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A RADICAL RECONSIDERATION OF SOME EARLY FINDINGS ON DETERRENCE
Key words: deterrence, punishment, prison, certainty, severity, homicide rates, states, findings, novel research methods
Jack P. Gibbs, Centennial Professor Emeritus, Vanderbilt University
{[READER: I am not writing this "paper" as even a rough draft of a prospective submission for publication, the immediate reason being that I am burned out and long ignorant of the relevant literature. Rather, what follows is a report of research (think of it as my hobby) in the form of a reconsideration of data that I published in a 1968 paper: "Crime, Punishment, and Deterrence," Southwestern Social Science Quarterly, Vol. 48, pp. 515-530. If you want to examine that paper and do not have ready access, inform me and I will send you a copy. Although I believe that the paper stimulated a renewal of interest in deterrence, it suffers principally from two defects. First, only three variables were considered (see Cols. 1, 3, and 4 of the attached Table 1), meaning that possible extralegal determinants of the homicide rate were ignored. Second, the statistical analysis was limited largely to tabular arrangements. My recent research at least partially overcomes the two defects of the original research, in addition to employing what may be a novel method (sets comparisons); and I hope you are interested enough in the findings to comment on them. For that matter, feel free to use the findings as you see fit; but I would appreciate citing me as the source, and I invite you to consider a joint paper on the subject with you as senior and "last say" author. My only reservation is that I would do nothing in the way of writing (beyond editing at your direction) because my prose is evidently chloroform in print and, if feasible, computing additional findings on request. To be sure, the data are old; but I hope that you join me in the belief that "historical dates" are irrelevant for science, and should the publication generate research on recent data the question "Do the findings hold after some 50 years?" would be interesting and perhaps important. Should you contemplate co-authoring, feel fee to considering recruiting a third co-author, a statistical expert but not opposed to innovations. Finally, one of the many shortcomings of this report is that space limitations precluded a consideration of policy implications. However, a "for publication version" should sneak in two points. First, evidence on the association between punishment and crime does have policy implication if only because it bears on the deterrence doctrine. Second, evidence of a link between some "extralegal" conditions (e.g., racial composition) and crime pose a policy dilemma, while the link for other kinds of extralegal conditions (e.g., income distribution) poses policy issues.}}
JUSTIFICATIONS APART FROM THE DETERRENCE QUESTION
The subsequently reported research has implications far beyond particular variables, especially for the social/behavioral sciences. The implications are suggested by an assertion. Whatever the quantitative variables in research by social/behavioral scientists, the bivariate association measure is bound to be substantially less than maximum (+1.0 or –1.0 in the cases of correlation coefficients). It will not do to argue that some instances of associational measures are commonly very near the maximum. To the contrary, if the absolute maximum is 1.0, in the social/behavioral sciences a report of as much as .90 will appear incredulous or suggest an artifact. As for being a constant though far less than at the maximum level, statistical associations in the social/behavioral sciences are "elastic," a term favored by economists. The term ceases to soothe once correctly translated as meaning "utterly unpredictable."
So there is a question that should be a major one for the social/behavioral sciences. Why is a measure of association between any two variables virtually certain to be far less than the maximum and rarely if ever anything like a constant? It is not satisfactory to reply by claiming that in the social/behavioral sciences associational measures rarely express a causal relation. Even if the relation is unquestionably causal, the association measure can be far less than maximum. More specifically, several possible contingencies determine the magnitude of a measure of association and perhaps even its direction--negative or positive.
PRINCIPAL POSSIBLE CONTINGENCIES
So the answer to the major question is that measures of bivariate association are extremely contingent on several conditions. That answer becomes informative and constructive only when extended to an identification of particular kinds of contingencies that are to some degree controllable by social/behavioral scientists. The present research focused on two such contingencies. Others are briefly recognized subsequently, but the two kinds in question have some bearing on the others. As for the focus on bivariate associations, the findings have implications for multivariate analysis; and the hope is that someone will extend the research in that direction, regression analysis in particular.
The Range of an Association
If he or she has thought about it seriously, no scientist is likely to deny that regardless of the variables any association may well be limited to a range of the values of one or both variables (i.e., their magnitudes). Such associational limits (commonly called the "ceiling" or "floor" effect) are perhaps especially prevalent in the social/behavioral sciences, but it is by no means peculiar to them. As a case in point, one major difference between the astrophysics of Newton and that of Einstein can be described in terms of range, velocity and acceleration in particular; and "black hole" phenomena are studies in association limits. Moreover, whatever the science, the very notion of an "ideal condition" commonly translates as a matter of the range of the values of variables.
Although what is henceforth designated as the "magnitude contingency" has received surprisingly little attention in the way of systematic research by social/behavioral scientists, it is readily amenable to investigation. All one need do is employ the "sets comparison method" (SCM). Described all too briefly, the method calls for the creation of at least two sets of units (individuals, populations, etc.) that differ as to the range of the values of some variable, X or Y in the bivariate case, meaning no overlap in the values of any two sets in the series. The SCM is explicated subsequently in greater detail, and its use is illustrated by Tables 2, 4, 6, 8, and 10, wherein six sets of the contiguous U. S. have been created such as to maximize interset contrasts in the intraset magnitudes of some variable's values. The tables should not be examined at length, for a much more detailed explication is offered later.
