Quantitative Methods in Early Criminology Research Paper

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The adoption of the “positivist approach” in the study of human behavior exposed early criminologists to a range of quantitative methods that allowed objective investigations of crime data. This research paper reviews the types of data and quantitative methods used by criminologists in the nineteenth century to describe the magnitude of crime, identify offenders’ unique characteristics, and search for the causes of deviance and crime. Similar to contemporary sources of “crime statistics,” data on crime and criminals during this period was collected by official criminal-justice agencies and by independent scholars who observed, surveyed, and conducted scientific experiments with criminals. Due to the absence of predictive statistical tools, data analysis had mainly involved (1) classifications of crime types and construction of frequency distributions, (2) calculations of crime rates, proportions, averages, and deviations, (3) comparisons between pairs of variables, and (4) estimations of the relationships between pairs of variables using tables and graphs. The important influences of these quantitative methods on the evolution of criminological theory are discussed.


Although the roots of criminological thinking could be traced back to the second half of the eighteenth century, it was not until the early nineteenth century, when “positivist” methods (i.e., all these methods that can predict crime and that are in harmony with the methods applied in the natural sciences (Beirne 1987)) were employed in the study of crime (Guerry 1833; Quetelet 1831) that criminology established itself as a legitimate modern social science. Drawing on the “positivist” assumption that quantitative methods should be applied in the social sciences (Quetelet 1831; Comte 1858), early criminologists adopted a range of quantitative tools (e.g., ratios and proportions, averages and deviations) in order to describe the crime problem, assess the causes of crime, and identify offenders’ unique characteristics. Indeed, some scholars proposed that criminologists adopted these “positivist” methodologies in order to justify the implementation of new strategies of penalty and correction (Foucault 1979). However, most would agree that by applying quantitative methods to the study of crime, our understating of human behaviors was extended, establishing the foundation to develop crime causation theories.

This research paper reviews the important quantitative methods adopted and used by criminologists during the nineteenth century. It begins with a brief overview on the emergence of the positivistic approach within the criminological discipline. It then describes the common data used by criminologists to study crime and its causes. Next, it elaborates the quantitative approaches employed by early criminologist to analyze crime and social data, using examples from early crime scholars’ works. Finally, this research paper concludes by discussing the unique influence of quantitative methodologies on the evolution of criminological theory. Importantly, this review encompasses articles and books that appeared between the years 1800 and 1900 and that were written in or translated into English.


Positivist criminology emerged in France during the early nineteenth century as a result of the shift from an amorphous penal system (led by the ancient re´gime until the mid-eighteenth century) to a more centralized system with a network of reform institutions (Beirne 1987). Influenced by enlightenment ideas of rationalism and humanism, and guided by the writings of prominent “classical school” philosophers (e.g., Cesare Beccaria and Jeremy Bentham), the stated objective of the new penal system was to promote moral rehabilitation among delinquent inmates (mainly alcoholics, idiots, immigrants, prostitutes, and petty and professional criminals). The penal institutions were designed to employ systematic strategies of surveillance and detention in an effort to “normalize” the conduct of the “dangerous class” (Beirne 1987). Soaring crime and increased recidivism at the beginning of the nineteenth century signaled the failure of these institutions to accomplish their task. In an effort to uncover the magnitude of crime in the country, the Ministry of Justice in France initiated in 1825 the first centralized national data collection of crime statistics. This resulted in a publication of the first annual report of national crime statistics in 1827 (Friendly 2007).

During the same time period, a positivist approach (i.e., an epistemology suggesting that natural phenomena could be empirically studied based on unbiased and objective scientific procedures) had dominated the scientific discourse within the physical sciences. Adherents of this approach suggested that unbiased scientific investigations should follow the positivist principles of observation, experiment, comparison, and historical methods (Timasheff 1967), and employ mathematical operationalization of the world. Acknowledging the unique contribution of positivist methods in the physical sciences, early social scientists (e.g., Quetelet (1831), and Comte (1858)) suggested that these methods and principles are also applicable to “social data.” According to Quetelet (1831), quantitative methods could be used in the study of social data if those data are able to stand outside of the observer and are capable of being analyzed by mathematical procedures. Drawing on Quetelet’s and Comte’s monumental works, early social scholars developed interest in “positivist” methods and implemented them using a range of social data. This trend also influenced many crime scholars, who adopted these quantitative tools and used them to analyze crime data.

