Statistical Analysis of Police Arrest Decisions: Smith & Visher
This paper examines Smith and Visher's (1981) landmark study on the situational determinants of police arrest decisions. It identifies the central independent variables analyzed — including suspect race, demeanor, crime seriousness, and victim preferences — and explains how the authors employed a multivariate probit model to assess each variable's relative contribution to arrest likelihood. The paper also describes how descriptive statistics were presented through cumulative density functions and Z scores, how statistical significance was used to reduce the full model from twelve to seven key variables, and how the authors depicted the complex interrelationships among variables through a causal model.
- Introduction and Overview of Smith and Visher's Study: Context and aim of the 1981 study
- Key Independent Variables Examined: Twelve variables influencing arrest likelihood identified
- Presentation of Descriptive Statistics: Use of tables, Z scores, and density functions
- Statistical Methods and Findings on Arrest Decisions: Probit model applied to test variable interactions
- Use of Statistical Significance and Model Reduction: Seven significant variables identified from twelve
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What makes this paper effective
- Directly addresses each analytical question in sequence, creating a clear and logical structure that is easy to follow.
- Accurately identifies and explains the methodological choices made by Smith and Visher, including the rationale for using a multivariate probit model rather than simpler bivariate tests.
- Demonstrates understanding of both descriptive and inferential statistics, distinguishing between what the chi-square test revealed and what the probit model added.
Key academic technique demonstrated
The paper effectively summarizes a quantitative social science study by explaining not just what the authors found, but how they used statistical tools — probit modeling, cumulative density functions, and significance screening — to arrive at and present those findings. This moves the analysis beyond mere description into methodological critique.
Structure breakdown
The paper is organized around four guiding questions: the central variables studied, the use of descriptive statistics, the presentation of findings, and the role of statistical significance. Each section builds on the previous one, moving from variable identification to data presentation to inferential analysis and finally to model reduction. This question-driven format suits a structured analytical response at the undergraduate level.
Introduction and Overview of Smith and Visher's Study
Smith and Visher (1981) conducted an influential study examining the situational determinants of police arrest decisions. Their goal was not simply to identify which factors correlated with arrest, but to assess the relative contributions of multiple independent variables simultaneously. To achieve this, they moved beyond simple bivariate tests and employed a multivariate probit model, allowing them to account for the complexity and potential interdependence of the variables involved.
Key Independent Variables Examined
Smith and Visher (1981) analyzed a series of independent variables previously identified by other studies as influencing the dependent variable — the likelihood of being arrested. Although a chi-square test revealed several factors to be significantly associated with arrest likelihood (Table 1), the aim of their research was to reveal the relative contributions of the many independent variables examined.
Toward this goal, the authors used a multivariate probit model to gauge the relative contributions of each independent variable to arrest likelihood. These variables included: whether police contact was initiated by a victim or by the police; whether the contact with the suspect took place in a public or private location; the presence of bystanders; whether a victim was present or absent; the victim's preferred course of action; the suspect's race, age, and gender; the suspect's demeanor; the relationship between victim and suspect (known or stranger); and the seriousness of the crime.
Presentation of Descriptive Statistics
The descriptive statistics were presented in table format. Rather than providing probability values, as is common practice today, the authors reported cumulative density functions (B) and raw Z scores (Tables 3 and 4). These values allow the reader to gauge the relative predicted contributions of the different variables to arrest likelihood.
The statistics were then used to evaluate the findings of prior studies, to discuss the relative importance of different variables on arrest likelihood, and to allow the authors to comment on possible interrelationships among the independent variables.
Statistical Methods and Findings on Arrest Decisions
The authors took the position that a large number of variables likely contribute to whether an arrest takes place, and that some of these variables probably interact in a dependent manner. The statistical analysis was used to test this theory, and the resulting data informed an authoritative discussion of the findings. By taking this approach, the authors were able to convey the significant degree of complexity involved in determining whether an arrest occurs. This complexity of variables and interrelationships was also depicted graphically in Figure 1 as a causal model.
References
Smith, D. A., & Visher, C. A. (1981). Street-level justice: Situational determinants of police arrest decisions. Social Problems, 29, 167–177.
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