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A crime index with Thurstone's scaling of crime severity
Journal of Criminal Justice 28 (2000) 237–244
A crime index with Thurstone’s scaling of crime severity Ying Keung Kwan*, Wai Cheung Ip, Patrick Kwan Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom Kowloon 306203, People’s Republic of China
Abstract In constructing a weighted crime index for Hong Kong, the Thurstone’s method of paired comparisons was used to assess the perceived relative seriousness of fifteen crime typologies. A telephone survey was conducted to collect data on respondents’ judgment on the seriousness of the fifteen crimes. The weights of the fifteen crimes constructed were then used to build up a time series of weighted crime index (WCI). The WCI performs differently from the unweighted crime index (UNCI) during the period 1976 to 1982. The validity of the weights has been tested and the WCI is considered as a better indicator of crime intensity. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Crime index; Perceived seriousness; Crime vignettes; Crime typologies; Paired comparisons; Scale value; Correlation
Introduction Unweighted crime rates as measured by the annual number of crime cases per hundred thousand persons have been used widely but are unsatisfactory in reflecting the intensity of crimes in a society as no consideration is given to the severity of crimes (Anderson & Newman, 1998; Wilkins, 1980). For example, a homicide and a theft are given equal weights in the calculations. To develop a better indicator of the prevalence of crime in a society, the relative seriousness of crimes needs to be assessed. There have been some misconceptions about crime seriousness. According to Rossi et al. (1974), crime seriousness is taken as a primitive concept for which investigators and respondents share a common meaning and hence, no formal definition is required. In such a situation, however, the concept will acquire a variety of meanings and confused research will be generated (Parton et al., 1991). There have been suggestions that the seriousness of crimes may be taken as an objective attribute and, therefore, may be derived by reference to the maximum permissible penalty for the offenses concerned. Black (1979) argued that crime seriousness is not an objective attribute but is subjec-
tively perceived among the citizens. Instead of explaining the crime severity by its legal penalty, efforts should be made to study the differences between legal penalties and the subjectively perceived seriousness of crimes. Hembroff (1987) showed that crime seriousness is an evaluation mediated by the social structural context in which it is embedded. Respondents’ perception of crime seriousness is a complex phenomenon resting on some attributes of crimes like victim harm and offender’s intentionality on the one hand, and on respondents’ socioeconomic attributes on the other (Newman, 1976). In studying crime severity it is important to provide a set of weights for building up a crime index to measure the intensity of crimes of a society. The subjectively perceived crime seriousness is meaningful when it is compared with its legal penalty. Any large discrepancies found in the comparisons would raise people’s attention about the appropriateness of the legal penalty of the crimes. The first serious attempts at evaluating crime severity were conducted by Sellin and Wolfgang in 1966 and in the 1980s, measures of crime severity were developed, for example, in the National Survey
* Corresponding author. Tel.: 852-2766-6962; fax: 852-2362-9045. E-mail address: [email protected] (Y.K. Kwan). 0047-2352/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S0 047-2352(00)00 0 3 9 - 8
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of Crime Severity (Wolfgang et al., 1985) and in the British Crime Survey (Pease, 1988). No attempt has been made, however, to construct an overall crime index for the crime intensity of a society. In these surveys on crime severity, there were two approaches for depicting crimes, namely, crime vignettes and crime typologies. When crime vignettes were used, the way crimes were described would certainly affect respondents’ evaluations. In this respect, dimensions of the framework for describing crimes were studied. Intentionality, victim harm (Forgas, 1980), offender’s status, and culpability (Hansel, 1987; Sebba, 1980) were found to be important dimensions. Different approaches were followed in constructing crime vignettes. Descriptions varied according to the number of dimensions adopted and the details input for each dimension (Scott & Al-Thakeb, 1980; Shaver, 1984; Wolfgang et al., 1985). There were clear distinctions in seriousness for crimes with different descriptions of the specific elements. For example, in Sellin and Wolfgang different levels of seriousness were assigned to bodily harm described as “receiving minor injuries, . . . treated and discharged, . . . hospitalized, . . . [and] killed” (1970, p. 243). Using the second approach, Hansel (1987) selected nine crime typologies: gambling, robbery, rape, disorderly conduct, homosexual acts between consenting adults, obscene phone calls, prostitution, theft, and assault. Respondents were asked to locate the typologies along ten dimensions such as harm done to the victim, immorality of the act, violence involved in the crime, property related, sex related, seriousness, and the degree being personal. It was found that there was significant disagreement in people’s conceptions of crime typologies in terms of the level of violence, amount of property harm, level of sex relatedness, and so on. For example, some respondents treated rape as a sexual crime, while others treated it as a violent crime. Crime typologies were structured differently for persons differing in social experience. Concerning the seriousness of the crime typologies, however, strong agreement was found. In addition, Parton et al. (1991) found that the variance of the seriousness score of crime typology was small and concluded that there was a normative consensus. As a crime typology is a composite term involving different levels of some specific elements, its seriousness score may be constructed from the scores of the specific elements of crime vignettes. Using the scores of specific elements of crimes constructed from the first approach, Sellin and Wolfgang (1970) calculated the average seriousness score of the crime typologies adopted in the Uniform Crime Reports. The score of a crime typology may be taken as the aver-
age score of the respondents’ judged values depending on their understanding of the crimes.
Research strategy Tai and Yiu (1994), the official statisticians, urged the need for constructing a weighted crime index in Hong Kong. This article records an attempt to measure the perceived crime severity and to construct a weighted crime index. In the study, crime typologies were used. There were three reasons for the choice. First, to construct a crime index, official statistics on crimes must be an important source of data and crime typologies are used in official statistics of Hong Kong. Second, people may have different understandings of crime typologies, as mentioned in the previous paragraph, although it has been found that there is a normative consensus about the seriousness of crime typologies. Third, Hong Kong is densely populated with efficient mass media communication. It has been well known for having consensus in opinions and actions about some issues in social, economic, financial, and political spheres. The normative consensus on crime seriousness should also be found in Hong Kong. A survey was to be conducted in Hong Kong to measure the relative seriousness of fifteen crime typologies. The results would provide a set of weights for the crimes and a time series of weighted crime index (WCI) would be constructed by applying the weights to the official statistics. The inadequacies of the unweighted crime index (UNCI), which is very often the only indicator of crime intensity of a society, would then be seen when compared with the WCI. Wolfgang et al. (1985) used the method of magnitude estimation to measure perceived seriousness of crimes. From a set of crimes, one was selected as a standard. The respondent was first asked to assign the standard a value. He/she was then instructed to assign each of the remaining crimes a value relative to the standard. According to Parton et al. (1991), the method requires that respondents have a common understanding of the task they have been asked to perform. They pointed out that if instructions are excessively complex then respondents may perceive some aspects of the task differently and provide divergent ratings to crimes with identical evaluation. There was evidence showing that Wolfgang’s approach failed to achieve the above requirement when the method of magnitude estimation was applied. Parton et al. (1991) recommended that considerable efforts be made in training respondents to meet the assumptions of magnitude estimation. In situations where it is im-