Crime Data

Similar to contemporary sources of “crime statistics” and “social data,” information on crime and criminals during the early nineteenth century was collected by (1) government officials (i.e., courts and police) and by (2) individual scholars observing, surveying, and conducting experiments with criminals.

Official Crime Data. Although official efforts to collect national crime data began in 1825, the systematic collection of population-based data (i.e., social data) was initiated in the mid-fifteenth century with the London Bills of Mortality (the London Bills of Mortality were collected weekly and established the main source of mortality statistics in fifteenth-century England) (Friendly 2007). Early analyses of these mortality data demonstrated the informative value that state and public officials could gain from such “social data.” As a consequence, by the mid-eighteenth century, governmental efforts to collect population-based data from its various agencies were expanding. The extensive collection of official crime statistics by the French Ministry of Justice in 1825 set the stage for the collection of data on criminal-justice agencies (e.g., police departments, courts, and prisons), as well as other population data (e.g., immigrants, prostitutes, literacy, and wealth). Beginning in the late 1830s, governmental efforts of crime data collection spread to England (Rawson 1839) and other European countries (e.g., Germany, Italy, Russia), and by the early 1850s were initiated in the USA. (Deflem 1997). While the accumulation of official crime statistics enabled early criminologists to develop an initial understanding on the distribution of crime and its magnitude, the availability of “social data” allowed these scholars to also test hypotheses regarding the social and ecological causes of crime.

Data Collected by Individual Scholars. In addition to official data collected by governmental officials, individual scholars gathered their own data on crime and delinquency directly from criminals. These scholars used a range of scientific methods – including observations, surveys, and experiments – to collect this information (Rafter 2004). Pinel, for instance, collected data on insane criminals using case studies and direct observations (Rafter 2004). Lombroso and his students collected measures of skulls, body, and morphological features of dead and alive criminals (Lombroso 1876; Lombroso and Ferrero 1893). These scholars also used experimental designs to collect data from criminals and noncriminals (Lombroso and Ferrero 1893). Finally, Mayhew (1862) and also Vidocq (Lindesmith and Levin 1937) used participant observations, testimonies by criminals, and life history documents to identify social gestures among prisoners and pickpockets. Although these methods of data collection were limited in scope, they yielded unique data sets that supported the development of biological and psychological perspectives on crime and shaped the evolution of criminological theory. The emergence of “quantitative methods” allowed early criminologists to empirically test the validity of these perspectives.

Quantitative Methods

Adolphe Quetelet was the first social scientist to apply quantitative methods in the study of crime. Drawing on his extensive background in mathematics and statistics, Quetelet believed that the same regularities and laws observed in the natural sciences could be identified in the social world. Identification of these laws, he suggested, should be based on a large amount of social data and involve the application of statistical methods and calculations (Beirne 1987; Stigler 1986). Following the publication of “Research on the Propensity for Crime at Different Ages” (Quetelet 1831), criminologists in France and around the globe implemented probability theory to describe the magnitude of crime (Guerry 1833; Rawson 1839; Levi 1880) and the work of criminal-justice agencies in their countries (Falkner 1889; Fletcher 1850; Mayhew 1862), to identify offenders’ unique characteristics (Lombroso, 1876, 1891), and to search for the causes of deviance and crime (Clay 1857; Quetelet 1842). In the absence of methodologies that estimate correlations and regression coefficients (These approaches were developed around 1890 by Francis Galton and Karl Pearson (Stigler 1986)), these early crime scholars produced scientific works that: (1) classified crimes by types and presented frequency distributions; (2) calculated crime rates, proportions, averages, and deviations; (3) compared pairs of variables; (4) estimated the relationships between pairs of variables; and (5) presented quantitative graphics.

