THIS STUDY FOCUSES ON THE NEGATIVE CORRELATIONS FOUND BETWEEN CERTAINTY OF SANCTION AND CRIME RATES WHICH POSSIBLY CAN BE EXPLAINED AS A COMPARATIVE TOOL USED TO MEASURE THESE TWO VARIABLES. THE NEGATIVE CORRELATION MAY TAKE THE SAME DIRECTION AS THE RELATION PREDICTED BY DETERRENCE THEORY. A POSSIBLE CONTAMINATION BETWEEN THE MEASURES OF INDEPENDENT VARIABLES (CERTAINTY OF SANCTION) AND DEPENDENT VARIABLES (PER CAPITA CRIME RATE) HAS EXISTED IN DETERRENCE RESEARCH THAT STRESSED THE CONSISTENT NEGATIVE RELATIONSHIP BETWEEN CRIME RATE AND SOME MEASURES OF PUNISHMENT (E.G., EXECUTION, IMPRISONMENT, AND ARREST). WHEN THE TWO RATIOS CONTAINING A COMMON TERM ARE CORRELATED, THE POSSIBILITY OF THE CORRELATION BEING A FRAUDULENT MATHEMATICAL MODIFICATION OF THE COMMON TERM EXISTS. ONE DATA SET WHICH CONSISTS OF CRIME RATES AND IMPRISONMENT ARE USED FOR ILLUSTRATION AND DEMONSTRATION TO DISCUSS THIS PROBLEM COMMON TO SOME DETERRENCE STUDIES. IT IS REPRESENTATIVE OF DATA ANALYZED IN CROSS-SECTIONAL DETERRENCE RESEARCH. THE FOLLOWING ALTERNATIVE RESOLUTIONS FOR DEALING WITH THE PROBLEMS OF CORRELATING RATIOS WHICH HAVE COMMON TERMS ARE EXAMINED: (1) THE THEORETICAL-MEANING RESOLUTION; (2) THE PEARSONIAN APPROXIMATION FORMULA AND NULL COMPARISON; (3) SIMULATION TECHNIQUES OF PEARSON AND CHAYES; (4) SCHUESSLER'S DECOMPOSITION INTO COMPONENT COVARIANCES; AND (5) PART CORRELATION AND THE USE OF RESIDUAL SCORES. THESE METHODOLOGICAL THEORIES WHICH ARE INTUITIVE, LOGICAL, OR EMPIRICAL ARE PRESENTED WITHIN LIMITS. IT IS SUBSTANTIVELY CONCLUDED THAT ASSERTIONS THAT DETERRENCE WORKS ARE PREMATURE. CURRENT VARIATIONS IN IMPRISONMENT RATES HAVE NOT BEEN SHOWN TO HAVE A CAUSAL EFFECT ON CRIME RATES. THE GENERAL METHODOLOGICAL CONCLUSION IS THAT THE MOST USEFUL TEST FOR THE EXISTENCE OF A COMMON-TERM MODIFICATION IN A BIVARIATE RATIO CORRELATION IS THE PART CORRELATION TECHNIQUE. WHEN ADDITIONAL VARIABLES ARE INCLUDED, THE SUGGESTED APPROACH IS TO BALANCE ONE OF THE TWO RATIO VARIABLES BY REVERTING TO THE COMMON TERM AND THEN PROCEEDING WITH THE STUDY FROM THERE. FORMULAS, TABULAR DATA, REFERENCES, AND NOTES ARE PROVIDED. (JCP)