Y.K. Kwan et al. / Journal of Criminal Justice 28 (2000) 237–244
possible to offer training to respondents, a simple method is preferred. Thurstone’s law of comparative judgment for paired comparison (Thurstone & Chave, 1929) provided an alternative approach to estimating the perceived seriousness of crime typologies. A thorough elaboration of Thurstone’s scaling method can be found in Torgenson (1958). The method has been particularly useful in measuring people’s subjective evaluations (i.e., the perceived seriousness of health symptoms) (Bowling, 1992; Hunt et al., 1986; Ip et al., 1995). The task is to position the compared stimuli on a psychological continuum. The formulation assumes that if the same pair of stimuli are presented to the same respondent several times, or to a group of subjects, each only once, then there will be a normally distributed number of discriminal processes on the psychological continuum. When confronted with two stimuli R1 and R2, then Thurstone’s law is given by the observation equation s 1 – s 2 = x 12 σ 12 + σ 22 – 2ρσ 1 σ 2 where s1 and s2 are the psychological scale values of the two compared stimuli; 1 and 2 are the standard deviations of the scale values of R1 and R2 on the same judgment, is their correlation; x12 is the unit normal deviate corresponding to the population of judgments P(R1 ⬎ R2). Thurstone considered the law of comparative judgment under five cases, which involved different assumptions, approximations, and degrees of simplification for practical use. When more restrictions are taken, the observation equation will be simpler. Horst (1941) and Mosteller (1951) showed that the usual procedure for obtaining estimates of scale values is a least squares solution. To evaluate the relative seriousness of a set of crimes, respondents are presented with a pair of crimes and asked to judge which one is more serious. From the proportion of times a crime is judged to be more serious than others, scores of seriousness can be constructed for the set of crimes. Data collection A survey was conducted to determine the relative seriousness of crimes. In Hong Kong, telephone interview is by far the most popular survey method adopted in nonofficial surveys (Bacon-Shone, 1994). More than 97 percent of households have a telephone. It provides a good medium for easy and direct access to respondents. Telephone interview was adopted in the present survey. The method of magni-
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tude estimation is not appropriate for telephone interviews as it requires complex instructions to the respondents, so as to avoid different understandings of the tasks to be performed. Thurstone’s method was adopted because it is simple. In the survey, each time a respondent was presented with two crimes, he/she was requested to judge their relative seriousness. If there were queries about the details of the crimes, the interviewer was instructed not to give any further information and to request the respondent to judge according to his/her own understanding of the crimes. This would ensure that respondents would rank the crimes according to their perceived seriousness of the crimes, which was the intention of this research. It was expected that there would be variations in the respondents’ understanding of the crimes, which in turn would affect individuals’ evaluations. As discussed previously, the seriousness scores constructed by Thurstone’s method would still be valid as measures of the average seriousness scores of the crimes. In the survey fifteen crime typologies were selected according to the criteria: frequencies of occurrence and legal penalties (Table 1). The crime typologies were: rape; indecent assault; murder; serious assault; robbery; blackmail and intimidation; snatching; burglary; theft; deception, fraud, and forgery; drug offense; criminal damages; possession of arms; unlawful society offense; and bribery and corruption. Unlawful society offense, according to the laws of Hong Kong, refers to the event of inciting a person to become a member of an unlawful society, or procuring subscription or aid for an unlawful society. Criminal damage refers to those crimes damaging another person’s property. Indecent assault is an indecent act on a woman or on a man without her/his consent. The Table 1 Crimes Number
Crime
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Rape Indecent assault Murder Serious assault Robbery Blackmail and intimidation Snatching Burglary Theft Deception, fraud, and forgery Drug offense Criminal damages Possession of arms Unlawful society offense Bribery and corruption
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interviewer did not explain the meaning of the crimes to the respondents. Respondents found no difficulty in understanding the crime typologies. A simple random sample was selected from the residential telephone directories. Each respondent was asked to compare a target crime with the other fourteen crimes and to judge which was more serious. Each respondent was asked to complete two sets of fourteen paired comparisons. Ten interviewers were recruited from the graduates in statistics to conduct the interviews. During the period of the fieldwork in July 1997, 864 respondents were interviewed and 636 respondents completed paired comparisons of two target crimes. Fifteen hundred sets of paired comparisons were obtained, making a total of 21,000 paired comparisons. For each type of paired comparison there were 200 trials. Results Thurstone’s method considers the proportion of times crime i is judged more serious than crime j. The results of the present study are given in the proportion matrix P shown in Table 2. The diagonal entries where a crime was compared to itself were set equal to .5. Rearranging the columns of matrix P in increasing order of total proportions, basic transformation matrix X shown in Table 3 was constructed. In matrix X, the crimes are arranged in columns of increasing order of perceived seriousness. The proportions of crimes 7, 12, and 13 were very close together, therefore, their order of seriousness may have changed in subsequent steps. The cell values of ma-
trix X are the unit normal deviates corresponding to the proportions given in matrix P. The next step of Thurstone’s method is to estimate the difference in scale values between two successive crimes. These differences are given in matrix D shown in Table 4. Note that a negative column sum means that the order of seriousness of the two relevant crimes should be reversed. The final order of crimes 7, 12, and 13 was (7, 12, 13), while the order was (12, 13, 7) according to total proportions. The column means are estimated differences in scale values between two successive crimes. For example, if the scale value of crime 9 is s9 then the scale value of crime 7 will be s7 ⫽ s9 ⫹ .179 and so on. The method estimates the differences of the scale values between any two successive crimes and not the actual scale values. The zero point of the scale should be located at “nil crime.” As obtained from the last row of matrix D, the mean of the differences of scale values of the crimes was .201. This would be a best estimate for the successive difference between two adjacent crimes. It was therefore used to estimate the difference between nil crime and the next more serious crime. In such a manner, a series of scale values can be obtained as: 0 for nil crime, 0 ⫹ .201 ⫽ .201 for crime 9, .201 ⫹ .179 ⫽ .380 for crime 7, and so on. These raw scale values and standardized scale values are given in Table 5, in which the standardized scale values were rescaled to sum to 100 for convenience and are referred to as the weights or scores associated with the perceived seriousness of the crimes. Murder, rape, drug offense, and robbery were perceived as the four most serious crimes by Hong Kong
Table 2 Matrix P: proportion of times crime i was judged more serious then crime j Crime i Crime j 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total
2
3
4
.500 .043 .821 .090 .957 .500 .968 .654 .179 .032 .500 .000 .910 .346 1.000 .500 .757 .171 .986 .286 .769 .256 .936 .526 1.000 .653 1.000 .917 .986 .606 .986 .845 .985 .721 1.000 .926 .887 .352 .958 .648 .568 .122 .797 .108 .955 .612 1.000 .881 .859 .500 .984 .797 .677 .387 .935 .532 .750 .139 .917 .264 11.739 5.44 13.788 7.974
5
6
7
8
9
10
11
12
13
14
15
.243 .231 .000 .014 .015 .113 .432 .045 .141 .323 .250 .829 .744 .347 .394 .279 .648 .878 .388 .500 .613 .861 .014 .064 .000 .014 .000 .042 .203 .000 .016 .065 .083 .714 .474 .083 .155 .074 .352 .892 .119 .203 .468 .736 .500 .231 .014 .028 .000 .113 .703 .045 .078 .355 .250 .769 .500 .056 .085 .074 .225 .689 .164 .156 .468 .347 .986 .944 .500 .563 .294 .676 .946 .478 .359 .742 .694 .972 .915 .437 .500 .088 .521 .892 .343 .312 .629 .681 1.000 .926 .706 .912 .500 .690 .878 .478 .391 .661 .792 .887 .775 .324 .479 .310 .500 .892 .239 .375 .565 .583 .297 .311 .054 .108 .122 .108 .500 .060 .031 .161 .111 .955 .836 .522 .657 .522 .761 .940 .500 .422 .565 .722 .922 .844 .641 .688 .609 .625 .969 .578 .500 .645 .639 .645 .532 .258 .371 .339 .435 .839 .435 .355 .500 .319 .750 .653 .306 .319 .208 .417 .889 .278 .361 .681 .500 1.483 8.980 4.248 5.287 3.434 6.226 11.542 4.150 4.200 7.441 7.568