Crime Classification and Frequency Distributions. Once crime data became available to social scientists, criminologists were particularly interested in understanding the magnitude of deviance and crime. To achieve this goal, scholars like Quetelet (1831), Rawson (1839), and others (Fletcher 1841; Guerry 1833) presented annual figures on the sheer number of persons charged, convicted, and acquitted with different types of offenses. Offense type classifications were either general (i.e., distinguishing between crimes against persons and crimes against property (Quetelet 1831)) or very detailed (i.e., presenting a breakdown of all reported offenses (Rawson 1839; Fletcher 1841)). With the distinction made by official crime agencies between offenses and offenders, scholars like Levi (1880) presented data on both the number of indictable offenses reported to the police and the number of persons apprehended for indictable offenses.

The accumulation of data on criminal-justice agencies allowed early criminologists to also describe the size, structure, and workload experienced by police stations and prisons. Levi (1880), for instance, reported the annual number of police officers in England and Wells between the years 1857 and 1878, while Fletcher (1850) provided detailed description of police wards’ force size, officers’ salaries, and workload in London. Prisons statistics were also popular during that time, with scholars like Mayhew (1862), Lombroso (1876), and Falkner (1889) describing the number of prisoners, their offenses, and sentence lengths in British, Irish, and American prisons, respectively.

Proportions, Rates, Averages, and Deviations. In order to allow a meaningful assessment of the magnitude of crime, early scholars adopted Laplace’s method of ratio estimation (Stigler 1986) and calculated the ratios of the annual offenses to population (Guerry 1833; Levi 1880), proportions of offenders per populations (Rawson 1839), and proportions of prisoners to population (Falkner 1889). Quetelet (1831) also calculated the conviction rates of criminal offenders in France between the years 1825 and 1830, dividing the number of convicted criminals by the number of accused. Quetelet interpreted these rates as probabilities, suggesting that they indicate the chances that an average person (whom nothing more is known about) is convicted of a crime.

Next to estimating the average propensities of offenders to be convicted, Quetelet also calculated the average values of his subjects’ physiques (i.e., weight, height). According to him, any aspect of a population that can be measured may produce an indicator that portrays the “average man” in that population (Quetelet 1831; Stigler 1986). This average score could then indicate either an actual physical characteristic (i.e., height, weight) or an estimated “propensity” (for instance, using crime rates to calculate the propensity to offend). Once known, this mean could be cross-tabulated with a range of demographic, social, and contextual indicators, and allow for the development of meaningful comparisons that could refine our understanding of the laws of the social world.

Comparison between Pairs of Variables. Drawing on Quetelet’s (1831, 1842) influential works, numerous early crime scholars compared the distribution of crime measures across a range of social groups, time periods, and geographical regions. These comparisons included calculations of social groups’ share in producing crime, and the overall proportions of offenders in the group. Results were mainly reported using tables. Levi (1880), for instance, reported that only 20 % of those committed to trial between the years 1857 and 1878 in England and Wales were women. Focusing on the differential involvement of different age groups in crime, Rawson (1839) Fletcher (1841) and Levi (1880) ordered several age categories (e.g., under 17 years, between 17 and 21 years) and compared the proportion of offenders in each category. These scholars also reported the proportion of male and female offenders across the different age categories. Finally, Fletcher (1841) calculated the “proportion of offenders” across level of instruction in the United Kingdom between the years 1836 and 1842, finding that less than 10 % of offenders were able to read and write well.

