BAYESIAN ANALYSIS OF CRIME RATE CHANGES IN BEFORE-AND-AFTER EXPERIMENTS - WORKING PAPER

• NCJ Number: 54879
• Author(s): T R WILLEMAIN
• Date Published: 1978
• Length: 21 pages
• Grant Number(s): 78N1-AX-0007
• Sponsoring Agency: US Dept of Justice; US Dept of Justice NIJ Pub
• Corporate Author: Massachusetts Institute of Technology
• Sale Source: National Institute of Justice/
• Language: English
• Country: United States of America

Annotation

BAYESIAN ANALYSES ARE DEVELOPED FOR DATA CONSISTING OF COUNTS OF CRIMES BEFORE AND AFTER THE INTRODUCTION OF AN EXPERIMENTAL CRIME CONTROL PROGRAM.

Abstract

A COMMON FORM OF PROGRAM EVALUATION IN THE FIELD OF CRIMINAL JUSTICE INVOLVES A 'BEFORE-AND-AFTER' COMPARISON OF CRIME RATES IN AN AREA TARGETED BY A NEW CRIME CONTROL PROGRAM. TWO BAYESIAN METHODOLOGIES FOR ANALYZING DATA WHICH CONSIST OF TWO SEQUENCES OF COUNTS OF RANDOM EVENTS ARE DEVELOPED. THE DATA SEQUENCES CONSIST OF THE DAILY NUMBER OF CRIMES DURING AN INTERVAL CONSISTING OF A 'BASELINE' FOLLOWED BY A 'TRIAL' PERIOD. MATHEMATICAL RESULTS ARE DEVELOPED FOR WHEN THE PERFORMANCE MEASURE OF INTEREST IS THE DIFFERENCE IN THE CRIME RATES. THE METHOD IS THEN APPLIED TO A REANALYSIS OF A NASHVILLE, TENN., EXPERIMENT ON THE IMPACT ON CRIME INDEX PART I CRIMES OF SATURATING SMALL AREAS WITH POLICE PATROL CARS. A PROCEDURE IS DEVELOPED WHEREBY THE COMPARISON OF PERIODS BEFORE AND AFTER THE PROGRAM IS MADE IN TERMS OF THE RATIO OF THE CRIME RATES. THE METHODOLOGY IS BASED ON A MATHEMATICAL MODEL OF CRIME OCCURRENCE WHICH HOLDS THAT THE NUMBER OF CRIMES IN A GIVEN INTERVAL OF TIME IS A POISSON VARIABLE. THE POISSON MODEL IS WELL-SUPPORTED BY THE NASHVILLE DATA. THIS ANALYTIC APPROACH HAS CERTAIN ADVANTAGES OVER BOTH CLASSICAL AND BAYESIAN ALTERNATIVES. THE ORIGINAL ANALYSIS OF THE NASHVILLE DATA (SEE NCJ-41730) USED STUDENT'S T-TEST TO EXAMINE THE STATISTICAL SIGNIFICANCE OF THE DIFFERENCE IN CRIME RATES BETWEEN BASELINE AND TRIAL PERIODS. THERE ARE TWO DRAWBACKS TO THIS APPROACH. FIRST, THE T-TEST ASSUMES THAT DAILY CRIME COUNTS VARY CONTINUOUSLY ACCORDING TO A GAUSSIAN DISTRIBUTION; WHEREAS, IN REALITY THE COUNTS ARE DISCRETE AND TYPICALLY NUMBER ONLY A FEW CRIMES PER DAY, MAKING THE GAUSSIAN A POOR APPROXIMATION. SECOND, THE STATISTICAL SIGNIFICANCE OF THE DIFFERENCE IN CRIME RATES IS LESS RELEVANT TO POLICY THAN THE DISTRIBUTION OF THE MAGNITUDE OF THE CHANGE IN CRIME RATE. A BAYESIAN ANALYSIS IS MORE USEFUL IN PRESENTING THE DISTRIBUTION OF THE CHANGE IN CRIME RATES, BUT CONVENTIONAL BAYESIAN APPROACHES TO SHIFTS IN THE LEVEL OF A TIME SERIES ARE BASED ON THE ASSUMPTION THAT THE VARIABLE OF INTEREST IS CONTINUOUS, WITH GAUSSIAN INCREMENTS FROM ONE TIME TO ANOTHER. AN APPROACH WHICH RECOGNIZES AND EXPLOITS THE DISCRETENESS OF THE DATA WOULD BE BETTER MATCHED TO THE PROBLEM. SUCH AN APPROACH IS DEVELOPED. (AUTHOR ABSTRACT MODIFIED--RCB)