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Table 3 Matrix X: normal deviates corresponding to proportions in matrix P with columns arranging in increasing order of total proportions Crime i Crime j 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
⫺2.178 ⫺.585 – ⫺1.450 – ⫺1.450 ⫺.541 ⫺1.352 .000 ⫺.496 ⫺1.167 .056 .278 ⫺.416 ⫺.812
12
13
7
8
2
10
⫺1.698 ⫺.284 – ⫺1.178 ⫺1.698 ⫺.977 ⫺.056 ⫺.404 ⫺.056 ⫺.710 ⫺1.557 .000 .197 ⫺.162 ⫺.589
⫺1.077 .000 ⫺2.154 ⫺.830 ⫺1.418 ⫺1.010 ⫺.360 ⫺.489 ⫺.278 ⫺.319 ⫺1.863 ⫺.197 .000 ⫺.372 .355
–
⫺2.195 ⫺.268 ⫺2.195 ⫺1.016 ⫺1.908 ⫺1.375 .160 .000 1.352 ⫺.053 ⫺1.237 .404 .489 ⫺.329 ⫺.469
⫺1.717 .000 ⫺1.858 ⫺.396 ⫺.949 ⫺.654 .393 .268 .585 ⫺.380 ⫺1.167 .284 .000 ⫺.287 ⫺1.085
⫺1.212 ⫺.460 ⫺.674 ⫺1.342 ⫺.736 ⫺.697 .380 .287 1.085 .396 .654 .949 ⫺1.725 ⫺1.518 ⫺1.383 – ⫺1.521 ⫺2.189 ⫺.380 ⫺.081 .631 .000 ⫺.064 .566 ⫺1.212 ⫺.372 ⫺.674 ⫺.566 ⫺.736 .000 ⫺.754 ⫺.081 ⫺.393 .064 .000 .736 .457 .649 .508 1.383 1.593 2.200 .053 .329 .469 1.016 1.375 1.908 .496 .416 .812 1.450 1.450 – .000 .162 .210 .380 .754 1.212 ⫺1.237 ⫺.989 ⫺1.221 ⫺1.237 ⫺.494 ⫺.532 .710 .162 .589 1.178 .977 1.698 .319 .372 .355 .831 1.010 1.418 ⫺.162 .000 ⫺.469 .081 .081 .372 ⫺.210 .469 .000 ⫺.631 .393 .674
⫺.393 – ⫺1.383 ⫺2.200 ⫺1.593 .000 ⫺.160 .541 ⫺.457 ⫺1.607 .056 .360 ⫺.649 ⫺.508
14
15
4
6
5
11
1
3
⫺.170 .000 .919 1.167 1.717 1.858 ⫺.832 ⫺.919 .000 1.237 1.342 – 0.532 .697 2.189 .494 .736 1.521 1.607 – – 1.237 2.195 2.195 1.167 2.178 – 1.237 1.212 1.725 .000 .170 .832 1.557 1.698 – 1.863 1.078 2.154 .989 .460 1.518 1.221 .674 1.383
the seriousness of crimes, there appears to be discrepancies between these evaluations and the legal penalties imposed in Hong Kong. The penalty of life imprisonment is forty-five years on average—the expected life duration of seventy-five years reduced by thirty years, the average age of the convicted (Sellin & Wolfgang, 1970). As reflected by the ratios of the weights of murder with other crimes, the legal penalty of lifelong imprisonment for murder in Hong Kong is not too heavy when compared with the penalties of other crimes. The extent to which people’s evaluations of the seriousness of crimes should be
citizens. The scores were 16.68, 12.53, 11.92, and 10.41, respectively. The four least serious crimes were theft (1.11), snatching (2.1), criminal damage (2.32), and possession of arms (2.55). The score of murder was about fifteen times of the score of theft, implying that fifteen cases of theft are equivalent to one case of murder in terms of Hong Kong citizens’ subjective evaluations. Eleven cases of theft are equivalent to one case of rape, ten cases of theft equivalent to one case of drug offense, and nine cases of theft to one case of robbery. If the weights truly reflect people’s evaluations of
Table 4 Matrix D: differences of normal deviates between crime j and its next less serious crime i Crime i,j Crime j 7,9
12,7
13,12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sum n Mean
–
.621 ⫺1.118 .284 ⫺.268 – ⫺.041 .348 ⫺.186 .280 ⫺.490 ⫺.033 ⫺.365 ⫺.304 .520 ⫺.085 .489 ⫺.222 1.630 .391 .266 ⫺.306 .626 ⫺.197 .601 ⫺.197 .489 ⫺.210 .043 .234 ⫺.114 .604 2.082 14 15 .043 .139
– .192 –
.109 –
.067 – ⫺.143 .541 1.192 .541 .039 ⫺.440 .000 .082 ⫺.233 .304 2.142 12 .179
.205 .502 .616 ⫺.056 ⫺.244 ⫺.597 ⫺.253 .050 ⫺.056 ⫺.163 .487 ⫺.081 .519 13 .040
8,13
2,8 .478 .268 .337 .620 .959 .721 .233 .268 ⫺.767 ⫺.327 .070 ⫺.120 ⫺.489 .042 ⫺.616 1.677 15 .112
10,2 .505 .380 .133 .016 ⫺.263 ⫺.100 .064 ⫺.215 ⫺.089 .380 ⫺.070 .426 .319 .125 .875 2.486 15 .166
14,10 .752 ⫺.093 .207 .299 .840 .673 .192 .276 ⫺.080 .162 .248 ⫺.548 .053 .162 .679 3.822 15 .255
15,14
4,15
6,4
5,6
11,5
1,11
3,1
⫺.214 ⫺.668 .606 .039 .527 .170 .919 .798 ⫺.689 .258 .295 .218 .550 .141 .135 – – ⫺.668 1.357 ⫺.087 .919 .712 ⫺.631 ⫺.064 .630 .671 .105 – ⫺.302 .108 ⫺.170 .736 .532 .165 1.492 ⫺.312 .457 ⫺.064 .736 ⫺.242 .242 .785 ⫺.141 .875 .210 .607 ⫺.593 – – .140 .547 .359 .533 ⫺.671 .958 .000 .396 .638 .000 – – 1.011 – .048 .170 .374 .458 .025 ⫺.025 .513 ⫺.232 ⫺.016 .743 ⫺.038 .532 .170 .662 .427 .589 ⫺.201 .721 ⫺.141 .141 – ⫺.017 .476 .179 .408 .445 ⫺.785 1.076 ⫺.469 .550 .000 .291 .617 ⫺.529 1.058 ⫺.469 ⫺.631 1.024 .281 .547 ⫺.547 .709 .500 1.775 3.254 5.029 3.824 1.539 8.274 15 14 14 14 14 14 11 .033 .127 .232 .359 .273 .110 .752
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Table 5 Construction of crime score Crime 9
7
12
13
8
2
10
14
15
4
6
5
11
1
3
Difference .000 .179 .040 .043 .139 .112 .166 .255 .033 .127 .232 .359 .273 .110 .752 Raw score .201 .380 .420 .463 .602 .714 .880 1.135 1.168 1.295 1.527 1.886 2.159 2.269 3.021 Score 1.11 2.10 2.32 2.55 3.32 3.94 4.85 6.26 6.44 7.14 8.43 10.41 11.92 12.53 16.68
taken into account in determining legal penalties is a controversial issue, but it is worthwhile to carry out some comparisons between the two. It was surprising to find that drug offense is perceived as a very serious crime in Hong Kong. It is even more serious than robbery. This may be related to some cultural and historical reasons. Hong Kong became a British colony in 1841 as a result of a war, called by the Chinese, the Opium War. The harm done to human beings with drugs like opium have been emphasized in society. On the other hand, the law in Hong Kong is based on British law with very different historical roots. The relative seriousness of drug offense, as reflected by the legal penalties, would be much less than that represented by the weights built up by perceived severity. The fifteen selected crimes represented more than 80 percent of the total number of cases of crimes during 1976–96. Using 1976 as the base year, a series of UNCI were constructed by simply relating the sum of the annual number of cases of the fifteen crimes in the current year to that of the base year. A series of WCI were constructed by applying the weights to the calculations. In Table 6, the WCI and UNCI present quite different pictures. Taking the figures of 1976 as a basis for comparison, the WCI fell by 30.3 percent from 100 to 69.7. The UNCI, on the other hand, fell by only 6.9 percent from 100 to 93.1. Looking at the UNCI, Hong Kong has not reduced crime much in the twenty years from 1976 to 1996, while the WCI indicates that Hong Kong has reduced crime significantly during this period. Taking a closer look at the series, the performance difference was formed mainly during the period 1976–82. The WCI fell from 100 to 89.8 during 1976 to 1982, while the UNCI rose from 100 to 118.2. During the later period (1982–96) both the WCI and UNCI recorded drops of similar magnitude (22.4 percent and 21.4 percent, respectively). The contrasting performance in the earlier period needs explanation. The UNCI may be broken down into three components, the serious crime index, the moderate-serious crime index, and the nonserious crime index, according to the values of their serious-
ness scores. Murder, rape, drug offense, and robbery were the serious crimes with weights above 10; possession of arms, criminal damages, snatching, and theft were the nonserious crimes with weights below 3; and the remaining crimes were classified as moderate-serious. From Table 7, it can be seen clearly that the serious crime index and the nonserious crime index move in opposite directions. The former dropped from 100 in 1976 to 78 in 1982, a fall of 22 percent; while the latter increased from 100 to 223, a rise of 123 percent, during the same period. This explains the contrasting performance of crime reduction presented by the WCI and the UNCI. During the period 1976–82, the incidence rate of robbery dropped from 200 to 162 and drug offense from 72 to 49; while theft rose from 274 to 604, snatching from 12 to 41, and criminal damages from 31 to 66. If citizens’ perceived seriousness of crimes
Table 6 Weighted crime index (WCI), unweighted crime index (UNCI), and GDP, 1976–1996 Year
WCI
UNCI
GDP
1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
100 80 74 77 85 84 90 88 86 87 81 82 85 87 89 85 77 68 82 84 70
100 90 73 93 106 109 118 118 114 117 109 109 104 105 112 114 107 104 108 111 93
100 116 136 178 226 272 307 339 409 433 498 613 725 835 928 1065 1242 1430 1610 1728 1905
Y.K. Kwan et al. / Journal of Criminal Justice 28 (2000) 237–244 Table 7 Serious and nonserious crime rates, 1976–1996a Year
Serious crime
Nonserious crime
1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
100 69 61 69 80 74 78 78 69 72 66 68 79 78 77 78 65 41 67 67 50
100 116 140 160 194 205 223 224 204 211 197 198 192 189 202 198 192 177 189 195 164
a
1976 rate as a standard.
