General Deterrent Effects of Imprisonment*

Transcription

1 64 I SOCIAL FORCES I vol. 51, sept John Kosa, Aaron Antonovsky, and Irving K. Zola (eds.), Poverty and Health. Cambridge: Harvard University Press. Twaddle, A. C "Health Decisions and Sick Role Variations." Journal of Health and Social Behavior 10(June ): Zborowski, M "Cultural Components in Reaction to Pain." In Dorrian Apple (ed.), Sociological Studies of Health and Sickness. New York: McGraw-Hill. Zola, I. K "Illness Behavior of the Working Class." In Arthur B. Shostak and William Gomberg (eds.), Blue Collar Worlds. Englewood Cliffs: Prentice-Hall "Culture and Symptoms." American Sociological Review 31 (October) : General Deterrent Effects of Imprisonment* CHARLES H. LOGAN, University of Connecticut ABSTRACT Correlation and regression techniques are applied to aggregate data on imprisonment and crime rates. Certainty of imprisonment shows a negative and possibly curvilinear association with crime rate; contrary to recent criticisms, this relation cannot be accounted for by an artifice in the indexes of these two variables. Severity of imprisonment shows a negative correlation with crime rate after controlling for the effects of certainty. Some evidence is found of interaction between certainty and severity in effects on crime rate. In spite of its theoretical importance for criminology, the question of the deterrent effectiveness of legal sanctions has received only limited empirical investigation. Most research has been devoted either to the effects of punishment on recidivism or to the effectiveness of capital punishment. Recent research (see Chiricos and Waldo, 1970; Gibbs, 1968; Gray and Martin, 1969; Logan, 1971 a; Tittle, 1969), however, has begun to focus on a more central question of deterrence: namely, the effects of legal punishment on general crime rates. Using states of the U.S. as units of analysis, these studies have related crime rates to indexes of certainty and severity of imprisonment, constructed for several different felonies. This research has consistently shown a negative relation between * Much of this research was done while the author was a Fellow of the NIMH Deviant Behavior Traineeship Program. Support was also received from the Indiana University Graduate School and computer time was provided by the I. U. Research Computing Center. Charles Tittle supplied helpful comments on parts of an early draft of this paper. certainty of imprisonment and crime rate (as per deterrence theory), while evidence for a deterrent effect of severity has appeared initially only for homicide. The present paper refines and extends the analysis of some previously examined aggregate data on imprisonment and crime rates (see Tittle, 1969). METHOD Official statistics published in National Prisoner Statistics and Uniform Crime Reports are analyzed by correlation and regression techniques, using states of the U.S. as the units of analysis. Gibbs, Tittle, and Chiricos and Waldo used nominal and ordinal techniques on similar data, but since the indexes used by them and in this study achieve the interval (in fact, ratio) level of measurement, there is no reason why interval techniques cannot be applied.' These techniques have substantial inter-! It might be objected that although the operational indexes are ratio scales, the ultimate theoretical variables they indicate may not be. For example, 10 years in prison is twice as long as 5,

2 Imprisonment and Deterrence I 65 pretational and methodological advantages, since they permit greater precision in expressing the simultaneous relations between three or more variables, in specifying the forms of relations, and in depicting the extent and nature of statistical interaction. The indexes used here are the same as those examined by Tittle, namely: A. Certainty of imprisonment I. For total felonies: number of admissions to state prisons, , divided by number of crimes known to police, For individual offense categories: number of admissions to state prisons, 1960 and 1963, divided by number of crimes known to police, 1959 and 1962 B. Severity of imprisonment mean length of time (in months) served by felony prisoners released from state prisons in 1960 C. Crime rate I. For total felonies: mean annual number of crimes for , divided by 1960 population 2. For individual offense categories: mean annual number of crimes, 1959 and 1962, divided. by 1960 population For notational simplicity in the tables, crime rate will often be symbolized by the letter y (since it is theoretically the dependent variable), certainty will be symbolized by the letter c, and severity will be symbolized by the letter s. Thus, rye will denote the correlation between crime rate and certainty, and so on. but is it twice as severe? This however, is a question of whether psychological severity is a linear function of actual severity. Thus, it is a matter of theoretical interpretation of findings in the light of an unmeasured intervening variable, not a matter of whether the level-of-measurement assumption necessary for correlation has been met. It is true that to test for the significance of correlations requires the assumption of bivariate normality, but see footnote 3 for reservations about the meaningfulness of significance tests when dealing, as here, with virtually whole populations. CERTAINTY OF IMPRISONMENT AND CRIME RATE Certainty of imprisonment shows a low to moderate linear correlation with crime rate for all felonies examined (see Table 1, "raw scores" column). The scatterplots for these relations, however, reveal that for several offenses, particularly for assault, there are extreme outliers on certainty and on crime rate, and patterns that suggest curvilinearity. The stronger the relation shown even by the linear model, the more clearly is there depicted a shallow downward hyperbola, asymptotic on the vertical axis (crime rate) and the abscissa (certainty). This suggests that departure from a simple linear model may increase