Numerous early studies also compared crime statistics across countries and various geographical regions (Levi 1880; Lombroso 1911; Rawson 1839; Fletcher 1850). Rawson (1839), for instance, compared the proportion of offenders within different age groups in England and France and found that in both countries, more than 30 % of male and female offenders were between 21 and 30 years of age. Analyzing data from England and Wales, Levi (1880) compared the average number of persons committed for trial across 51 counties and found substantial variation across counties. Finally, Falkner (1889) compared the proportion of female convicts in 27 states, finding high proportion of female convicts in North Carolina and Maryland, yet low proportions in Texas and Colorado. It should be noted that in the absence of appropriate methodologies allowing examination of significant differences (for instance, t-tests and/or one way ANOVA), early criminologists were limited in the informative value of their comparisons.

While comparisons of crime proportions and averages were common among early scholars that used official crime data, such comparisons were rare among scholars like Lombroso and his students that collected data directly from criminals (using observations and experiments). Thanks to the relatively low number of observations, these scholars used the actual values of the measures to generate comparisons between individuals. In the “Criminal Man,” for instance, Lombroso (1876) compared the circumference of 66 criminals’ skulls, and reported that these skulls were “abnormally small.” In the third edition of this book, Lombroso also presented comparisons between the anomalies in the brains of 28 criminals as well as comparison between the anomalous physical characteristics of 219 male criminals. Indeed, Lombroso’s comparisons were accepted with suspicion in the criminological field. Nevertheless, along with comparisons of crime proportions and averages, these comparisons set the stage for the emergence of the first attempts to assess relationships between pairs of variables, and provided fertile ground for the development of sociological, psychological, and biological explanations of crime.

Estimations of the Relations between Pairs of Variables. In further efforts to identify the causes of deviance and crime, several criminologists investigated the joint variation between crime indicators and social, psychological, and biological measures. In the absence of methodological tools allowing statistical estimation of the relationships between measures, these scholars used tables to organize the values of their measures and then looked for consistent variation between these measures. Rev. John Clay (1857), for instance, was interested in the relationship between the number of criminals, beer houses, and schools attendants in geographic areas. To test these relationships, he composed a table listing 40 counties in England and presented the number of criminals (per 100,000 of the population), beer houses (per 100,000 people), and attendants at school (per 10,000) in each county. Observing the joint variation of these measures, Clay determined that beer houses are associated with high levels of crime, while attendance in school is associated with low levels.

This approach allowed early scholars who represented different criminological perspectives to empirically assess the validity of their theoretical arguments. Lombroso and Ferrero (1893), for instance, compared the variation of cranial capacities across groups of normal and criminal females. In line with Lombroso’s theory of the criminal man (Lombroso 1876), these authors found that the cranial capacity of female criminals and prostitutes was lower than the cranial capacities of normal females. Focusing on the social causes of deviance and crime, Durkheim (1897) compared the variation of suicide rates with the percentage of married couples across 16 Italian provinces. Consistent with the assumption that low integration increases the probability of suicide, Durkheim found that provinces with a low percentage of marriages experienced high suicide rates, while provinces with a high percentage of marriages experienced low rates. The availability of quantitative graphics further supported these early comparisons, allowing visualization of the relationship between measures.

Quantitative Graphics. By the end of the first half of the nineteenth century, all the major modern forms of data visualization (including bar-charts, histograms, time-series charts, and thematic maps) had already been invented (Beniger and Robyn 1978; Friendly 2009) and their advantage in presenting patterns, distributions, anomalies, and variations of measures was highly acknowledged. Guerry (1833) and Quetelet (1831) took active part in developing these statistical graphics. Guerry (1833), for instance, was first to produce histograms (Karl Pearson coined the term “histogram” in 1895 to describe this form of statistical graphical presentation (Stigler 1986)) by arranging ordered categories for continuous measures (i.e., age, months) and using columns of equal width to represent the frequency of each category of the data (Beniger and Robyn 1978; Friendly 2007). Generating a histogram to compare the distribution of different types of crimes over age categories, Guerry observed that indecent assault is more common during childhood and less frequent during adulthood. In his late editions of L’uomo delinquente, Lombroso (1889, 1896) also employed bargraphs and histograms to compare the distributions of criminals’ and noncriminals’ cranial capacities, height and arm span, and parents’ age. Finally, Dexter (1899) composed a histogram to compare the frequency of murder and suicide incidents over conditions of temperature. Interestingly, although utilizing bar-graphs for comparison purposes, there is no indication that early criminologists were aware of the scatterplot (first scatterplot was published in 1833 in an astronomy journal (Friendly 2007)).