were included in the calculation, the intensity of crimes in Hong Kong should have been reduced during this period. Discussion The validity of the WCI depends on the validity of the set of weights of the fifteen crimes. Owing to the subjective and experience-based nature of the responses, an acceptable absolute standard for the weights was lacking and its criterion validity could not be tested. The extent to which the relative seriousness of the crimes was represented by the weights is difficult to assess. Two types of tests can be performed. One type is the internal check provided by Thurstone’s method. Another type is an external check on the conformity of the performance of the crime index to some patterns that have been established in the literature. Thurstone’s method has an advantage: The paired comparisons themselves provide an internal check on validity. As each respondent has to complete two sets of comparisons, two kinds of contradictions can be tested. Direct contradiction happens when a respondent judges crime A as more serious than crime B, and then the other way round later. In the survey, sixty-three cases of direct contradictions were found. Another contradiction is known as a circular triad. It occurs when crime A is judged by a respondent as more serious than crime B,
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crime B more serious than crime C, but then crime C is more serious than crime A. In the survey 201 cases of circular triads were found. As there were a total of 17,804 paired comparisons that were subjected to these tests, the proportion of contradictions was small. A large number of contradictions would mean that Thurstone’s method was not appropriate. On the other hand, a small proportion of contradictory comparisons supports the appropriateness of the method and the validity of the results. Pyle and Deadman (1994) constructed an econometric model relating property crimes to economic activities. Using postwar Britain as an example, the relationship between the business cycle and property crime was found. Deadman and Pyle (1997) confirmed further the reverse relationship between GDP growth and the property crime rate. One may doubt whether trends in economic indicators always correlate strongly with crime rates, although they did find support in the WCI in Hong Kong. Hong Kong experienced rapid economic growth during the period from 1976 to 1996 with the exceptions of 1982, 1985, 1989, and 1990. In the years of economic recession, both the WCI and the UNCI experienced either a rise or a fall, less than the average deceleration of the downward trend in crime rates, conforming to Pyle and Deadman’s pattern. During the entire period 1976–96, Hong Kong recorded a rise of eighteen times in GDP (Table 6). The WCI is a better indicator than the UNCI as it recorded a drop of 30.3 percent, while UNCI recorded a drop of only 6.9 percent. During the period 1976–82, the GDP rose from 100 to 307. The WCI conformed to the pattern, recording a fall of 10.2 percent in crime, while the UNCI deviated from the pattern with a rise of 18.2 percent in crime. Conformity of the WCI to economic performance can be measured by the correlation coefficient between GDP and crime rates. The correlation coefficient between GDP and WCI was ⫺.449. The coefficient of determination was .202, implying that 20.2 percent of the variations in crime can be explained by the changes in GDP. On the other hand, when UNCI was tested for correlation with the GDP, no significant relationship was found. The WCI, not the UNCI, gave a more valid indication of crime intensity in Hong Kong. The validity of the seriousness scores were further tested by comparisons with other measures of crime severity, namely, legal penalties and the seriousness scores constructed in other studies. The maximum penalties of the fifteen crimes were correlated with the seriousness scores, resulting in a correlation coefficient of .80. The Sellin and Wolfgang crime seri-
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ousness scores in the Uniform Crime Report (1970) were constructed from the components’ scores obtained by magnitude estimation on crime vignettes. When they were collated with the corresponding seriousness scores of the present study, constructed by Thurstone’s scaling method on crime typologies, an exponential relationship was found. Using the log values of Sellin and Wolfgang’s scores, a very high correlation coefficient of .93 was obtained. Finally, using the split-half method, the survey results were divided randomly into two groups of equal size. Separate seriousness score estimates of the fifteen crimes were obtained for each group. A high correlation coefficient (r ⫽ .986) was found between the estimates of the two groups. These tests suggest that the scale is valid and reliable. The unweighted crime rate has been widely used as an indicator of the intensity of crime in a society, although the results here show that it may give very misleading results. In Hong Kong, the UNCI presented a misleading picture of a very small reduction in crime despite tremendous economic achievement in the last twenty years under British rule. If crimes are to be weighted in the construction of a crime index, the relative seriousness of crimes needs to be measured. Thurstone’s scaling method of paired comparisons provides a simple and reliable method, especially when telephone interviews are used. The present results indicate some discrepancies between the perceived seriousness of crimes and the legal penalties. Further studies in this area are needed. The WCI is a better indicator of crimes than the UNCI, which can be very misleading. In many cities, the UNCI is the only summary index of crimes. Caution is needed when using it as an indicator in measuring crimes. It is recommended that a survey, similar to the one used here, be carried out so that a WCI can be constructed. References Anderson, P. R., & Newman D. J. (1998). Introduction to Criminal Justice. Boston, MA: McGraw-Hill. Bacon-Shone, J. (1994). Household telephone surveys in Hong Kong. 1990 Proceeding of the Section on Survey Research Methods, Annual Meeting of the Alexandria VA: American Statistical Association (pp. 393–395). Alexandria, VA: American Statistical Association. Black, D. (1979). Common sense in the sociology of law. Am Soc Rev 44, 18–27. Bowling, A. (1992). Measuring Health: A Review of Quality of Life Measurement Scales. London: Open University Press.
Deadman, D. F., & Pyle, D. J. (1997). Forecasting recorded property crime using a time-series econometric model. Br J Crim 37, 437–445. Forgas, J. P. (1980). Images of crime: a multidimensional analysis of individual differences in crime perception. Int J Psych 15, 287–299. Hansel, M. (1987). Citizen crime stereotypes—normative consensus revisited. Crim 25, 455–485. Hembroff, L. A. (1987). Seriousness of acts and social contexts: a test of Black’s theory of behavior of law. Am J Soc 93, 322–347. Horst, A. P. (1941). Prediction of personal adjustment. Soc Sci Res Council Bul 48. Hunt, S. M., McEwen J., & Mckenna, S. P. (1986). Measuring Health Status. London: Croom Helm. Ip, W. C., Kwan Y. K., & Pong, T. Y. (1995). A health status indicator for the Chinese elderly in Hong Kong. Int J Bio-Med Computing 40, 133–137. Mosteller, F. (1951). Remarks on the method of paired comparisons I. the least squares solution assuming equal standard deviations and equal correlations. Psychometrika 16, 3–11. Newman, G., (1976). Comparative Deviance. New York: Elsevier. Parton, D. A., Hansel, M., & Stratton, J. R. (1991). Measuring crime seriousness: lessons from the National Survey of Crime Severity. Br J Crim 31, 72–85. Pease, K. (1988). Judgments of Crime Seriousness: Findings from the 1984 British Crime Survey. London: Home Office. Pyle, D. J., & Deadman, D. F. (1994). Crime and the business cycle in postwar Britain. Br J Crim 34, 339–357. Rossi, P. H., Waite, E., Boise, C. E., & Perk, R. (1974). Seriousness of crimes. Am Soc Rev 39, 224–237. Scott, J. E. & Al-Thakeb, F. (1980). Perceptions of deviance cross-culturally. In G. R. Newman (Ed.), Crime and Deviance: A Comparative Perspective (pp. 42–67). London: Sage Publications. Sebba, L. (1980). Is Mens Rea a component of perceived offense seriousness? J Crim Law & Crim 71, 124–135. Sellin T., & Wolfgang M. E. (1970). Measurement of Delinquency. New Delhi: Wiley Eastern Private Limited. Shaver, K. G. (1984). Attribution of Blame: Causality, Responsibility, and Blameworthiness. New York: SpringerVerlag. Tai, H. S., & Yiu, F. K. H. (1994). Measurement of crime. Bul Hong Kong Stat Soc 17(1), 6–9. Thurstone, L. L., & Chave, E. J. (1929). Measurement of Attitudes. Chicago, IL: University of Chicago Press. Torgenson, W. S. (1958). Theory and Methods of Scaling. New York: John Wiley & Sons. Wilkins, L. T. (1980). World crime: to measure or not to measure? In G. R. Newman (Ed.), Crime and Deviance: A Comparative Perspective (pp. 17–41). London: Sage Publications. Wolfgang, M., Figlio, R. M., Tracy, P. E., & Singer, S. J. (1985). National Survey of Crime Severity (NCJ-96017). Washington, DC: U.S. Government Printing Office.