the correlations further. The possibility of curvilinearity in the relation between certainty of imprisonment and crime rate is suggested not only by observation of the scatterplots, but by some other considerations as well. First, it makes intuitive sense to suppose that the greatest effects of certainty may lie in the difference between zero or nearzero certainty and some higher level, while there may be an upper limit of saturation, or diminishing returns, beyond which increasing certainty has less of an impact on crime rate. Second, as Gray and Martin (1969: 392) point out a linear model can have the drawback of im~lying negative crime rates: an impossibility. Further, it implies some maximal level that crime rate achieves when certainty is zero, whereas deterrence theory would predict that crime rate should be free to rise indefinitely as certainty approaches zero, depending on other conditions. As mentioned above, the scatterplots do seem to describe this pattern of a shallow downward curve, steep at lower levels of certainty and flatter at upper levels of certainty. The main body of values curve only slightly, while a few extreme outlying values suggest the sharper bends at each end. The most convenient and easily interpretable means of handling both a slight curve and the problem of extreme scores is to adjust the scores by some such procedure as a log transformation. This simplifies the relationship by straightening the bends of the plot to better approximate a straight line, and it improves the normality of the marginal distributions by reducing skewness toward higher values of each variable.

3 66 I SOCIAL FORCES I vol. 51, sept Table 1. Correlation Between Certainty of Imprisonment and Crime Rate, With and Without Log Transformations (raw Gain scores) (logs) in Offense rye rye Strength N All felonies -.47" -.50" Homicide Robbery -.51" -.59" Sex offenses -.53" -.73" Assault " Burglary -.46" -.46" Larceny b Auto theft _.2ge a = p <.001. b = p <.01. c = P <.05. When the relation between certainty and crime rate is measured using log transformations (base 10) on both of these variables, rather than raw scores, the results are as shown in Table 1. This procedure does seem to improve the fit of the prediction line somewhat, but not consistently. For five of the offense categories, use of log transformations raises the strength of the relation, though only slightly for two of these. For two offenses the relation decreases in strength, one very slightly and one moderately. It appears, then, that for some offenses there may be a curve in the relation between certainty of imprisonment and crime rate, as shown by these data.s Once the effects of outliers, and of a possible curvilinearity, have been adjusted for by logarithmic transformations, the findings show a moderate to fairly strong negative relation between certainty of imprisonment and crime rate. For only one offense is this relation statistically nonsignificant both with and without log transformations." 2 The major effect of the log transformations seems to be in reducing the effects of a few very extreme outlying values on certainty and crime rate. This is particularly the case with assault and larceny. Whether these extreme values are simply deviant cases or represent a real curve in the relation must remain an open question at this point, but the latter is at least a reasonable possibility. 3 There is some dispute about the meaningfulness of testing the significance of associations found in the study of virtually a total population. (Here, N=4S, out of a population of 50.) In the absence of any firm resolution of this problem, It is important to note, at this point, the very low levels of certainty of imprisonment and the extremely small variations of this variable. (see Table 2). For homicide, there are about 47 persons imprisoned for every 100 crimes recorded. No other felony approaches this level.' For most felonies, the average certainty of imprisonment is between.01 (auto theft) and.14 (robbery). Thus, certainty of imprisonment is not only low, but consistently low across states. For example, for all felonies, with a mean of.06 and a standard deviation of.03, about 95 percent of the states will have values of certainty of imprisonment between 0 and.12. Only sex offenses has much variation in certainty of imprisonment (S.D. =.34).5 Moreover, sex offenses is the only felony to have both a moderately high probability of imprisonment and a sizeable variation in that probability. Perhaps partly as a consequence of this, it also has the highest correlation between certainty of imprisonment and crime rate. The consistently low level of certainty of imprisonment makes the size of its relation to crime rate fairly impressive, since low variation in an independent variable ordinarily depresses a correlation coefficient. Thus, this analysis has shown a relationship of considerable strength between certainty of punishment and crime rate. Before turning to the relation between severity of imprisonment and crime rate, it is necessary to deal with the question of whether the correlation between certainty and crime rate could be a spurious artifact of the way in which those variables are measured. This question deserves detailed examination, since the issue is it seems best, when dealing with total populations, to report significance levels but to place interpretational emphasis on the strength of associations found rather than on their statistical significance. 4 The mean of.42 for sex offenses is somewhat misleading because of the effect of several extreme (high) values; thus the median of.29 gives a better estimate. 5 The relatively high standard deviation of.34 for assault is misleading because of the influence of one extremely high value of certainty. For this offense, the interquartile range provides a better estimate of dispersion. Thus, for assault the middle half of the states have probabilities of imprisonment between.02 and.os-very uniform indeed.

