Conclusions from the history of research into the effects of police force size on crime—1968 through 2013: a historical systematic review



We describe and explain how the findings from nonexperimental studies of the relationship between police force size and crime have changed over time.


We conduct a systematic review of 62 studies and 229 findings of police force size and crime, from 1971 through 2013. Only studies of U.S. policing and containing standard errors of estimates were included. Using the robust variance estimation technique for meta-analysis, we show the history of study findings and effect sizes. We look at the influence of statistical methods and units of analysis, and time period of studies’ data, as well as variation in police force size over time.


Findings vary considerably over time. However, compared to research standards and in comparison to effect sizes calculated for police practices in other meta-analyses, the overall effect size for police force size on crime is negative, small, and not statistically significant. Changes in research methods and units of analysis cannot account for fluctuations in findings. Finally, there is extremely little variation in police force size per capita over time, making it difficult to estimate the relationship with reliability.


This line of research has exhausted its utility. Changing policing strategy is likely to have a greater impact on crime than adding more police.

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  1. 1.

    Sociological Abstracts, Social Science Abstracts (SocialSciAbs), Social Science Citation Index, Arts and Humanities Search (AHSearch), Criminal Justice Abstracts, National Criminal Justice Reference Service (NCJRS) Abstracts, Educational Resources Information Clearinghouse (ERIC), Legal Resource Index, Dissertation Abstracts, Government Publications Office, Monthly Catalog (GPO Monthly), Google Scholar, Online Computer Library Center (OCLC) SearchFirst, CINCH data search, and C2 SPECTR (The Campbell Collaboration Social, Psychological, Educational and Criminological Trials Register).

  2. 2.

    If beta, the standardized regression coefficient, is reported in the estimated regression model, we use beta as the effect size. Standard errors of betas were calculated by applying formula: \( SE\left(\beta \right)=\frac{1-{r}^2}{\sqrt{n-1}} \), where r is Pearson or Spearman correlation coefficient. However, if a study reports the raw coefficient estimate (= b) as a result of a linear regression, we calculate the standardized coefficient by applying formula: \( \beta =\frac{SD(X)}{SD(Y)}b \), where SD(Y) is the standard deviation of the outcome variable while SD(X) is the standard deviation of the police force size variable used in the study. The standard error for beta is obtained by applying formula: \( SE\left(\beta \right)=\frac{SD(X)}{SD(Y)}SE(b) \). If the standard error was not reported, we obtained it from the confidence interval.

  3. 3.

    This is consistent with the results from conventional random-effects model we ran as an exploratory analysis for comparison.

  4. 4.

    We provide a full list of effect sizes with forest plot for 229 findings in Appendix B.


* Denotes a study included in both the systematic review and meta-analysis

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We are grateful to Francis Cullen, Alfred Blumstein, Christopher Sullivan, John Wooldredge, and Aaron Chalfin for their suggestions on our earlier research leading to the current paper. We also wish to thank SooHyun O and Natalie Martinez for helping us with various aspects and comments on this topic. Finally, we owe our gratitude to the referees and editors for their many insightful suggestions. We are particularly grateful to David Wilson for his tough and important comments; they greatly improved the paper.

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Correspondence to YongJei Lee.

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Lee, Y., Eck, J.E. & Corsaro, N. Conclusions from the history of research into the effects of police force size on crime—1968 through 2013: a historical systematic review. J Exp Criminol 12, 431–451 (2016).

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  • Police force size
  • Systematic review
  • Meta-analysis
  • Policing strategy