A crime index with Thurstone’s scaling of crime severity Ying Keung Kwan*, Wai Cheung Ip, Patrick Kwan Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom Kowloon 306203, People’s Republic of China
Abstract In constructing a weighted crime index for Hong Kong, the Thurstone’s method of paired comparisons was used to assess the perceived relative seriousness of fifteen crime typologies. A telephone survey was conducted to collect data on respondents’ judgment on the seriousness of the fifteen crimes. The weights of the fifteen crimes constructed were then used to build up a time series of weighted crime index (WCI). The WCI performs differently from the unweighted crime index (UNCI) during the period 1976 to 1982. The validity of the weights has been tested and the WCI is considered as a better indicator of crime intensity. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Crime index; Perceived seriousness; Crime vignettes; Crime typologies; Paired comparisons; Scale value; Correlation
Introduction Unweighted crime rates as measured by the annual number of crime cases per hundred thousand persons have been used widely but are unsatisfactory in reflecting the intensity of crimes in a society as no consideration is given to the severity of crimes (Anderson & Newman, 1998; Wilkins, 1980). For example, a homicide and a theft are given equal weights in the calculations. To develop a better indicator of the prevalence of crime in a society, the relative seriousness of crimes needs to be assessed. There have been some misconceptions about crime seriousness. According to Rossi et al. (1974), crime seriousness is taken as a primitive concept for which investigators and respondents share a common meaning and hence, no formal definition is required. In such a situation, however, the concept will acquire a variety of meanings and confused research will be generated (Parton et al., 1991). There have been suggestions that the seriousness of crimes may be taken as an objective attribute and, therefore, may be derived by reference to the maximum permissible penalty for the offenses concerned. Black (1979) argued that crime seriousness is not an objective attribute but is subjec-
tively perceived among the citizens. Instead of explaining the crime severity by its legal penalty, efforts should be made to study the differences between legal penalties and the subjectively perceived seriousness of crimes. Hembroff (1987) showed that crime seriousness is an evaluation mediated by the social structural context in which it is embedded. Respondents’ perception of crime seriousness is a complex phenomenon resting on some attributes of crimes like victim harm and offender’s intentionality on the one hand, and on respondents’ socioeconomic attributes on the other (Newman, 1976). In studying crime severity it is important to provide a set of weights for building up a crime index to measure the intensity of crimes of a society. The subjectively perceived crime seriousness is meaningful when it is compared with its legal penalty. Any large discrepancies found in the comparisons would raise people’s attention about the appropriateness of the legal penalty of the crimes. The first serious attempts at evaluating crime severity were conducted by Sellin and Wolfgang in 1966 and in the 1980s, measures of crime severity were developed, for example, in the National Survey
* Corresponding author. Tel.: 852-2766-6962; fax: 852-2362-9045. E-mail address: [email protected] (Y.K. Kwan). 0047-2352/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S0 047-2352(00)00 0 3 9 - 8
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of Crime Severity (Wolfgang et al., 1985) and in the British Crime Survey (Pease, 1988). No attempt has been made, however, to construct an overall crime index for the crime intensity of a society. In these surveys on crime severity, there were two approaches for depicting crimes, namely, crime vignettes and crime typologies. When crime vignettes were used, the way crimes were described would certainly affect respondents’ evaluations. In this respect, dimensions of the framework for describing crimes were studied. Intentionality, victim harm (Forgas, 1980), offender’s status, and culpability (Hansel, 1987; Sebba, 1980) were found to be important dimensions. Different approaches were followed in constructing crime vignettes. Descriptions varied according to the number of dimensions adopted and the details input for each dimension (Scott & Al-Thakeb, 1980; Shaver, 1984; Wolfgang et al., 1985). There were clear distinctions in seriousness for crimes with different descriptions of the specific elements. For example, in Sellin and Wolfgang different levels of seriousness were assigned to bodily harm described as “receiving minor injuries, . . . treated and discharged, . . . hospitalized, . . . [and] killed” (1970, p. 243). Using the second approach, Hansel (1987) selected nine crime typologies: gambling, robbery, rape, disorderly conduct, homosexual acts between consenting adults, obscene phone calls, prostitution, theft, and assault. Respondents were asked to locate the typologies along ten dimensions such as harm done to the victim, immorality of the act, violence involved in the crime, property related, sex related, seriousness, and the degree being personal. It was found that there was significant disagreement in people’s conceptions of crime typologies in terms of the level of violence, amount of property harm, level of sex relatedness, and so on. For example, some respondents treated rape as a sexual crime, while others treated it as a violent crime. Crime typologies were structured differently for persons differing in social experience. Concerning the seriousness of the crime typologies, however, strong agreement was found. In addition, Parton et al. (1991) found that the variance of the seriousness score of crime typology was small and concluded that there was a normative consensus. As a crime typology is a composite term involving different levels of some specific elements, its seriousness score may be constructed from the scores of the specific elements of crime vignettes. Using the scores of specific elements of crimes constructed from the first approach, Sellin and Wolfgang (1970) calculated the average seriousness score of the crime typologies adopted in the Uniform Crime Reports. The score of a crime typology may be taken as the aver-
age score of the respondents’ judged values depending on their understanding of the crimes.
Research strategy Tai and Yiu (1994), the official statisticians, urged the need for constructing a weighted crime index in Hong Kong. This article records an attempt to measure the perceived crime severity and to construct a weighted crime index. In the study, crime typologies were used. There were three reasons for the choice. First, to construct a crime index, official statistics on crimes must be an important source of data and crime typologies are used in official statistics of Hong Kong. Second, people may have different understandings of crime typologies, as mentioned in the previous paragraph, although it has been found that there is a normative consensus about the seriousness of crime typologies. Third, Hong Kong is densely populated with efficient mass media communication. It has been well known for having consensus in opinions and actions about some issues in social, economic, financial, and political spheres. The normative consensus on crime seriousness should also be found in Hong Kong. A survey was to be conducted in Hong Kong to measure the relative seriousness of fifteen crime typologies. The results would provide a set of weights for the crimes and a time series of weighted crime index (WCI) would be constructed by applying the weights to the official statistics. The inadequacies of the unweighted crime index (UNCI), which is very often the only indicator of crime intensity of a society, would then be seen when compared with the WCI. Wolfgang et al. (1985) used the method of magnitude estimation to measure perceived seriousness of crimes. From a set of crimes, one was selected as a standard. The respondent was first asked to assign the standard a value. He/she was then instructed to assign each of the remaining crimes a value relative to the standard. According to Parton et al. (1991), the method requires that respondents have a common understanding of the task they have been asked to perform. They pointed out that if instructions are excessively complex then respondents may perceive some aspects of the task differently and provide divergent ratings to crimes with identical evaluation. There was evidence showing that Wolfgang’s approach failed to achieve the above requirement when the method of magnitude estimation was applied. Parton et al. (1991) recommended that considerable efforts be made in training respondents to meet the assumptions of magnitude estimation. In situations where it is im-