4 Imprisonment and Deterrence I 67 Table 2. Distribution of Values of Certainty of Imprisonment: Mean, Median, Standard Deviation, and Interquartile Range (Inter- Standard quartile Offense Mean (Median) Deviation Range) All felonies.06 (.05).03 (.03) Homicide.47 (.48).15 (.19) Robbery.14 (.14).06 (.09) Sex offenses.42 (.29).34 (.26) Assault.11 (.05).34 (.06) Burglary.03 (.03).02 (.02) Larceny.04 (.02).07 (.03) Auto theft.01 (.01).01 (.02) Figures refer to ratio of persons imprisoned to crimes recorded. likely to arise in many types of deterrence research relating some index of certainty of punishment to some index of violation rate. It can be shown that an alleged artifactual effect is not a real problem, while a related but distinct form of spuriousness does need to be considered and empirically ruled out. TWO POSSIBLE SOURCES OF SPURIOUSNESS The measures of certainty of imprisonment used by Gibbs, Gray and Martin, Tittle, Chiricos and Waldo, and in this study, take the form of a ratio of admissions to prison divided by crimes known to police, which may be symbolized as AIC. The measures of crime rate consist of a ratio of crimes known to police divided by some population base, which may be symbolized as CIP. It has been suggested (see Chiricos and Waldo, 1970: ; Tittle, 1969: ) that the existence of a common term, C, in the measures of the two variables (AIC; CIP) may produce a certain amount of spuriousness when the two indexes are correlated. Specifically, the two terms may have a spurious inverse correlation because as C increases AIC will decrease while CIP will increase. This effect will occur, however, only under three special conditions: (l) when A = P, or (2) when A and P are constant, or (3) when A, C, and P are unrelated. But obviously admissions to prison do not equal population size, these two variables are not constant in the data examined, and they have a high positive correlation with each other and with number of crimes (the larger the population, the more crimes, the more admissions to prison). The literature dealing with spuriousness in the correlation of ratio variables is relatively small and often obscure, at least to sociologists (e.g., Brown et al., 1914; Kuh and Meyer, 1955: Madansky, 1964; McNemar, 1969: ; Neifeld, 1927; Pearson, 1897; Rangarajan and Chatterjee, 1969; Yule, 1910; Yule and Kendall, 1950: ). But it seems to be regarded as well established that when the two ratios are theoretically meaningful as ratios, and the hypotheses are stated in terms of these ratios, then the question of spuriousness due to indexical artifice does not arise (Kuh and Meyer, 1955; McNemar, 1969:181; Rangarajan and Chatterjee, 1969). Spuriousness of this sort becomes a problem only when the common term is used to standardize, or otherwise adjust, two variables, rather than to create entirely new variables. Thus, we can justifiably argue that, in the present context, the problem of spuriousness due to indexical artifice in ratio correlation does not logically arise." An analogy may make the issue clearer. We would not assert that the association between speed of driving and efficiency of gasoline consumption is a spurious result of their common numerator (miles-per-hour and miles-per-gal Ion). It is precisely because the components (distance, time, consumption) are so interrelated that we create new variables by taking their ratios. However, there is another way in which a common term can create a spurious correlation between two ratios, other than through indexical artifice. This can occur when the common term has simultaneous causal effects (rather than simply mathematical effects) on each of the two ratio-variables. In the car analogy, it is known that the more miles a car is driven the lower its top speed and the less efficient its gas consumption. This is not an indexical effect, but a causal effect of wear and tear on both speed and efficiency. It should therefore be handled like any other disturbance term-i.e., by some method of control. 6 The writer has discovered that some readers will remain unconvinced by a logical rejection of the problem of indexical artifice and would prefer to see an empirical solution. Such skeptics are referred to footnote 10, below, and to Logan (l97ia: ; 1971b).