In addition to bar-charts and histograms, time-series charts were commonly used by early scholars (Guerry 1833; Lombroso 1876; Du Bois 1899; Dexter 1899; Mayhew 1862). Taking advantage of increasingly accumulating annual crime data, scholars produced time-series plots to describe the fluctuation of crime over time. Guerry, for instance, presented a time-series line graph of death sentences and executions in France between the years 1825 and 1855 (Friendly 2007). Employing the unique visualization allowed by time-series diagrams, Mayhew (1862) produced a time-series chart describing the fluctuation of corn price and the ratio of criminals to population between the years 1834 and 1849 in London. Finally, Lombroso (1896) produced a graphical analysis of periodic variation of alcohol consumption in ten countries (including the USA) between the years 1870 and 1895.

The invention of the statistical shaded map by Dupin in 1826 (Friendly 2007) initiated a series of publications featuring shaded maps and describing the distribution of crime rates across geographical regions. Balbi and Guerry were first to use shaded maps for portraying crime rates across the departments of France (Friendly 2007). In their innovative work, these scholars also compared the spatial distribution of crime against persons and crime against property and education level using a set of shaded maps of

France (Friendly 2007). In 1833, Guerry refined these maps (using more complete data) and added three additional shaded maps displaying the distribution of illegitimate births, donations to the poor, and suicide in France. Guerry’s unique approach that compared the spatial distribution of crime data over a range of social measures had been accepted with enthusiasm in the criminological field, and was adopted by many prominent scholars (Quetelet 1842; Levi 1880; Mayhew 1862; Durkheim 1897; Lombroso 1876). Drawing on Enrico Ferri’s analysis of homicide in Italy, Lombroso (1876), for instance, compared the spatial distribution of murder, parricide, and poisoning in Italy. Levi (1880) presented the spatial distribution of indictable offenses and offenses subject to summary jurisdiction between the years 1857 and 1876 across counties in England and Wells and compared it with the spatial distribution of ignorance, amount of savings, and poverty. Finally, Durkheim (1897) presented shaded maps displaying the spatial distribution of suicide rates across counties in France and compared it with the spatial distribution of wealth, family size, and alcoholism.

Summary And Conclusions

In sum, the accumulation of crime data and the adoption of quantitative methods to study crime supported early criminologists’ efforts to describe the magnitude of crime, identify offenders’ unique characteristics, and search for the causes of deviant behaviors. These data and methods paved the way for the development of “positivist criminology.” Indeed, the common quantitative tools available during the nineteenth century were relatively limited in their ability to generate statistical inferences from a sample. Nevertheless, these initial methodologies permitted the construction of frequency distributions, calculations of crime rates, proportions, averages and deviations, and comparisons between pairs of variables. These methods were employed in a considerable amount of early criminological studies and extended our understanding of crime and delinquency.

Next to their value in describing criminals and crime, these early quantitative methods also influenced the evolution of criminological theories. Specifically, the shift from a traditional medieval view of the universe to a philosophy favoring physical facts required empirical validation of scientific explanations of the world. According to this new philosophy, the world could be characterized by mathematical and statistical principles that a rational mind could grasp. The major advantage of these early quantitative tools was their ability to operationalize the world (e.g., producing crime rates) and investigate the relationships between different constructs through scientific research. This allowed early crime scholars to offer theoretical explanation for the causes of crime, draw research hypotheses from these theories, test these hypotheses empirically, and then refine their explanations. Lombroso’s (1867) consistent modification of his original thesis of the criminal man is only one example of this process. Thus, the application of quantitative methods in the study of crime shifted the focus of criminological research from narrow discrete observations to broader discussions portraying general principles on the causes of crime.


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