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possible to offer training to respondents, a simple method is preferred. Thurstone’s law of comparative judgment for paired comparison (Thurstone & Chave, 1929) provided an alternative approach to estimating the perceived seriousness of crime typologies. A thorough elaboration of Thurstone’s scaling method can be found in Torgenson (1958). The method has been particularly useful in measuring people’s subjective evaluations (i.e., the perceived seriousness of health symptoms) (Bowling, 1992; Hunt et al., 1986; Ip et al., 1995). The task is to position the compared stimuli on a psychological continuum. The formulation assumes that if the same pair of stimuli are presented to the same respondent several times, or to a group of subjects, each only once, then there will be a normally distributed number of discriminal processes on the psychological continuum. When confronted with two stimuli R1 and R2, then Thurstone’s law is given by the observation equation s 1 – s 2 = x 12 σ 12 + σ 22 – 2ρσ 1 σ 2 where s1 and s2 are the psychological scale values of the two compared stimuli; 1 and 2 are the standard deviations of the scale values of R1 and R2 on the same judgment, is their correlation; x12 is the unit normal deviate corresponding to the population of judgments P(R1 ⬎ R2). Thurstone considered the law of comparative judgment under five cases, which involved different assumptions, approximations, and degrees of simplification for practical use. When more restrictions are taken, the observation equation will be simpler. Horst (1941) and Mosteller (1951) showed that the usual procedure for obtaining estimates of scale values is a least squares solution. To evaluate the relative seriousness of a set of crimes, respondents are presented with a pair of crimes and asked to judge which one is more serious. From the proportion of times a crime is judged to be more serious than others, scores of seriousness can be constructed for the set of crimes. Data collection A survey was conducted to determine the relative seriousness of crimes. In Hong Kong, telephone interview is by far the most popular survey method adopted in nonofficial surveys (Bacon-Shone, 1994). More than 97 percent of households have a telephone. It provides a good medium for easy and direct access to respondents. Telephone interview was adopted in the present survey. The method of magni-
239
tude estimation is not appropriate for telephone interviews as it requires complex instructions to the respondents, so as to avoid different understandings of the tasks to be performed. Thurstone’s method was adopted because it is simple. In the survey, each time a respondent was presented with two crimes, he/she was requested to judge their relative seriousness. If there were queries about the details of the crimes, the interviewer was instructed not to give any further information and to request the respondent to judge according to his/her own understanding of the crimes. This would ensure that respondents would rank the crimes according to their perceived seriousness of the crimes, which was the intention of this research. It was expected that there would be variations in the respondents’ understanding of the crimes, which in turn would affect individuals’ evaluations. As discussed previously, the seriousness scores constructed by Thurstone’s method would still be valid as measures of the average seriousness scores of the crimes. In the survey fifteen crime typologies were selected according to the criteria: frequencies of occurrence and legal penalties (Table 1). The crime typologies were: rape; indecent assault; murder; serious assault; robbery; blackmail and intimidation; snatching; burglary; theft; deception, fraud, and forgery; drug offense; criminal damages; possession of arms; unlawful society offense; and bribery and corruption. Unlawful society offense, according to the laws of Hong Kong, refers to the event of inciting a person to become a member of an unlawful society, or procuring subscription or aid for an unlawful society. Criminal damage refers to those crimes damaging another person’s property. Indecent assault is an indecent act on a woman or on a man without her/his consent. The Table 1 Crimes Number
Crime
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Rape Indecent assault Murder Serious assault Robbery Blackmail and intimidation Snatching Burglary Theft Deception, fraud, and forgery Drug offense Criminal damages Possession of arms Unlawful society offense Bribery and corruption
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interviewer did not explain the meaning of the crimes to the respondents. Respondents found no difficulty in understanding the crime typologies. A simple random sample was selected from the residential telephone directories. Each respondent was asked to compare a target crime with the other fourteen crimes and to judge which was more serious. Each respondent was asked to complete two sets of fourteen paired comparisons. Ten interviewers were recruited from the graduates in statistics to conduct the interviews. During the period of the fieldwork in July 1997, 864 respondents were interviewed and 636 respondents completed paired comparisons of two target crimes. Fifteen hundred sets of paired comparisons were obtained, making a total of 21,000 paired comparisons. For each type of paired comparison there were 200 trials. Results Thurstone’s method considers the proportion of times crime i is judged more serious than crime j. The results of the present study are given in the proportion matrix P shown in Table 2. The diagonal entries where a crime was compared to itself were set equal to .5. Rearranging the columns of matrix P in increasing order of total proportions, basic transformation matrix X shown in Table 3 was constructed. In matrix X, the crimes are arranged in columns of increasing order of perceived seriousness. The proportions of crimes 7, 12, and 13 were very close together, therefore, their order of seriousness may have changed in subsequent steps. The cell values of ma-
trix X are the unit normal deviates corresponding to the proportions given in matrix P. The next step of Thurstone’s method is to estimate the difference in scale values between two successive crimes. These differences are given in matrix D shown in Table 4. Note that a negative column sum means that the order of seriousness of the two relevant crimes should be reversed. The final order of crimes 7, 12, and 13 was (7, 12, 13), while the order was (12, 13, 7) according to total proportions. The column means are estimated differences in scale values between two successive crimes. For example, if the scale value of crime 9 is s9 then the scale value of crime 7 will be s7 ⫽ s9 ⫹ .179 and so on. The method estimates the differences of the scale values between any two successive crimes and not the actual scale values. The zero point of the scale should be located at “nil crime.” As obtained from the last row of matrix D, the mean of the differences of scale values of the crimes was .201. This would be a best estimate for the successive difference between two adjacent crimes. It was therefore used to estimate the difference between nil crime and the next more serious crime. In such a manner, a series of scale values can be obtained as: 0 for nil crime, 0 ⫹ .201 ⫽ .201 for crime 9, .201 ⫹ .179 ⫽ .380 for crime 7, and so on. These raw scale values and standardized scale values are given in Table 5, in which the standardized scale values were rescaled to sum to 100 for convenience and are referred to as the weights or scores associated with the perceived seriousness of the crimes. Murder, rape, drug offense, and robbery were perceived as the four most serious crimes by Hong Kong
Table 2 Matrix P: proportion of times crime i was judged more serious then crime j Crime i Crime j 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total
2
3
4
.500 .043 .821 .090 .957 .500 .968 .654 .179 .032 .500 .000 .910 .346 1.000 .500 .757 .171 .986 .286 .769 .256 .936 .526 1.000 .653 1.000 .917 .986 .606 .986 .845 .985 .721 1.000 .926 .887 .352 .958 .648 .568 .122 .797 .108 .955 .612 1.000 .881 .859 .500 .984 .797 .677 .387 .935 .532 .750 .139 .917 .264 11.739 5.44 13.788 7.974
5
6
7
8
9
10
11
12
13
14
15
.243 .231 .000 .014 .015 .113 .432 .045 .141 .323 .250 .829 .744 .347 .394 .279 .648 .878 .388 .500 .613 .861 .014 .064 .000 .014 .000 .042 .203 .000 .016 .065 .083 .714 .474 .083 .155 .074 .352 .892 .119 .203 .468 .736 .500 .231 .014 .028 .000 .113 .703 .045 .078 .355 .250 .769 .500 .056 .085 .074 .225 .689 .164 .156 .468 .347 .986 .944 .500 .563 .294 .676 .946 .478 .359 .742 .694 .972 .915 .437 .500 .088 .521 .892 .343 .312 .629 .681 1.000 .926 .706 .912 .500 .690 .878 .478 .391 .661 .792 .887 .775 .324 .479 .310 .500 .892 .239 .375 .565 .583 .297 .311 .054 .108 .122 .108 .500 .060 .031 .161 .111 .955 .836 .522 .657 .522 .761 .940 .500 .422 .565 .722 .922 .844 .641 .688 .609 .625 .969 .578 .500 .645 .639 .645 .532 .258 .371 .339 .435 .839 .435 .355 .500 .319 .750 .653 .306 .319 .208 .417 .889 .278 .361 .681 .500 1.483 8.980 4.248 5.287 3.434 6.226 11.542 4.150 4.200 7.441 7.568