5 68 I SOCIAL FORCES I vol. 51, sept To return to the problem at hand, there may be a causal effect of the absolute number of crimes on certainty of imprisonment. The situation is complicated by the fact that certainty of imprisonment and number of crimes may have reciprocal effects on each other (certainty may deter crimes, while crimes make demands on the legal system than can affect certainty). This suggests the following model:.e: ~AIC 1 ~CIP What is required is a technique that eliminates any possible spuriousness due to simultaneous effects of C on AIC and CIP (AIC ~ C ~ CIP) without at the same time destroying the reciprocal effects of C and AIC on each other and, ultimately, on CIP (C ~ AIC ~ CIP) nor removing the possible operation of C as an intervening variable (AIC ~ C ~ CIP). No such technique is known to the writer. Second best is to apply a method that overcontrols as little as possible, which may then be used as a conservative test for the existence of a possible spurious effect. The technique of part correlation is more useful for this purpose than ordinary partial correlation. In part correlation, one variable is related to a second variable from which the effect of a third variable has been removed. It involves the correlation of one variable with the residuals of a second, as opposed to partial correlation, which correlates the residuals of each of the first two yariables after they have each been regressed on a third.' In terms of the present problem, the part correlation r.,/cic/p.c) expresses the correlation of crime rate with certainty of 7 The general formula for part correlation is: 'It - rl3t" r1(l.,) =_r;---;- v 1-r" where r1(,.3) refers to the correlation between 1 and the residuals of 2 regressed on 3. See Dubois (1957:60-62) and McNemar (1969:186). Table 3. Relation of Crime Rate (C/P) to Certainty of Imprisonment (A/C) With and Without Controlling for Effect of Common Term by Means of Part Correlation Offense All felonies Homicide Robbery Sex offenses Assault Burglary Larceny Auto theft a = p <.001. b = p <.01. c = P <.05. punishment after the effects of the common terms, C, have been removed from the measure of crime rate. H Table 3 compares these part correlations with the corresponding zero-order correlations." The relations between crime rate and certainty of imprisonment weaken somewhat, but quite clearly do not disappear, when the effect of absolute number of crimes is partialled out of the measures of crime rate. This indicates that the relations between certainty and crime rate that were found in these data cannot be said to be due to a spurious result of simultaneous 8 It was reasoned that both the partial correla and the part correlation rc/pia/c.i/e) tion re/p s rc.o ro/pa/o -.44 b " -.55" b -.38 b -.29 c ra/o CO/P.O) -.31 c " -.42 b -.14 _.39 b -.30 c -.31 c might unduly restrict the already very limited variation in AIC, which could lower its association with C/ P as a purely statistical effect. Hence the part correlation rsrc.crr.c) should involve the least amount of overcontrolling. Actually, it turns out to be rather arbitrary from which variable we remove the effects of number of crimes (C). The values of rc/pia/c.i/c) are comparable to those of ra/<'lc/p.e) shown in Table 3. (lic is used here instead of C in order to meet the linearity assumption. AIC is a curvilinear function of C but a linear function of lic. See Fleiss and Tanur (1971 :44). The values of r"/h'/c.i/c) are: total felonies = -.34 e ; homicide = -.12; robbery = -.45 a ; sex offenses = -.39 a ; assault = -.30 e ; burglary = -.42 b ; larceny = -.33 e ; auto theft = The values of rc».'/c differ slightly from those of r vc in Table 1 because the measures of C/P and A / C were recalculated from the original components, A, C, and P, by computer transformation, while r.. was computed from the decimal values for crime rate and certainty calculated independently by Tittle. Therefore, the mild discrepancies are not too surprising. In any case, what is important here is not the absolute size of the relations, but comparison of the zero-order correlations with the part correlations.

