from 0 to 90%.

Acclimatization and Aptitude Test Performance

THE Navy Classification Battery is normally administered to all recruits during their third day at the Naval Training Center. Administrative personnel at the Naval Training Center, San Diego, felt that recruits might not be sufficiently acclimatized by the third day to do their best on these tests. Thus, on February 15, 1957, classification testing was changed to the recruits’ ninth day instead. However, since it was considered desirable to maintain a uniform time of testing at all training centers, testing was returned to the third day on March 21, 1957. The data provided by this period of ninth-day testing permitted a determination of whether there was, in fact, any difference in aptitude test performance after a longer period of acclimatization.