Journal of Criminal Law and Criminology Volume 66 | Issue 2 Article 8 1975 Scaling Seriousness: An Evaluation of Magnitude and Category Scaling Techniques George S. Bridges Nancy S. Lisagor Follow this and additional works at: https://scholarlycommons.law.northwestern.edu/jclc Part of the Criminal Law Commons, Criminology Commons, and the Criminology and Criminal Justice Commons Recommended Citation George S. Bridges, Nancy S. Lisagor, Scaling Seriousness: An Evaluation of Magnitude and Category Scaling Techniques, 66 J. Crim. L. & Criminology 215 (1975) This Symposium is brought to you for free and open access by Northwestern University School of Law Scholarly Commons. It has been accepted for inclusion in Journal of Criminal Law and Criminology by an authorized editor of Northwestern University School of Law Scholarly Commons. TMI JoURNAL OFCRImINAL LW & CRIMINOLOGY Vol. 66, No. 2 Copyright g 1975 by Northwestern University School of Law Printed in U.S.A. SCALING SERIOUSNESS: AN EVALUATION OF MAGNITUDE AND CATEGORY SCALING TECHNIQUES GEORGE S. BRIDGES* AND NANCY S. LISAGOR** Unidimensional attitude scaling in social re- by delinquency should be measured by scaling search encompasses a variety of measurement attitudes. It was argued: techniques. A relevant issue in the application The criteria for determining degrees of s- of any of these, however, is the extent to riousness must ultimately be determined by which different procedures yield similar re- someone's or some group's subjective interpre- sults. For example, one might expect that since tation. If weights were assigned by a few crim- magnitude and category scales represent two inologists engaged in the task of construct- distinct and different types, of scaling, each ing a mathematical model, we should regard would generate different sets of results. In cat- this as an arbitrary determination. But if egorical analysis, the subjects' judgements in- judgments were elicited from theoretically volve placing responses into intervals or cate- meaningful and large social groups, consensus gories; magnitude scaling involves judging might produce a series of weighted values that strength or salience and order on a more ex- meaningful and large social groups, consensus would have validity.... Although no external pansive and continuous scale. Research in objective criteria, beyond people's judgments, psychophysical scaling suggests, however, that exists for producing a continum of seriousness category and magnitude scales are logarithmi- of delinquent acts, there are objective methods cally related." The purpose of this present re- of measurement which have been developed port is to empirically display the relationship into psychological 'laws' relating two different between these scale types within -the context of kinds of psychological scales, these methods the measurement of delinquency. It is thought can be applied to such nonphysical dimensions that insight on selecting scale types for delin- as the gradual seriousness of deviant behavior.3 quency research can be gained by examining To determine the scalability of their stimuli, whether similar seriousness scores result from Sellin and Wolfgang empirically compared cat- these methods. egory and magnitude scales. The latter tech- In 1964 Sellin and Wolfgang developed a nique was then selected for developing the se- seriousness index of delinquent events 2 where- riousness index. Their choice of method was in they asserted that the social harm caused based on the presumed theoretical strengths of * George S. Bridges is a Research Assistant at magnitude over category scaling, rather than the Center for Studies in Criminology and Criminal on any differences that were produced in the Law, University of Pennsylvania, Philadelphia, Pennsylvania. scale data. This decision is the focal point of ** Nancy S. Lisagor is an Assistant Professor analysis in this paper. First, however, a brief at the Department of Sociology at Stockton State review and discussion of scaling techniques is College, Pomona, New Jersey. The authors wish to express their gratitude to necessary. Professors Marvin E. Wolfgang and Phillip C. The unidimensional scaling methods that Sagi for their advice and support. Also, thanks go have been developed thus far serve at least two to Robert M. Figlio for the use of data from his dissertation. This paper grew out of a project un- important measurement functions. The most dertaken by Ms. Lisagor in a graduate seminar at common of these functions involves the con- the University of Pennsylvania. 