6 Imprisonment and Deterrence I 69 effects of the number of crimes on certainty of imprisonment and on crime rate.w It remains to be seen whether correlation techniques can add further to our information about the relation between severity of imprisonment and crime rate, or about the possibility of statistical interaction between certainty and severity of imprisonment affecting the relation of either variable to crime rate. SEVERITY OF IMPRISONMENT AND CRIME RATE: A HIDDEN RELATION? Using zero-order correlation, a significant negative relation between severity of imprisonment and crime rate is found only for homicide, while for other offenses the relation is near zero or weakly positive (see Table 4, r., column). There might be several possible explanations of this finding, other than the simple one that there may in fact be no deterrent effect of severity of imprisonment. There may be interaction between severity and certainty, such that severity operates as a deterrent only under conditions of high or low certainty. This alternative is treated in the next section. A second possibility is that there may be a positive reverse effect of crime rate on severity, which would tend to obscure any negative (deterrent) effect of severity on crime rate that might exist. That is, states with high crime rates may react by imposing stiffer sentences on offenders who are caught and punished. A third interpretation is that a possibly existing deterrent effect of severity on the general crime rate may be hidden by a backlash effect of punishment on those punished (i.e., on recidivism). A fourth 10 It should be remembered that the part correlations "overcontrol," in that they eliminate not only spurious effects but also some possible causal effects that would be consistent with deterrence theory. This is thus a very conservative test for spuriousness. It should also be noted that, although used here to reject the possibility of spurious correlation between two ratios due to simultaneous causal effects of a common term, the part correlations also provide empirical confirmation that the associations found between certainty of imprisonment and crime rate are not due to a purely mathematical connection between the ratios used to measure those two variables (i.e., they provide an empirical solution to the indexical artifice question, which was dismissed earlier on logical grounds). possibility is that a true negative relation between severity of imprisonment and crime rate is obscured by the operation of some third variable that is either positively or negatively related to both severity and crime rate. It is probable that certainty of imprisonment may constitute one such third variable. There are several reasons for expecting certainty and severity of imprisonment to be negatively related. When penalties are low, we may expect the legal system, at least at the judicial level, to operate more smoothly, automatically, and relentlessly, so that certainty of imprisonment will be relatively high. Juries may be more willing to convict and defendants may be more willing to plead guilty or to accept a conviction without appeal. The higher the penalty, the greater the reluctance on the part of judicial authorities to charge that particular offense, and the harder to get a conviction (for illustrations of this effect see Campbell and Ross, 1968; Hall, 1952:chap. 4; Tappan, 1949). It is also possible that the less the certainty of detection, arrest, and conviction, the more will judges compensate by "throwing the book" at those offenders that finally do get convicted. In contrast, the more effectively the system operates (the higher the certainty) the less threatening and uncontrollable will the behavior seem, thus making it more eligible for leniency. And finally, the widespread use of plea bargaining raises certainty of conviction while simultaneously lowering severity. The discussion above suggests that the following model might obtain at least at the judicial level of the legal sanctioning system: 'IS'~:~ty~ Certainty (c) /crime Rate If this model is correct, and assuming the interdependence of certainty and severity to have a greater effect on the relation of severity to crime rate than on the relation of certainty to crime rate, the following empirical relations should hold: 1. r., should be negative, and (y)

7 70 I SOCIAL FORCES I vol. 51, sept ry" should move toward -1.0 relative to r1l These predicted outcomes were examined, with findings as shown in Table Table 4 indicates that the data are consistent with the model presented above. All eight relations between certainty and severity are negative. The relation between certainty and crime rate stays almost exactly the same when severity is controlled. But when certainty is controlled, the relation between severity and crime rate becomes negative for all felonies except auto theft. For homicide and assault, the negative partial correlation between severity and crime rate is statistically significant (p <.01 for homicide, p <.05 for assault; but see footnote 3). The stronger the negative relation between certainty and severity (r,.,), the greater the negative shift in the relation between severity and crime rate when certainty is controlled. It thus appears that while certainty of imprisonment seems to have a direct and independent negative relation to crime rate, severity, if it has a deterrent effect, does not operate independently of certainty. Severity may have a negative relation to crime rate that is