SUMMER 2013 415 THE NEED TO CAREFULLY INTERPRET THE STATISTICS REPORTING THE ACCURACY OF A NARCOTICS DETECTION DOG: APPLICATION TO SOUTH DAKOTA V. NGUYEN, STATE OF FLORIDA V. HARRIS AND SIMILAR CASES Joseph L. Gastwirth* ABSTRACT: Before searching people or property, police need “probable cause.” In United States v. Place, the Supreme Court held that dog sniffs of vehicles, stopped for lawful purposes, are not a search. Lower courts have held that a positive alert by a trained narcotics dog can establish probable cause for a search of the car. Many courts use the fraction of positive identifications in which drugs were found to assess the reliability of the dog, and thus to decide whether the alert established probable cause. In the medical test literature, this summary statistic is called the predictive value of a positive test (PVP). By itself, it does not measure the accuracy of the sniffs or medical test. There are two components to assessing the accuracy of a dog sniff or test. These are the probability that the dog sniff correctly classifies an item containing contraband as having it and the probability the sniff correctly exonerates an item not containing contraband. The PVP depends on both these probabilities and on the prevalence of contraband in the places the dog has examined. The same PVP can arise when (1) an accurate dog sniffs items with a low prevalence of contraband and (2) a much less accurate dog examines items with a high prevalence of drugs. It is mathematically impossible to estimate the two accuracy rates of a narcotics dog from the field perfor- mance data typically submitted by the state to show the narcotics dog is reliable. The problem arises because one needs three equations to estimate the prevalence and the two accuracy rates but the data only provide two. These issues will be illustrated on data from cases. Furthermore, the number of test sniffs in many certifications is too small to provide a statistically reliable measure of the dog’s accuracy and the preva- lence of drugs in the items sniffed is usually at least 50%. Rather than continuing to rely on an inappropriate measure of the accuracy of dog sniffs, courts should require more information concerning the accuracy of dogs in their training sessions, certifica- tions, and in the field. In conjunction with obtaining better information on the preva- lence of drugs in commonly occurring settings—such as vehicles stopped for routine traffic violations or items examined after police have received a “tip”—having access to dog accuracy rates would provide the legal system with sufficient information to estimate both measures of accuracy of a narcotics dog and its PVP, which would assist courts in determining whether the police had probable cause. *Department of Statistics, George Washington University (jlgast@gwu.edu). Acknowledgements: It is a pleasure to thank Professor Edward K. Cheng, Professor David H. Kaye, Dr. Barry I. Graubard, and two anonymous reviewers for many helpful comments and suggestions and Drs. Kristen Meier and Gregory Campbell of the FDA for providing the updated guidelines for evaluating diagnostic and screening tests.