NCJ Number
65447
Journal
Sociological Methods and Research Volume: 8 Issue: 3 Dated: (FEBRUARY 1980) Pages: 341-362
Date Published
1980
Length
22 pages
Annotation
STATISTICAL PROCEDURES WHICH CAN BE USED TO MEASURE POPULATION DIVERSITY AT THE QUALITATIVE OR NOMINAL LEVEL AND WHICH HAVE VARIANCE-BASED INTERPRETATIONS ARE REVIEWED.
Abstract
POPULATION DIVERSITY IS DEFINED AS THE DISTRIBUTION OF POPULATION ELEMENTS ALONG A CONTINUUM OF HOMOGENEITY OR HETEROGENEITY WITH RESPECT TO ONE OR MORE VARIABLES. THIS DEFINITION MAY INCLUDE RELIGIOUS, ECONOMIC, ATTITUDINAL, AND DEMOGRAPHIC PHENOMENA, AS WELL AS IMPORT AND EXPORT STRUCTURE, DISTRIBUTION OF SERVICES BETWEEN INDUSTRIES, AND THE STRUCTURE OF GROSS NATIONAL PRODUCT. THE MAIN CONCERN HERE IS THE AMOUNT OF VARIATION IN ONE OR MORE VARIABLES. MOST RESEARCH QUESTIONS INVOLVING POPULATION DIVERSITY CANNOT BE ANALYZED BY CONVENTIONAL VARIANCE-BASED STATISTICS WHICH ASSUME THAT VARIABLES ARE QUANTITATIVE. THE PRESENT MEASURES HAVE DIRECT ANALOGIES TO THE MORE TRADITIONAL VARIANCE-BASED STATISTICS FOR CONTINUOUS DATA. THEIR ABILITY TO RELATE TWO OR MORE QUALITATIVE VARIABLES BY USING SUMMARY MEASURES DEFINED IN TERMS OF PROPORTIONATE REDUCTION IN VARIANCE OR UNCERTAINTY IS ESPECIALLY ATTRACTIVE. TWO DIFFERENT YET RELATED STATISTICS WERE DEVELOPED HERE, ONE BASED ON ALL POSSIBLE PAIRWISE DIFFERENCES BETWEEN OBSERVATIONS AND THE OTHER BASED ON INFORMATION THEORY. SIMILARLY, TWO APPROACHES TO THE PARTITIONING OF VARIANCE WERE OUTLINED, ONE BASED ON AN ANALYSIS OF VARIANCE ANALOGY AND THE OTHER BASED ON A DECOMPOSITION OF JOINT UNCERTAINTY. INFORMATION THEORY, ABLE TO HANDLE BOTH TYPES OF PARTITIONING, WAS SHOWN TO BE THE MORE GENERAL APPROACH. IN ADDITION, THE INFORMATION-THEORETIC APPROACH LEADS TO SEVERAL FORMS OF THE DECOMPOSITION OF JOINT ENTROPY WHICH COULD HAVE DIFFERENT RESEARCH APPLICATIONS. NOTES AND A REFERENCE LIST ARE INCLUDED. (AUTHOR ABSTRACT MODIFIED--CFW)