either counteracted by an indirect, positive effect on crime rate through lowering certainty, or else obscured by simultaneous negative effects of certainty on both severity and crime rate. It should be remembered that controlling for certainty removes only one of several confounding factors in the relation between severity and crime rate. Others still remain-such as, a possible reverse positive effect of crime rate on severity, or a positive "specific" effect, as op- 11 While ordinarily it might be preferable to use regression coefficients in this sort of model testing, the correlation coefficients were deemed adequate to test this particular model. First, it is predicted that ry " will change signs or at least drop to zero. In either of these cases, r will behave like b. Second, given that this is the case, correlation coefficients are used because they are more familiar and interpretable to most sociologists. 12 The values of r-, differ from those of Table I because N was lowered for some offenses to correspond to the N for severity. "c:«was computed with log transformations on c because the outliers on c were such as to distort the relationship as measured by r without transformation, while ry, was computed without log transformation because the slight outliers on y were not such as to bend a prediction line through the untransformed values. Table 4. Zero-order and Partial Correlations Between Certainty of Imprisonment, Severity of Imprisonment, and Crime Rate Offense 'e's rye rys. c. ry,c, ry,c,.8 N All felonies Homicide Robbery Sex offenses Assault Burglary Larceny Auto theft 'ys.c = --C='y=8=-=('=-y'-=-,'-=-)(="="-=-)_ f VI - ':'c Y l ~ r~'8 c' = log c; s' = log y. posed to a negative "general" effect, of severity on criminal conduct. If these problems were adequately handled, the negative partial relation between severity and crime rate might well be stronger. INTERACTION BETWEEN CERTAINTY AND SEVERITY It is reasonable to suggest that certainty and severity of punishment may interact in such a way that the existence, strength, or form of the relation of each to crime rate is dependent on the value of the other. Accordingly, the data were analyzed by the following procedure: for each offense category, the cases (states) were divided into the 20 highest and the 20 lowest on severity of prison sentence, forming two subsamples. Within each subsample, a logarithmic transformation was made on certainty and crime rate. The values of the correlation coefficient (ry,) and the regression coefficient (by,) were then computed. This procedure was then repeated with the cases divided into the 20 highest and 20 lowest on certainty of imprisonment, and the values of ry. and by, were examined under these two conditions. The results are shown in Tables 5 and 6. Table 5 indicates that the regression of crime rate on certainty of imprisonment has a steeper negative slope under the condition of high severity for five of the offense categories (including All Felonies), though this effect is mild. The correlations are also stronger under the condition of high severity, overall and for four of the seven individual felonies, while remaining almost exactly the same for three other felonies under both conditions.

8 Imprisonment and Deterrence I 71 Table 5. Correlation Between Crime Rate and Certainty of Imprisonment Under High and Low Severity' Table 6. Correlation Between Crime Rate and Severity of Imprisonment Under High and Low Certainty Low Severity High Severity Low Certainty High Certainty Offense rye (bye) rye (bye) Offense ry, (by,) ry, (by,) All felonies -.42 (-.38) -.63 (-.44) All felonies -.21 ( ) -.17 ( ) Homicide -.21 ( -.44) -.33 (-.54) Homicide -.43 ( ) -.36 ( ) Robbery -.53 ( -1.05) -.54 (-.74) Robbery -.16 ( ).30 (.00024) Sex offenses -.72 (-.55) -.71 (-.91) Sex offenses -.06 ( ).21 (.00031) Assault -.63 (-.63) -.62 ( -.61) Assault -.13 ( ).04 (.00018) Burglary -.34 (-.36) -.46 (-.27) Burglary -.29 ( ).23 (.00354) Larceny -.44 (-.20) -.59 (-.25) Larceny.18 (.00324) -.14 ( ) Auto theft -.20 (-.09) -.32 (-.11) Auto theft.24 (.00253).08 (.00073) 'y = logy;c = loge. Table 6 is difficult to interpret since the regression coefficients are all exceedingly small and fairly unreliable, given the generally low correlations. However, the general pattern (if any) that appears is that severity has slightly greater deterrent effect (higher negative b) under low certainty. (This effect is smallest for homicide, which may be because certainty of imprisonment is never very low for this offense.) For four offenses, the negative effect appears only under low certainty, while for two others it is stronger under low certainty. This might mean that only when certainty of imprisonment is very low does length of imprisonment enter into deterrence. Above some given level of certainty, even the shortest prison term may be severe enough that adding to it is superfluous.p In sum, this analysis suggests, though not in a clear-cut or consistent fashion, that very severe punishment may bolster the deterrent effect of certainty of imprisonment, but that in a general sense severity of imprisonment is a deterrent, if at all, mainly when certainty of imprisonment is low. 13 The deviating findings for larceny and auto theft may indicate a second curve in the pattern. When certainty is too low, severity may have no deterrent effect for a different reason: since the penalty is not a real threat, its severity has no effect. It should be remembered, though, that certainty