The Annals of Applied Statistics

Precinct or prejudice? Understanding racial disparities in New York City’s stop-and-frisk policy

Sharad Goel, Justin M. Rao, and Ravi Shroff

Full-text: Open access


Recent studies have examined racial disparities in stop-and-frisk, a widely employed but controversial policing tactic. The statistical evidence, however, has been limited and contradictory. We investigate by analyzing three million stops in New York City over five years, focusing on cases where officers suspected the stopped individual of criminal possession of a weapon (CPW). For each CPW stop, we estimate the ex ante probability that the detained suspect has a weapon. We find that in more than 40% of cases, the likelihood of finding a weapon (typically a knife) was less than 1%, raising concerns that the legal requirement of “reasonable suspicion” was often not met. We further find that blacks and Hispanics were disproportionately stopped in these low hit rate contexts, a phenomenon that we trace to two factors: (1) lower thresholds for stopping individuals—regardless of race—in high-crime, predominately minority areas, particularly public housing; and (2) lower thresholds for stopping minorities relative to similarly situated whites. Finally, we demonstrate that by conducting only the 6% of stops that are statistically most likely to result in weapons seizure, one can both recover the majority of weapons and mitigate racial disparities in who is stopped. We show that this statistically informed stopping strategy can be approximated by simple, easily implemented heuristics with little loss in efficiency.

Article information

Ann. Appl. Stat., Volume 10, Number 1 (2016), 365-394.

Received: January 2015
Revised: September 2015
First available in Project Euclid: 25 March 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Criminology discrimination racial profiling risk assessment Fourth Amendment


Goel, Sharad; Rao, Justin M.; Shroff, Ravi. Precinct or prejudice? Understanding racial disparities in New York City’s stop-and-frisk policy. Ann. Appl. Stat. 10 (2016), no. 1, 365--394. doi:10.1214/15-AOAS897.

