On Tuesday morning, I heard a piece on Morning Edition about human bias and drug-sniffing dogs. Sometimes there is the Clever Hans effect. Sometimes the person really wanted to find something, so the person decided to intepret the dog’s behavior as a signal. Sometimes the dog would signal when there were no drugs. (I will not speculate about dogs’ motives.)

Were I still teaching college students – or if I were still teaching in an environment in which long contextual tangents were part of the schtick – I would add this to my repertoire for the Bayes Theorem unit. For those who don’t know Bayes Theorem, what it pretty much comes down to is that if the rate of true positives is less than the rate of false positives, then most of your positive results are going to be false positives.

Say what you will about “Math across the curriculum” initiatives, I really like this problem, especially for college students. When it comes to probability problems, most students are not going to do math at a casino. And the casino-math is pretty boring: it says that if you are going to Vegas just to have fun, you are pretty likely to lose money. But these days everyone on Facebook is a Constitutional scholar! You can entertain yourself for hours arguing about the Fourth Ammendment with strangers. Also, you might know someone who has been stopped by cops for some less-than-justified reason.

And that brings us to the Supreme Court. Over 10 years ago, in my teaching heyday, the Supreme Court ruled on Illinois vs. Caballes. Roy Caballes was stopped by police for some reason. A drug-sniffing dog signalled that there were drugs in the car. His car was searched, and the police found drugs. Caballes argued that the dog-sniff was a search under the Fourth Ammendment and required probable cause. The state argued that the dog-sniff was not a search and not subject to Fourth Ammendment scrutiny, but that it could establish probable cause for a search.

The arguments tend to stay pretty constitutitonal. Is a dog-sniff a search? What are your rights with respect to contraband?

And Justice Scalia gets into the Bayes Theorem side of things, noting:

I mean, surely you’d concede that the search is unreasonable if, for every – every one time, you – you make somebody open his bag because the dog actually smells narcotics, 99 times you make somebody open his bag because he has apples in it.

But the reliability of the dog is not at question in this case, as the attorney for the state points out:

You do not have the probable cause question before you. This dog was determined to be reliable by the trial court and the Illinois Appellate Court, and it was not part of the Illinois Supreme Court’s decision.

So Bayes Theorem did not make its way into the Supreme Court at the time.

I would be interested in seeing the reliability rates for the dogs being certified in the program described in the radio piece as well as their reliability in the field.

Technology note: To those who are reading this blog via the RSS feed (which might only be me at this point), every time I change certain general settings for the pages, the entire feed republishes itself. Apologies in advance for any annoyance.