of imprisonment does not have a very great range of variability, which means that "high" and "low" conditions of certainty (as they occur in these data) may not be effectively different from each other. This, and the unreliability in b produced by a low r, makes it necessary to describe and interpret very tentatively the differences in the effect of severity on crime rate under high and low certainty. SUMMARY AND DISCUSSION The overall picture that emerges from these data is as follows: there is a moderate negative relation between certainty of imprisonment and crime rate, which may be curvilinear. The zero-order correlation of severity of imprisonment and crime rate is not in the predicted (negative) direction (except for homicide), but when the effects of certainty as either an explaining or an intervening variable are removed, the relation for severity moves in the expected direction (toward a negative relation). The relation between certainty and crime rate is increased in strength and slope under conditions of high severity, relative to conditions of low severity. But the effect of severity on crime rate, not strong or consistent to begin with, appears somewhat stronger under conditions of low certainty. It is clear that the major finding of a moderately strong negative relationship between certainty of imprisonment and crime rate is consistent with deterrence theory. In fact, in view of certain considerations, the outcome is actually quite impressive. Low variation in an independent variable (recall Table 2) ordinarily depresses a correlation coefficient simply as a consequence of statistical effect. Moreover, the major deterrent effect of legal punishment may inhere in its mere potentiality, a factor that is constant and uniform from state to state. Hence, it is conceivable that the primary deterrent effect of legal sanction-threats may have been manifest even in the state with the lowest certainty of imprisonment. Furthermore, just as a large portion of the population may be deterred by even a slight possibility of imprisonment, another portion might require a very high probability of imprisonment-or

9 72 I SOCIAL FORCES I vol. 51, sept other legal punishment-to be deterred from crime. Thus, the findings may represent the variation in crime rate that can be explained by a small variation in certainty of imprisonment when potentiality is held relatively (but not completely) constant at a low level. If so, more impressive evidence would require a much greater range of variation than normally would occur in a given society under stable conditions.>' There is an additional sense in which the correlations between certainty of imprisonment and crime rate might be seen in the present context as surprisingly strong. A crucial link between deterrence theory and empirical research using data of the sort examined here concerns the relationship between actual certainty of imprisonment and the perceptions of certainty held by the population. Data on actual certainty of imprisonment by state will reveal deterrent effects only to the extent that there is at least a rough correspondence between variation in statewide average levels of actual certainty and variations in statewide average levels of perceived certainty. This indicates the importance of data on perceptions of punishment at the individual level. But it also indicates that, given the necessity to assume the existence of an unmeasured and probably only crudely corresponding intervening link (perceptions) between actual certainty and crime rate, the relations found between these latter two variables are much stronger than one would expect. In light of all these limitations, the results of this reanalysis of official data appear to provide considerable support for the major proposition of deterrence theory, at least as regards certainty of punishment. It is hard to escape the conclusion that the likelihood of punishment has an important role in increasing conformity to the law. H The restricted range of variation in certainty could also be hiding a stronger pattern of curvilinearity. The present suggestive pattern might appear more definitely if there were more states having extreme high scores on certainty. It would be good to know whether this curve is a real one, since it suggests that there may be little to gain by the widely urged strategy of continuously raising the certainty of imprisonment-at least not much beyond the upper end of its presently low range. The findings for severity of imprisonment are not so impressive. But here again several considerations suggest the probable conservatism of the present findings. The intervening variable of perceived severity probably corresponds only very crudely with actual severity, as was argued in the case of certainty. Further, just as a minimal possibility of imprisonment may be sufficient deterrent for a great portion of the population, so may increasing lengths of imprisonment be superfluous. For another segment of the population-those residing in high crime rate areas or who are members of high crime-prone groups-imprisonment for the usual amounts of time may be regarded as a normal fact of life, constituting an acceptable risk. For such a population component, either an increase in certainty or a drastic increase in severity would probably be required to increase deterrence. Thus, an optimal test of the deterrent effects of severity of legal punishment would be possible only where there was little variation in certainty but a