U.S. flag

An official website of the United States government, Department of Justice.

NCJRS Virtual Library

The Virtual Library houses over 235,000 criminal justice resources, including all known OJP works.
Click here to search the NCJRS Virtual Library

SYSTEM OF PAIRED ASYMMETRIC MEASURES OF ASSOCIATION FOR USE WITH ORDINAL DEPENDENT VARIABLES

NCJ Number
68078
Journal
Social Forces Volume: 58 Issue: 4 Dated: (JUNE 1980) Pages: 1178-1194
Author(s)
K S CRITTENDEN; A C MONTGOMERY
Date Published
1980
Length
17 pages
Annotation
THIS PAPER DISCUSSES A FRAMEWORK FOR CLASSIFYING PROPORTIONATE REDUCTION IN ERROR MEASURES DESCRIBING THE RELATIONSHIP BETWEEN NOMINAL OR ORDINAL INDEPENDENT VARIABLES AND AN ORDINAL DEPENDENT VARIABLE.
Abstract
MANY VARIABLES OF INTEREST TO SOCIOLOGISTS ARE MEASURED ORDINALLY. IN ADDITION TO HAVING THE SYMMETRICAL PROPERTIES OF THE NOMINAL SCALE, AN ORDINAL SCALE IS ASYMMETRICAL IN THE SENSE THAT CERTAIN SPECIAL RELATIONSHIPS MAY HOLD BETWEEN A AND B WHICH DO NOT HOLD FOR B AND A. AN ORDINAL LEVEL OF MEASUREMENT DOES NOT SUPPLY ANY INFORMATION ABOUT THE MAGNITUDE OF THE DIFFERENCES BETWEEN ELEMENTS. WE KNOW ONLY THAT A IS GREATER THAN B, BUT WE CANNOT SAY HOW MUCH GREATER. DEVELOPMENTS IN ECONOMETRICS AND LOG-LINEAR ANALYSIS HAVE MADE POWERFUL STATISTICAL TECHNIQUES AVAILABLE FOR THE ANALYSIS OF CAUSAL RELATIONS AMONG INTERVAL AND NOMINAL VARIABLES, YET THESE TECHNIQUES ARE NOT ADAPTED TO THE REQUIREMENTS OF ORDINAL VARIABLES. THERE IS A NEED FOR MEASURES OF ASSOCIATION SUITABLE FOR TESTING AND GENERATING ASYMMETRIC CAUSAL THEORETICAL STATEMENTS. THE ARTICLE EXAMINES SEVERAL MEASURES OF ASSOCIATION SUITABLE FOR USE WITH ORDINAL VARIABLES. MEASURES DISCUSSED INCLUDE GAMMA, SOMERS ASYMMETRIC MEASURE OF ASSOCIATION, AND FREEMAN'S COEFFICIENT OF DIFFERENTIATION, THETA. A CLASSIFICATION OF ASYMMETRIC, PROPORTIONATE REDUCTION IN ERROR MEASURES IS DEVELOPED, DESCRIBING RELATIONSHIPS BETWEEN NOMINAL OR ORDINAL INDEPENDENT VARIABLES AND ORDINAL DEPENDENT VARIABLES UNDER THREE METHODS FOR ESTIMATING PREDICTIVE ERROR. IMPLICATIONS OF THE USE OF PAIRED NOMINAL-ORDINAL AND ORDINAL-ORDINAL MEASURES OF ASSOCIATION ARE EXPLORED. TABLES ILLUSTRATING THE PROBLEMS OF ORDINAL ASSOCIATION, REFERENCES, AND AN APPENDIX ON DERIVATION OF ERROR TERMS ARE PROVIDED. (EMG)

Downloads

No download available

Availability