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Table 3 Matrix X: normal deviates corresponding to proportions in matrix P with columns arranging in increasing order of total proportions Crime i Crime j 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
⫺2.178 ⫺.585 – ⫺1.450 – ⫺1.450 ⫺.541 ⫺1.352 .000 ⫺.496 ⫺1.167 .056 .278 ⫺.416 ⫺.812
12
13
7
8
2
10
⫺1.698 ⫺.284 – ⫺1.178 ⫺1.698 ⫺.977 ⫺.056 ⫺.404 ⫺.056 ⫺.710 ⫺1.557 .000 .197 ⫺.162 ⫺.589
⫺1.077 .000 ⫺2.154 ⫺.830 ⫺1.418 ⫺1.010 ⫺.360 ⫺.489 ⫺.278 ⫺.319 ⫺1.863 ⫺.197 .000 ⫺.372 .355
–
⫺2.195 ⫺.268 ⫺2.195 ⫺1.016 ⫺1.908 ⫺1.375 .160 .000 1.352 ⫺.053 ⫺1.237 .404 .489 ⫺.329 ⫺.469
⫺1.717 .000 ⫺1.858 ⫺.396 ⫺.949 ⫺.654 .393 .268 .585 ⫺.380 ⫺1.167 .284 .000 ⫺.287 ⫺1.085
⫺1.212 ⫺.460 ⫺.674 ⫺1.342 ⫺.736 ⫺.697 .380 .287 1.085 .396 .654 .949 ⫺1.725 ⫺1.518 ⫺1.383 – ⫺1.521 ⫺2.189 ⫺.380 ⫺.081 .631 .000 ⫺.064 .566 ⫺1.212 ⫺.372 ⫺.674 ⫺.566 ⫺.736 .000 ⫺.754 ⫺.081 ⫺.393 .064 .000 .736 .457 .649 .508 1.383 1.593 2.200 .053 .329 .469 1.016 1.375 1.908 .496 .416 .812 1.450 1.450 – .000 .162 .210 .380 .754 1.212 ⫺1.237 ⫺.989 ⫺1.221 ⫺1.237 ⫺.494 ⫺.532 .710 .162 .589 1.178 .977 1.698 .319 .372 .355 .831 1.010 1.418 ⫺.162 .000 ⫺.469 .081 .081 .372 ⫺.210 .469 .000 ⫺.631 .393 .674
⫺.393 – ⫺1.383 ⫺2.200 ⫺1.593 .000 ⫺.160 .541 ⫺.457 ⫺1.607 .056 .360 ⫺.649 ⫺.508
14
15
4
6
5
11
1
3
⫺.170 .000 .919 1.167 1.717 1.858 ⫺.832 ⫺.919 .000 1.237 1.342 – 0.532 .697 2.189 .494 .736 1.521 1.607 – – 1.237 2.195 2.195 1.167 2.178 – 1.237 1.212 1.725 .000 .170 .832 1.557 1.698 – 1.863 1.078 2.154 .989 .460 1.518 1.221 .674 1.383
the seriousness of crimes, there appears to be discrepancies between these evaluations and the legal penalties imposed in Hong Kong. The penalty of life imprisonment is forty-five years on average—the expected life duration of seventy-five years reduced by thirty years, the average age of the convicted (Sellin & Wolfgang, 1970). As reflected by the ratios of the weights of murder with other crimes, the legal penalty of lifelong imprisonment for murder in Hong Kong is not too heavy when compared with the penalties of other crimes. The extent to which people’s evaluations of the seriousness of crimes should be
citizens. The scores were 16.68, 12.53, 11.92, and 10.41, respectively. The four least serious crimes were theft (1.11), snatching (2.1), criminal damage (2.32), and possession of arms (2.55). The score of murder was about fifteen times of the score of theft, implying that fifteen cases of theft are equivalent to one case of murder in terms of Hong Kong citizens’ subjective evaluations. Eleven cases of theft are equivalent to one case of rape, ten cases of theft equivalent to one case of drug offense, and nine cases of theft to one case of robbery. If the weights truly reflect people’s evaluations of
Table 4 Matrix D: differences of normal deviates between crime j and its next less serious crime i Crime i,j Crime j 7,9
12,7
13,12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sum n Mean
–
.621 ⫺1.118 .284 ⫺.268 – ⫺.041 .348 ⫺.186 .280 ⫺.490 ⫺.033 ⫺.365 ⫺.304 .520 ⫺.085 .489 ⫺.222 1.630 .391 .266 ⫺.306 .626 ⫺.197 .601 ⫺.197 .489 ⫺.210 .043 .234 ⫺.114 .604 2.082 14 15 .043 .139
– .192 –
.109 –
.067 – ⫺.143 .541 1.192 .541 .039 ⫺.440 .000 .082 ⫺.233 .304 2.142 12 .179
.205 .502 .616 ⫺.056 ⫺.244 ⫺.597 ⫺.253 .050 ⫺.056 ⫺.163 .487 ⫺.081 .519 13 .040
8,13
2,8 .478 .268 .337 .620 .959 .721 .233 .268 ⫺.767 ⫺.327 .070 ⫺.120 ⫺.489 .042 ⫺.616 1.677 15 .112
10,2 .505 .380 .133 .016 ⫺.263 ⫺.100 .064 ⫺.215 ⫺.089 .380 ⫺.070 .426 .319 .125 .875 2.486 15 .166
14,10 .752 ⫺.093 .207 .299 .840 .673 .192 .276 ⫺.080 .162 .248 ⫺.548 .053 .162 .679 3.822 15 .255
15,14
4,15
6,4
5,6
11,5
1,11
3,1
⫺.214 ⫺.668 .606 .039 .527 .170 .919 .798 ⫺.689 .258 .295 .218 .550 .141 .135 – – ⫺.668 1.357 ⫺.087 .919 .712 ⫺.631 ⫺.064 .630 .671 .105 – ⫺.302 .108 ⫺.170 .736 .532 .165 1.492 ⫺.312 .457 ⫺.064 .736 ⫺.242 .242 .785 ⫺.141 .875 .210 .607 ⫺.593 – – .140 .547 .359 .533 ⫺.671 .958 .000 .396 .638 .000 – – 1.011 – .048 .170 .374 .458 .025 ⫺.025 .513 ⫺.232 ⫺.016 .743 ⫺.038 .532 .170 .662 .427 .589 ⫺.201 .721 ⫺.141 .141 – ⫺.017 .476 .179 .408 .445 ⫺.785 1.076 ⫺.469 .550 .000 .291 .617 ⫺.529 1.058 ⫺.469 ⫺.631 1.024 .281 .547 ⫺.547 .709 .500 1.775 3.254 5.029 3.824 1.539 8.274 15 14 14 14 14 14 11 .033 .127 .232 .359 .273 .110 .752
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Table 5 Construction of crime score Crime 9
7
12
13
8
2
10
14
15
4
6
5
11
1
3
Difference .000 .179 .040 .043 .139 .112 .166 .255 .033 .127 .232 .359 .273 .110 .752 Raw score .201 .380 .420 .463 .602 .714 .880 1.135 1.168 1.295 1.527 1.886 2.159 2.269 3.021 Score 1.11 2.10 2.32 2.55 3.32 3.94 4.85 6.26 6.44 7.14 8.43 10.41 11.92 12.53 16.68
taken into account in determining legal penalties is a controversial issue, but it is worthwhile to carry out some comparisons between the two. It was surprising to find that drug offense is perceived as a very serious crime in Hong Kong. It is even more serious than robbery. This may be related to some cultural and historical reasons. Hong Kong became a British colony in 1841 as a result of a war, called by the Chinese, the Opium War. The harm done to human beings with drugs like opium have been emphasized in society. On the other hand, the law in Hong Kong is based on British law with very different historical roots. The relative seriousness of drug offense, as reflected by the legal penalties, would be much less than that represented by the weights built up by perceived severity. The fifteen selected crimes represented more than 80 percent of the total number of cases of crimes during 1976–96. Using 1976 as the base year, a series of UNCI were constructed by simply relating the sum of the annual number of cases of the fifteen crimes in the current year to that of the base year. A series of WCI were constructed by applying the weights to the calculations. In Table 6, the WCI and UNCI present quite different pictures. Taking the figures of 1976 as a basis for comparison, the WCI fell by 30.3 percent from 100 to 69.7. The UNCI, on the other hand, fell by only 6.9 percent from 100 to 93.1. Looking at the UNCI, Hong Kong has not reduced crime much in the twenty years from 1976 to 1996, while the WCI indicates that Hong Kong has reduced crime significantly during this period. Taking a closer look at the series, the performance difference was formed mainly during the period 1976–82. The WCI fell from 100 to 89.8 during 1976 to 1982, while the UNCI rose from 100 to 118.2. During the later period (1982–96) both the WCI and UNCI recorded drops of similar magnitude (22.4 percent and 21.4 percent, respectively). The contrasting performance in the earlier period needs explanation. The UNCI may be broken down into three components, the serious crime index, the moderate-serious crime index, and the nonserious crime index, according to the values of their serious-
ness scores. Murder, rape, drug offense, and robbery were the serious crimes with weights above 10; possession of arms, criminal damages, snatching, and theft were the nonserious crimes with weights below 3; and the remaining crimes were classified as moderate-serious. From Table 7, it can be seen clearly that the serious crime index and the nonserious crime index move in opposite directions. The former dropped from 100 in 1976 to 78 in 1982, a fall of 22 percent; while the latter increased from 100 to 223, a rise of 123 percent, during the same period. This explains the contrasting performance of crime reduction presented by the WCI and the UNCI. During the period 1976–82, the incidence rate of robbery dropped from 200 to 162 and drug offense from 72 to 49; while theft rose from 274 to 604, snatching from 12 to 41, and criminal damages from 31 to 66. If citizens’ perceived seriousness of crimes
Table 6 Weighted crime index (WCI), unweighted crime index (UNCI), and GDP, 1976–1996 Year
WCI
UNCI
GDP
1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
100 80 74 77 85 84 90 88 86 87 81 82 85 87 89 85 77 68 82 84 70
100 90 73 93 106 109 118 118 114 117 109 109 104 105 112 114 107 104 108 111 93
100 116 136 178 226 272 307 339 409 433 498 613 725 835 928 1065 1242 1430 1610 1728 1905
Y.K. Kwan et al. / Journal of Criminal Justice 28 (2000) 237–244 Table 7 Serious and nonserious crime rates, 1976–1996a Year
Serious crime
Nonserious crime
1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
100 69 61 69 80 74 78 78 69 72 66 68 79 78 77 78 65 41 67 67 50
100 116 140 160 194 205 223 224 204 211 197 198 192 189 202 198 192 177 189 195 164
a
1976 rate as a standard.
