RULE FOR INFERRING INDIVIDUAL-LEVEL RELATIONSHIPS FROM AGGREGATE DATA

• NCJ Number: 50109
• Journal: American Sociological Review Volume: 43 Issue: 4 Dated: (AUGUST 1978) Pages: 557-572
• Author(s): G FIREBAUGH
• Date Published: 1978
• Length: 16 pages
• Corporate Author: American Sociological Review; American Sociological Review
• Publication Format: Article
• Publication Type: Report (Study/Research)
• Language: English
• Country: United States of America

Annotation

THIS PAPER DEALS WITH THE PROBLEM OF CROSS-LEVEL BIAS WHICH MAY OCCUR WHEN USING AGGREGATE-LEVEL DATA TO INFER INDIVIDUAL-LEVEL RELATIONSHIPS. A SINGLE THEORETICAL DECISION RULE IS PRESENTED.

Abstract

UNDER CERTAIN CONDITIONS AGGREGATE-LEVEL DATA PROVIDE UNBIASED ESTIMATES OF INDIVIDUAL-LEVEL RELATIONSHIPS. A SINGLE THEORETICAL DECISION RULE IS PRESENTED: 'BIAS IS ABSENT WHEN, AND ONLY WHEN, THE GROUP MEAN OF THE INDEPENDENT VARIABLE (X) HAS NO EFFECT ON Y, WITH X CONTROLLED.' THE RULE IS INTRODUCED, DEMONSTRATED FOR THE GENERAL N-VARIABLE CASE, COMPARED WITH PRIOR DISCUSSIONS OF CROSS-LEVEL INFERENCE, AND ILLUSTRATED. STATISTICAL SUPPORT IS PRESENTED FOR THE DISCUSSION. THE ILLUSTRATION IS BASED ON THE 1930 CENSUS DATA USED BY ROBINSON IN 1950 TO STUDY THE RELATIONSHIP BETWEEN RACE AND ILLITERACY, A PAPER FREQUENTLY CITED IN DISCUSSIONS OF CROSS-LEVEL BIAS. THE FINAL SECTION DISCUSSES THE IMPLICATIONS OF THIS 'ABSENCE OF BIAS' RULE FOR THE CONVERSE TYPE OF CROSS-LEVEL INFERENCE: THE USE OF INDIVIDUAL-LEVEL DATA TO ESTIMATE AGGREGATE-LEVEL RELATIONSHIPS. AN EXTENSIVE BIBLIOGRAPHY IS APPENDED. (AUTHOR ABSTRACT MODIFIED - GLR)