1See A. Shinn, Relations Between Scales, in struction of empirical indices that describe the MEASUREMENT IN THE SOCIAL SCIENCES (H. Bla- strength and direction of individual and group lock ed. 1974). Shinn gives a comprehensive dis- attitudes. By these methods, data can be ana- cussion of this literature and the scaling principles related to this logarithmic transformation of the lyzed with a focus on the attitudinal composi- tion of either an entire sample or any of the scale2 scores. T. SELUN & M. WOLFGANG, THE MEAsURE- MENT OF DELINQUENCY (1964). 3 Id. at 237. BRIDGES AND LISAGOR [Vol. 66 individuals within it. A second function, which scores. In this vein, Sellin and Wolfgang ini- is of specific interest to this research involves tially investigated whether this psychophysical estimating the magnitude of questionnaire or property held for their non-physical serious- interview stimuli. The focus here, as developed ness stimuli. They employed Helm's principle by Thurstone and later greatly extended by of equal precision or dispersion by standardiz- Stevens, is directed towards locating estimates ing the variances of their rater's catetory judg- of stimuli on an empirical range of strength or ments for each stimulus. This effectively trans- salience. Shinn, in his development of a scale formed the non-linear plot of the category and typology, suggested that these stimulus-cen- log-magnitude mean scores into a linear one. tered methods could be classified into two In so doing, the logarithmic relation between types: magnitude and category scales. The for- the scales was confirmed. mer amounts to a continuous ratio scale, a nu- This finding has at least two important im- mercial range with an absolute zero point. Sub- plications for measuring the seriousness of de- jects utilizing a magnitude scale evaluate the linquency. Perhaps most importantly, it sug- magnitude of stimuli by assigning them scores gests that seriousness can be measured psycho- that represent points on a psychological scale. physically, as a response to physical stimuli Category scaling, as primarily developed by would be. Secondly, the log-linear relation- Thurstone, involves constructing a rank- ship evidenced in this experiment between ordered continuum of stimuli. In the most com- scales confirms that the scale scores are a log- mon technique of successive categories, sub- linear function of one another. Thus, log-mag- jects are presented with a questionnaire item nitude and equal variance category scores with, or stimulus, and then are directed to locate it of course, some measurement error, are di- along a scale of successive categories (usually rectly related ways of estimating the ranging from low to high) that best describes seriousness of delinquent events. The proper- stimulus magnitude. Statistical estimates of the ties of psychophysical scaling developed by "true" stimuli magnitudes for both magnitude Stevens and others are, therefore applicable to and category techniques are then derived from this topic in criminological research. sample distributions of such judgments. In ef- A second aspect of Sellin and Wolfgang's fect, scales of the stimuli, as well as estimates scale development, however, is their final of their magnitude, are thus obtained. choice of scale design. Despite the direct loga- 4 It has been argued and shown by Helm, rithmic relation between the methods, it is 6 7 Ekman,5 Ekman and Kuennapas, and Stevens argued that the magnitude scales have added that the log-linear relationship connecting dimensions of validity that extend beyond this magnitude and category scales is dependent log-linear function. Since the scale values are upon the dispersions of the judgments made by determined by the subject rather than the ex- subjects. If judgments on the category scale perimenter, as is the case in the category de- are homoscedastic (have equal variance) for sign, Sellin and Wolfgang argue that magni- all stimuli, and the dispersions of judgments tude estimation better taps the "true" on the magnitude scales are heteroscedastic psychological effects of stimuli. Secondly, it is and directly function with scale value, then a implicitly argued that the breadth of range in logarithmic transformation of the magnitude magnitude scales, being so much greater than judgments will lead directly to the category that of category scales, enhances accuracy in measurement by providing "intrinsically more 4Helm, Messick & Tucker, Psychological Mod- information" about judgments. Due to these els for Relating Discriminationand Magnitude Es- advantages, Sellin and Wolfgang chose to se- timation Scales, 68 PSYCHOLOGICAL REVIEW 121 lect magnitude scaling over the category tech- (1961). 5 Ekman, Measurement of Moral Judgment: A nique for the index construction of seriousness. Comparison of Scaling Methods, 15 PERCEPTUAL The focus of this present research is to dem- AND MOTOR SKILLS 3 (1962). and 6 Ekman & Kuennapas, Scales of Aesthetic onstrate the similarity