A modification of the method of successive intervals

A modification of the method of successive intervals is presented which yields scale values correlating .995 with those from Thurstone's method described by Saffir. Values yielded by the present method can be obtained in 25 per cent of the time required by the older method and are shown to be, on apriori grounds, more reliable as well.     

An empirical evaluation of multidimensional successive intervals

The multidimensional method of successive intervals and the method of complete triads are applied to similarity judgments of Munsell colors varying in brightness, saturation, and hue. Both methods yield configurations that correlate highly with the Munsell color structure. This validation of these scaling methods in an area of known dimensionality indicates their applicability for exploration in areas of unknown dimensionality. This study was supported in part by the Office of Naval Research contract N6onr-270-20 with Princeton University and also in part by funds from the National Science Foundation. The research was carried out when the author was an Educational Testing Service Psychometric Fellow at Princeton University.     

The validity of the successive intervals method of psychometric scaling

The degree to which scale values computed by the method of successive intervals diverge from theoretically true values is seen to be due to three types of error: error due to inequalities in variances of the distributions from which the scale values are computed, error due to non-normality of the distributions, and sampling error. The contribution of each type of error to the total error is evaluated; the latter is seen to be surprisingly small under appropriate conditions. Certain aspects of the formal methodology underlying scaling procedures are also briefly considered.This paper reports research undertaken in cooperation with the Quartermaster Food and Container Institute for the Armed Forces, and has been assigned number 475 in the series of papers approved for publication. The views or conclusions contained in this report are those of the authors. They are not to be construed as necessarily reflecting the views or indorsement of the Department of Defense.     

An axiomatic formulation and generalization of successive intervals scaling

A formal set of axioms is presented for the method of successive intervals, and directly testable consequences of the scaling assumptions are derived. Then by a systematic modification of basic axioms the scaling model is generalized to non-normal stimulus distributions of both specified and unspecified form.     

The law of comparative judgment in the successive intervals and graphic rating scale methods

The law of comparative judgment is applied to the successive intervals and graphic rating scale methods. A procedure for estimating the modal discriminal process and discriminal dispersion of the stimuli, as well as the value of the boundaries of the intervals on the continuum, is given. From the estimated values it is possible to determine the theoretical proportions and to compare them with the actual experimental proportions. The agreement between these values is an indication of the adequacy of the assumptions made.     

The estimation of the discriminal dispersion in the method of successive intervals

A new algebraic formula is derived for estimation of the discriminal dispersion in the method of successive intervals. The legitimate use of the formula requires that as many normal deviates as possible be present in the matrix. For this reason, it is recommended that deviates corresponding to the interval (0.01, 0.99) of the cumulative proportions be used, instead of those corresponding to (0.05, 0.95), the interval used by Edwards and Thurstone. Computations on data published by Edwards and Thurstone showed that when adjustment was made for variability in dispersions calculated by the formula of this paper, a reduction of fifty per cent in mean absolute discrepancy was produced. Since the formula is easy to use and avoids the disadvantages of its predecessors, it should have fairly wide applicability in psychological research.This research was supported in part by the United States Air Force under Contract No. AF 33(038)-25726 monitored by Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use and disposal in whole and in part by or for the United States Government. The writer is grateful to Dr. A. L. Edwards for a critical reading of an earlier version of this paper, and to Dr. L. H. Lanier and Dr. L. M. Stolurow for editorial advice on the present version, which was written at the University of Illinois. The editors ofPsychometrika have informed the writer that H. J. A. Rimoldi and M. Hormaeche (7) have independently derived the same formula for the discriminal dispersion from a different set of postulates using the law of comparative judgment.     

A note on the internal consistency of the sexual orientation method

The S.O.M. was administered to two samples of homosexuals. There was some reduction in the number of inconsistent response patterns when a modified scoring system was used. Further examination of the data indicated that an inconsistent style of response might not be simply an index of faking.     

Using the score method to construct asymmetric confidence intervals: An SAS program for content validation in scale development

Expert review sessions are often conducted to determine the content validity of scale items. The accurate quantification of content validity is usually limited by a relatively small number of experts as well as by a small number of rating categories. These factors, combined with the bounded and discrete nature of rating scale categories, hinder use of traditional methods for computing standard errors and confidence intervals. Using an application of the score method, researchers can construct an asymmetric interval that is better suited for these situations. SAS code is provided to automate the computations, and a discussion of two methods for using the obtained results for content validation decisionmaking follows.     

A score method of constructing asymmetric confidence intervals for the mean of a rating scale item

This article presents a generalization of the Score method of constructing confidence intervals for the population proportion (E. B. Wilson, 1927) to the case of the population mean of a rating scale item. A simulation study was conducted to assess the properties of the Score confidence interval in relation to the traditional Wald (A. Wald, 1943) confidence interval under a variety of conditions, including sample size, number of response options, extremeness of the population mean, and kurtosis of the response distribution. The results of the simulation study indicated that the Score interval usually outperformed the Wald interval, suggesting that the Score interval is a viable method of constructing confidence intervals for the population mean of a rating scale item.     

Imputation of missing categorical data by maximizing internal consistency

This paper suggests a method to supplant missing categorical data by reasonable replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.We thank Anneke Bloemhoff of NIPG-TNO for compiling and making the Dutch Life Style Survey data available to use, and Chantal Houée and Thérèse Bardaine, IUT, Vannes, France, exchange students under the COMETT program of the EC, for computational assistance. We also thank Donald Rubin, the Editors and several anonymous reviewers for constructive suggestions.     

An investigation of the role of scale values in the DS/AHP method of multi‐criteria decision making

DS/AHP is a method of multi‐criteria decision making based on the Dempster–Shafer theory of evidence and the analytic hierarchy process. Central to the utilization of DS/AHP is the composing of preference judgements on identified groups of decision alternatives (DA) across a number of criteria against all the DA present in the problem in question. This paper exposits a series of results whose objectives are to aid in the development of an effective set of preference scale values for use within DS/AHP. These results relate directly to the concomitant level of ignorance (uncertainty) with the judgements made on a single criterion. Two particular directions of investigation are undertaken, firstly in determining the necessary number of scale values available and secondly finding the necessary differences between scale values, dependent on whether an arithmetic or geometric progression is the basis for the scale values. Through an example, the implications and utilization of these results within DS/AHP are illustrated. Copyright © 2003 John Wiley & Sons, Ltd.