A major limitation of the SCM should be recognized at the outset. Whatever the variables, in a particular application of the SCM (here, Tables 2-11) the maximum value of the manipulated variable (e.g., the homicide rates in the case of Table 10) could be less than the level at which the contingency becomes detectable. However, in such a case the possible contingency remains only a possibility and, hence, can be ignored in attempting to explain variation in the intraset association among the sets.
Whatever the limitations of the SCM and problems in its use, one advantage is especially strategic for the social/behavioral sciences. Many commentators have suggested that the paucity of opportunities for genuine experiments in those sciences is an enormous handicap. If so, the SCM is all the more important, for it offers what may be the closest approximation for the literal control of variables, something those conventional statistical techniques (e.g., partial correlation, regression coefficients) only nominally offer.
Amount of Variance as the Second Contingency
Any measure of association presumes variation in values. Accordingly, it appears to follow that the association coefficients (e.g., the product-moment coefficient of correlation, r) in any instance is contingent on the amount of variance in the values of at least one of the variables. The stress on "appears" signifies more than recognition of the need for the ceteris paribus qualification. The kind of contingency in question has received far less attention than it deserves, at least in the sociological literature; consequently, the exact basis for presuming it is somewhat obscure. Evidently, an increase in variance may be such as to overcome, so to speak, measurement error and/or the influence of variables (known or unknown) excluded from the association measure (i.e., exogenous variables). Even so, the reduction of the influence of measurement error would appear to be manifested more (if not entirely) when the association measure is ordinal (rho or tau). Be that as it may, the sets comparison method (SMC) has been employed in constructing Tables 3, 5, 7, 9, and 11 so as to maximize interset contrast as regards the amount of intraset variance in the values of each Table 1 variable, commencing (Table 3) with the estimated certainty of a prison sentence for criminal homicide.
{{ READER: I have a dim memory of H. Blalock treating amount of variance, either in a book or in a journal article, but that was many years ago.}}
Only a glance at the tables will suffice, for they are fully explicated subsequently. For the moment it will suffice to say that (as in the case the magnitude contingency) evidence of an associational contingency need not extend to a demonstration of causation, even presuming, unrealistically, some accepted demonstration method. Rather, there is only one question: how much and in what direction does the association (bivariate or multivariate) vary from one set to another?
OTHER POSSIBLE CONTINGENCIES
This report is focused on magnitude and variance as possible contingencies in the association between the homicide rate and the four other variables in Table 1. That would be a major limitation even if the research had been extended to other populations (e.g., U.S. cities, other countries) and variables in addition to those in Table 1. Specifically, the research could be extended enormously without going beyond the Table 1 data. The immediate reason is that the present research employed only the product-moment coefficient of correlation (r) as the measure of association. The underlying assumptions in the use of r--linearity and normally distributed values--point to two associational contingencies that receive less attention than magnitude and variance. Both the association form and the distribution of values are contingencies if an inappropriate association measure has been employed. Compelling evidence of the appropriateness of r would call for the extension of the present research to the use of eta and some ordinal association measure.
Turning to measurement error as a possible contingency, some inferences are made subsequently, but they are limited to the possible relevance of the amount of intraset variance. Going beyond that would not have been feasible even if there were some accepted procedure for estimating measurement error and its impact on an association.
Finally, the relevance of exogenous causes as a contingency is considered only in connection with the four possible correlates of the homicide rate, those in Cols. 2-5 of Table 1. A far greater number is suggested in the literature on homicide (though my knowledge ceased about 2000), and there are serious questions about the possible correlates in Table 1. Even the "percent black" is not a complete measure of racial differentiation; and there are all manner of indicators of "poverty prevalence" in addition to Col. 5 of Table 1, even though I believe that the outcome would be more or less the same for any alternative.
{{READER: Why did I not attempt to remedy all of the foregoing? My resources (including longevity) are limited, and the patience of readers is surely relevant. Nonetheless, I hope that someone will expand the research if only to overcome the limitations and defects of my work.}}
THE FOREMOST PRELIMINARY CONSIDERATION
The research described here was undertaken in the belief that conventional measures of statistical association do not reveal the contingencies under consideration fully, if at all. As an illustrative case, consider Table 1 and Col. 21 of Table 6 in which sets of states have been created such as to maximize interset contrasts in the intraset percent of black residents (i.e., magnitude manipulation). As for Table 1, the maximum interstate correlation (plus or minus r) of the homicide rate (H) is with the percent black residents (B), which is .838. As such things go in the social/behavioral sciences (including criminology), that coefficient is truly substantial; but there is no way whatever that it implies anything like the six rBH coefficients shown in Col. 21 of Table 6 (one coefficient for each of the six sets of states). None exceeds .588, one is -.436, and the average rBH for the six sets is only .221, all evidence that the B/H correlation is extremely contingent and puzzling. It is puzzling if only because r[(B/M)(rBH)] = .216 in the bottom panel of Table 6 indicates that there is virtually no interset association between intraset magnitude of B and the intraset B/H correlation, meaning no sign of a "range effect." To make the point again (indeed, again and again), conventional statistical technique do not resolve the puzzle, not even analysis of variance or co-variance because they differ in several respects from the use of the sets comparison method. (SCM). Possible explanations of the puzzle and several others are introduced subsequently, but it should be made clear that the foremost goal is the demonstration of contingencies discovered through SCM, not their explanation. Without such demonstrations, the merits of the SCM becomes moot.