Export citation


  • Antonovics, K. and Knight, B. G. (2009). A new look at racial profiling: Evidence from the Boston police department. Rev. Econ. Stat. 91 163–177.
  • Anwar, S. and Fang, H. (2006). An alternative test of racial prejudice in motor vehicle searches: Theory and evidence. Am. Econ. Rev. 96 127–151.
  • Arrow, K. (1973). The theory of discrimination. Discrimination in Labor Markets 3 3–33.
  • Ayres, I. (2002). Outcome tests of racial disparities in police practices. Justice Research and Policy 4 131–142.
  • Bach, F. R., Heckerman, D. and Horvitz, E. (2006). Considering cost asymmetry in learning classifiers. J. Mach. Learn. Res. 7 1713–1741.
  • Becker, G. S. (1993). Nobel lecture: The economic way of looking at behavior. J. Polit. Econ. 101 385–409.
  • Becker, G. S. (2010). The Economics of Discrimination. Univ. Chicago press, Chicago, IL.
  • Berk, R. (2012). Criminal Justice Forecasts of Risk: A Machine Learning Approach. Springer Science & Business Media, Berlin.
  • Bottou, L. (1998). Online learning and stochastic approximations. On-line Learning in Neural Networks 17 9–42.
  • Coviello, D. and Persico, N. (2013). An economic analysis of black–white disparities in NYPD’s stop and frisk program. Available at
  • Czerlinski, J., Gigerenzer, G. and Goldstein, D. G. (1999). How good are simple heuristics? In Simple Heuristics That Make Us Smart 97–118. Oxford Univ. Press, Oxford.
  • Daniels et al. v. the City of New York (2001). 198 F.R.D. 409, 411, 422, S.D.N.Y.
  • Davis v. City of New York (2013). No. 10 Civ. 0699.
  • Diggle, P. (1985). A kernel method for smoothing point process data. Applied Statistics 34 138–147.
  • Eberhardt, J. L., Goff, P. A., Purdie, V. J. and Davies, P. G. (2004). Seeing black: Race, crime, and visual processing. J. Pers. Soc. Psychol. 87 876–893.
  • Epp, C. R., Maynard-Moody, S. and Haider-Markel, D. P. (2014). Pulled over: How Police Stops Define Race and Citizenship. Univ. Chicago Press, Chicago, IL.
  • Ewens, M., Tomlin, B. and Wang, L. C. (2014). Statistical discrimination or prejudice? A large sample field experiment. Rev. Econ. Stat. 96 119–134.
  • Fagan, J. and Geller, A. (2014). Following the script: Narratives of suspicion in Terry stops in street policing. Columbia Public Law Research Paper 14-410.
  • Fernández-Delgado, M., Cernadas, E., Barro, S. and Amorim, D. (2014). Do we need hundreds of classifiers to solve real world classification problems? J. Mach. Learn. Res. 15 3133–3181.
  • Floyd v. City of New York (2013). 959 F. Supp. 2d 540, S.D.N.Y.
  • Gelman, A., Fagan, J. and Kiss, A. (2007). An analysis of the New York City Police Department’s “stop-and-frisk” policy in the context of claims of racial bias. J. Amer. Statist. Assoc. 102 813–823.
  • Gigerenzer, G. and Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychol. Rev. 103 650.
  • Goeman, J. J. (2010). $L_{1}$ penalized estimation in the Cox proportional hazards model. Biom. J. 52 70–84.
  • Grogger, J. and Ridgeway, G. (2006). Testing for racial profiling in traffic stops from behind a veil of darkness. J. Amer. Statist. Assoc. 101 878–887.
  • Illinois v. Wardlow (2000). 528 U.S. 119.
  • Knowles, J., Persico, N. and Todd, P. (2001). Racial bias in motor vehicle searches: Theory and evidence. J. Polit. Econ. 109.
  • Kyung, M., Gill, J., Ghosh, M. and Casella, G. (2010). Penalized regression, standard errors, and Bayesian lassos. Bayesian Anal. 5 369–411.
  • Legewie, J. (2016). Racial profiling in stop-and-frisk operations: How local events trigger periods of increased discrimination. Am. J. Sociol. To appear.
  • Lerman, A. E. and Weaver, V. (2014). Staying out of sight: Concentrated policing and local political action. Ann. Am. Acad. Polit. Soc. Sci. 651 6–21.
  • Ligon v. City of New York (2013). No. 12 Civ. 2274 (SAS).
  • Lovie, A. D. and Lovie, P. (1986). The flat maximum effect and linear scoring models for prediction. J. Forecast. 5 159–168.
  • Michigan Dept. of State Police v. Sitz (1990). 496 U.S. 444.
  • Milgram, A., Holsinger, A. M., Vannostrand, M. and Alsdorf, M. W. (2015). Pretrial risk assessment: Improving public safety and fairness in pretrial decision making. Federal Sentencing Reporter 27 216–221.
  • Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. J. Mach. Learn. Res. 12 2825–2830.
  • Persico, N. (2009). Racial profiling? Detecting bias using statistical evidence. Annual Review of Economics 1 229–254.
  • Ridgeway, G. (2006). Assessing the effect of race bias in post-traffic stop outcomes using propensity scores. J. Quant. Criminol. 22 1–29.
  • Ridgeway, G. (2007). Analysis of racial disparities in the New York Police Department’s stop, question, and frisk practices. Rand Corporation.
  • Ridgeway, G. and MacDonald, J. M. (2009). Doubly robust internal benchmarking and false discovery rates for detecting racial bias in police stops. J. Amer. Statist. Assoc. 104 661–668.
  • Rudovsky, D. and Rosenthal, L. (2013). Debate: The constitutionality of stop-and-frisk in New York City. U. Pa. L. Rev. Online 162 117–117.
  • Terry v. Ohio (1968). 392 U.S. 1.
  • Ustun, B. and Rudin, C. (2014). Methods and models for interpretable linear classification. Preprint. Available at arXiv:1405.4047.
  • Wilson, J. Q. and Kelling, G. L. (1982). Broken windows. Atlantic Monthly 249 29–38.