great range of variation in severity, from very mild to quite severe. Two other possible factors that may be obscuring an actual deterrent effect of severity of imprisonment on crime rate have been mentioned previously: (1) the possibility that severity of imprisonment may have crime-inducing effects on the persons punished while having deterrent effects on others, and (2) crime rate may have a positive effect on severity of imprisonment by generating harsh reaction on the part of authorities. While the findings do seem to substantiate a deterrence argument, certain inadequacies in the analysis require caution in making this interpretation. First, there is no assurance that the causal order is from punishment to crime rather than the reverse. There are a priori grounds for expecting both a positive and a negative effect of crime rate on certainty or severity of imprisonment. As just noted, high crime rates might cause punitive public and judicial reactions, raising severity. Alternatively, Tittle (1969: 420) suggests that high crime rates might cause crowded prison conditions, encouraging greater use of parole, thus lowering severity, as measured here. In a similar way, high crime rates might cause a strain on the

10 Imprisonment and Deterrence I 73 law enforcement and judicial machinery, lowering its efficiency, thus lowering certainty. Alternatively, high crime rates might increase the commitment of public resources to the enforcement and judicial systems, thus raising certainty. It is clear that in the absence of well-developed theory, a priori reasoning produces opposite predictions about the reverse effects of crime rate on certainty and severity of imprisonment, a problem that cannot be resolved with these data. Second, there is always the possibility that unmeasured and uncontrolled variables may account for the negative relations found between certainty or severity of imprisonment and crime rate. For example, normative consensus (favoring the legal norms) might lower crime rate for non-deterrent reasons, while at the same time increasing certainty of punishment by increasing public support of and involvement in law enforcement. Similarly, many other possible explaining, intervening, or interactive variables will eventually need to be identified and taken into account in empirical research on deterrence. Finally, caution is imperative because the data are limited to one time period, to a certain set of crimes, and to only one type of legal punishment: imprisonment. Even if one considers only the major felonies on the grounds that they represent the "core" of criminal conduct, it would be desirable to expand the analysis to a different (and preferably broader and more recent) time period, and to different types or levels of legal punishment." Despite these cautions, however, the data have clearly shown an association between crime and punishment that is strong enough to warrant not only further research on deterrence but perhaps a general reexamination of some of the old rationalistic and utilitarian images of criminal behavior that criminologists may have too hastily abandoned. REFERENCES Brown, J. W., M. Greenwood, Jr., and F. Wood "A Study of Index Correlations." Jour- 15 Data on certainty of arrest and crime rate have been examined with results supportive of deterrence theory. See Logan (1971a: ). nal of the Royal Statistical Society 77(February): Campbell, D. T., and H. L. Ross "The Connecticut Crackdown on Speeding: Time-Series Data in Quasi-experimental Analysis." Law and Society Review 3(August) : Chiricos, T. G., and G. P. Waldo "Punishment and Crime: An Explanation of Some Empirical Evidence." Social Problems 18(Fall): Dubois, Philip H Multivariate Correlational Analysis. New York: Harper & Row. Fleiss, J. L., and J. M. Tanur "A Note on the Partial Correlation Coefficient." American Statistician 25(February) : Gibbs, J. P "Crime, Punishment and Deterrence." Southwestern Social Science Quarterly 48(March) : Gray, L. N., and J. D. Martin "Punishment and Deterrence: Another Analysis of Gibbs' Data." Social Science Quarterly 50(September): Hall, Jerome Theft, Law, and Society. 2d ed. Indianapolis: Bobbs-Merrill. Kuh, E., and J. R. Meyer "Correlation and Regression Estimates When Data Are Ratios." Econometrica 23(October) : Logan, C. H. 1971a. "Legal Sanctions and Deterrence from Crime." Ph.D. dissertation, Indiana University b. "On Punishment and Crime (Chiricos and Waldo, 1970): Some Methodological Commentary." Social Problems 19(Winter): Madansky, A "Spurious Correlation Due to Deflating Variables." Econometrica 32(October) : McNemar, Quinn Psychological Statistics. 4th ed. New York: Wiley. Neifeld, M. R "A Study of Spurious Correlation." Journal of the American Statistical Association 22(September) : Pearson, K "On a Form of Spurious Correlation Which May Arise When Indices Are Used in the Measurement of Organs." Proceedings of the Royal Society of London 60: Rangarajan, C., and S. Chatterjee "A Note on Comparison Between Correlation Coefficients of Original and Transformed Variables." American Statistician 23(October) : Tappan, P. W "Habitual Offender Laws in the United States." Federal Probation 13 (March) : Tittle, C. R "Crime Rates and Legal Sanctions." Social Problems 16(Spring) : Yule, G. U "On the Interpretation of Correlations Between Indices on Ratios." Journal of the Royal Statistical Society 73(June) : Yule, G. Udny, and Maurice G. Kendall An Introduction to the Theory of Statistics. 14th ed. New York: Hafner.