For Doug Andrews, a little word of mouth from former students has led to statewide advances in the world of criminal investigation.
Known as hypergeometric probability distribution or “hypergeometrics,” Andrews’ statistical sampling approach has not only changed how the Bureau of Criminal Identification and Investigation (BCI&I) conducts its work, it has also improved operational efficiency by saving the state time and thousands of dollars in evidence testing.
Prior to Andrews’ method, all materials confiscated by police that were suspected to be crack rocks or pills with controlled substances required extensive testing.
“They can’t just go to court with that suspicion,” Andrews said. “The materials need to be actually tested to see whether they’re really crack or oxycodone or something illegal or at least controlled, hence the team of forensic scientists.
“However, it can take a lot of time, energy, money and other resources to test every single rock or pill,” Andrews continued. “So the big idea with stat sampling is that you can test a smaller sample of the whole batch, and then make a projection/inference about the whole batch with a certain degree of certainty (beyond a reasonable doubt). And for sentencing purposes, they may not need to establish that all of the rocks are really crack, but just need a bulk amount.”
As such, if the police, for example, found 100 pills upon arrest, they would need to show that at least 60 contained the illegal or controlled substance to get a misdemeanor. With hypergeometrics, Andrews helped the forensic scientists to see that they would actually only need to test nine.
“If all nine tested pills turned out positive (as they almost always do), they can be very confident in their claim that at least 60 of all 100 pills are positive,” he explained. “Here’s the logic: if fewer than 60 of all 100 pills were positive, there would be less than a 1 percent chance that all nine sampled pills would be positive. Therefore, it’s very unlikely that fewer than 60 of the sampled pills are positive in the first place. That is the logic behind the inference from this kind of statistical sampling.”
Getting the BCI&I to incorporate this type of statistical analysis into its testing procedures first required Andrews to test the software being used to ensure that it was doing all the probability calculations correctly. He then conducted training sessions with the forensic science team – mostly chemists who analyze the chemical composition of suspected drugs, but also some ballistics specialists, as well as fingerprinting and handwriting analysts.
After demonstrating the sampling techniques, including the critical role of random selection, and the probability techniques to determine sample size, Andrews worked on getting the scientists’ intuition to the point at which they understood why it all works so they could defend the results with confidence in court.
“That’s where my expertise not only as a professional consulting statistician but as a stat educator was crucial,” Andrews said. “I needed to teach them why they could be at least 99 percent sure that at least 60 of the100 pills are positive, when they only tested nine of them.”
The result of Andrews’ work is that the BCI&I has drastically reduced the number of items tested, which has saved time, money, effort, reagents, and other materials and resources in general. BCI&I has since applied hypergeometrics in the examination of glass fragments as well as to casework audits, one of which included more than 2,000 pieces of evidence. The Ohio State Highway Patrol (OSHP) also recently learned of Andrews’ method, and it, too, has begun to implement the statistical sampling approach.
“I would call the work I did a total success,” Andrews said. “Both the BCI&I and now the OSHP really seem to understand and embrace this stuff, can defend it, and can use it to improve their operations. Plus, I get to share my passion for helping others with statistical expertise.” –Karen Gerboth ‘93