were included in the calculation, the intensity of crimes in Hong Kong should have been reduced during this period. Discussion The validity of the WCI depends on the validity of the set of weights of the fifteen crimes. Owing to the subjective and experience-based nature of the responses, an acceptable absolute standard for the weights was lacking and its criterion validity could not be tested. The extent to which the relative seriousness of the crimes was represented by the weights is difficult to assess. Two types of tests can be performed. One type is the internal check provided by Thurstone’s method. Another type is an external check on the conformity of the performance of the crime index to some patterns that have been established in the literature. Thurstone’s method has an advantage: The paired comparisons themselves provide an internal check on validity. As each respondent has to complete two sets of comparisons, two kinds of contradictions can be tested. Direct contradiction happens when a respondent judges crime A as more serious than crime B, and then the other way round later. In the survey, sixty-three cases of direct contradictions were found. Another contradiction is known as a circular triad. It occurs when crime A is judged by a respondent as more serious than crime B,
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crime B more serious than crime C, but then crime C is more serious than crime A. In the survey 201 cases of circular triads were found. As there were a total of 17,804 paired comparisons that were subjected to these tests, the proportion of contradictions was small. A large number of contradictions would mean that Thurstone’s method was not appropriate. On the other hand, a small proportion of contradictory comparisons supports the appropriateness of the method and the validity of the results. Pyle and Deadman (1994) constructed an econometric model relating property crimes to economic activities. Using postwar Britain as an example, the relationship between the business cycle and property crime was found. Deadman and Pyle (1997) confirmed further the reverse relationship between GDP growth and the property crime rate. One may doubt whether trends in economic indicators always correlate strongly with crime rates, although they did find support in the WCI in Hong Kong. Hong Kong experienced rapid economic growth during the period from 1976 to 1996 with the exceptions of 1982, 1985, 1989, and 1990. In the years of economic recession, both the WCI and the UNCI experienced either a rise or a fall, less than the average deceleration of the downward trend in crime rates, conforming to Pyle and Deadman’s pattern. During the entire period 1976–96, Hong Kong recorded a rise of eighteen times in GDP (Table 6). The WCI is a better indicator than the UNCI as it recorded a drop of 30.3 percent, while UNCI recorded a drop of only 6.9 percent. During the period 1976–82, the GDP rose from 100 to 307. The WCI conformed to the pattern, recording a fall of 10.2 percent in crime, while the UNCI deviated from the pattern with a rise of 18.2 percent in crime. Conformity of the WCI to economic performance can be measured by the correlation coefficient between GDP and crime rates. The correlation coefficient between GDP and WCI was ⫺.449. The coefficient of determination was .202, implying that 20.2 percent of the variations in crime can be explained by the changes in GDP. On the other hand, when UNCI was tested for correlation with the GDP, no significant relationship was found. The WCI, not the UNCI, gave a more valid indication of crime intensity in Hong Kong. The validity of the seriousness scores were further tested by comparisons with other measures of crime severity, namely, legal penalties and the seriousness scores constructed in other studies. The maximum penalties of the fifteen crimes were correlated with the seriousness scores, resulting in a correlation coefficient of .80. The Sellin and Wolfgang crime seri-
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ousness scores in the Uniform Crime Report (1970) were constructed from the components’ scores obtained by magnitude estimation on crime vignettes. When they were collated with the corresponding seriousness scores of the present study, constructed by Thurstone’s scaling method on crime typologies, an exponential relationship was found. Using the log values of Sellin and Wolfgang’s scores, a very high correlation coefficient of .93 was obtained. Finally, using the split-half method, the survey results were divided randomly into two groups of equal size. Separate seriousness score estimates of the fifteen crimes were obtained for each group. A high correlation coefficient (r ⫽ .986) was found between the estimates of the two groups. These tests suggest that the scale is valid and reliable. The unweighted crime rate has been widely used as an indicator of the intensity of crime in a society, although the results here show that it may give very misleading results. In Hong Kong, the UNCI presented a misleading picture of a very small reduction in crime despite tremendous economic achievement in the last twenty years under British rule. If crimes are to be weighted in the construction of a crime index, the relative seriousness of crimes needs to be measured. Thurstone’s scaling method of paired comparisons provides a simple and reliable method, especially when telephone interviews are used. The present results indicate some discrepancies between the perceived seriousness of crimes and the legal penalties. Further studies in this area are needed. The WCI is a better indicator of crimes than the UNCI, which can be very misleading. In many cities, the UNCI is the only summary index of crimes. Caution is needed when using it as an indicator in measuring crimes. It is recommended that a survey, similar to the one used here, be carried out so that a WCI can be constructed. References Anderson, P. R., & Newman D. J. (1998). Introduction to Criminal Justice. Boston, MA: McGraw-Hill. Bacon-Shone, J. (1994). Household telephone surveys in Hong Kong. 1990 Proceeding of the Section on Survey Research Methods, Annual Meeting of the Alexandria VA: American Statistical Association (pp. 393–395). Alexandria, VA: American Statistical Association. Black, D. (1979). Common sense in the sociology of law. Am Soc Rev 44, 18–27. Bowling, A. (1992). Measuring Health: A Review of Quality of Life Measurement Scales. London: Open University Press.
Deadman, D. F., & Pyle, D. J. (1997). Forecasting recorded property crime using a time-series econometric model. Br J Crim 37, 437–445. Forgas, J. P. (1980). Images of crime: a multidimensional analysis of individual differences in crime perception. Int J Psych 15, 287–299. Hansel, M. (1987). Citizen crime stereotypes—normative consensus revisited. Crim 25, 455–485. Hembroff, L. A. (1987). Seriousness of acts and social contexts: a test of Black’s theory of behavior of law. Am J Soc 93, 322–347. Horst, A. P. (1941). Prediction of personal adjustment. Soc Sci Res Council Bul 48. Hunt, S. M., McEwen J., & Mckenna, S. P. (1986). Measuring Health Status. London: Croom Helm. Ip, W. C., Kwan Y. K., & Pong, T. Y. (1995). A health status indicator for the Chinese elderly in Hong Kong. Int J Bio-Med Computing 40, 133–137. Mosteller, F. (1951). Remarks on the method of paired comparisons I. the least squares solution assuming equal standard deviations and equal correlations. Psychometrika 16, 3–11. Newman, G., (1976). Comparative Deviance. New York: Elsevier. Parton, D. A., Hansel, M., & Stratton, J. R. (1991). Measuring crime seriousness: lessons from the National Survey of Crime Severity. Br J Crim 31, 72–85. Pease, K. (1988). Judgments of Crime Seriousness: Findings from the 1984 British Crime Survey. London: Home Office. Pyle, D. J., & Deadman, D. F. (1994). Crime and the business cycle in postwar Britain. Br J Crim 34, 339–357. Rossi, P. H., Waite, E., Boise, C. E., & Perk, R. (1974). Seriousness of crimes. Am Soc Rev 39, 224–237. Scott, J. E. & Al-Thakeb, F. (1980). Perceptions of deviance cross-culturally. In G. R. Newman (Ed.), Crime and Deviance: A Comparative Perspective (pp. 42–67). London: Sage Publications. Sebba, L. (1980). Is Mens Rea a component of perceived offense seriousness? J Crim Law & Crim 71, 124–135. Sellin T., & Wolfgang M. E. (1970). Measurement of Delinquency. New Delhi: Wiley Eastern Private Limited. Shaver, K. G. (1984). Attribution of Blame: Causality, Responsibility, and Blameworthiness. New York: SpringerVerlag. Tai, H. S., & Yiu, F. K. H. (1994). Measurement of crime. Bul Hong Kong Stat Soc 17(1), 6–9. Thurstone, L. L., & Chave, E. J. (1929). Measurement of Attitudes. Chicago, IL: University of Chicago Press. Torgenson, W. S. (1958). Theory and Methods of Scaling. New York: John Wiley & Sons. Wilkins, L. T. (1980). World crime: to measure or not to measure? In G. R. Newman (Ed.), Crime and Deviance: A Comparative Perspective (pp. 17–41). London: Sage Publications. Wolfgang, M., Figlio, R. M., Tracy, P. E., & Singer, S. J. (1985). National Survey of Crime Severity (NCJ-96017). Washington, DC: U.S. Government Printing Office.