### Young Republicans and the Liberal Academy

Today I learned that most of the students in my gen-ed class are probably of a somewhat conservative bent. Probably their views don't match up exactly with the louder voices on talk radio, but it seems like they aren't the sorts to donate money to the ACLU.

On Monday we did a bunch of problems in class about false positive rates in medical tests and other similar situations. Typically the way these problems go is that a small fraction of the population is "positive" for a certain attribute (be it a disease or something else) and there is a fallible test. We look at what happens if you test the general population, and we calculate the probability that a positive test means that the person really is positive for the condition. Typically, if the prevalence of the condition is fairly low, the false-positives far outnumber the true-positives, and the chances that you really are positive for the condition is not that great.

One of the examples that we did dealt with drug-sniffing dogs, as described in

Using those numbers, you'll find that if the dog signals that you have drugs, then there is about a 3% chance that you are carrying drugs.

One of the homework questions had the students recalculate this for a 12.5% false-positive rate and a 60% false-positive rate. These numbers give an overall dog-accuracy rate of 1.7% and 7.5%, respectively. As a follow-up it asked whether they believed that a positive dog-sniff should count as probable cause for a search.

Almost every student in my class said yes. They said that they felt that if you had nothing to hide, then you shouldn't mind being searched.

Because of the way that I structure homework assignments in this class, I don't have to assign a point-value to that question. Homework is graded on a 0/1 scale; everyone who makes an effort and turns it in gets full credit. If there was a difference of opinion, maybe we could have a class discussion about it. I suppose that I will quietly take solace in the statistic that young people tend not to vote.

On Monday we did a bunch of problems in class about false positive rates in medical tests and other similar situations. Typically the way these problems go is that a small fraction of the population is "positive" for a certain attribute (be it a disease or something else) and there is a fallible test. We look at what happens if you test the general population, and we calculate the probability that a positive test means that the person really is positive for the condition. Typically, if the prevalence of the condition is fairly low, the false-positives far outnumber the true-positives, and the chances that you really are positive for the condition is not that great.

One of the examples that we did dealt with drug-sniffing dogs, as described in

*Illinois v. Caballes*. The Supreme Court ruled that a positive dog-sniff was probable cause for searching your car. Based on information from the CDC, about 8% of Americans over the age of 12 have used illegal drugs in the past month, so we estimated that about 1% of people were carrying illegal drugs in their car. We also assumed that if you have drugs, that the dog will always find them. Based on Justice Souter's dissent (which said that the false-positive rate for the dogs is believed to be 12.5% to 60%), we assumed that the false-positive rate for the dogs is 30%.Using those numbers, you'll find that if the dog signals that you have drugs, then there is about a 3% chance that you are carrying drugs.

One of the homework questions had the students recalculate this for a 12.5% false-positive rate and a 60% false-positive rate. These numbers give an overall dog-accuracy rate of 1.7% and 7.5%, respectively. As a follow-up it asked whether they believed that a positive dog-sniff should count as probable cause for a search.

Almost every student in my class said yes. They said that they felt that if you had nothing to hide, then you shouldn't mind being searched.

Because of the way that I structure homework assignments in this class, I don't have to assign a point-value to that question. Homework is graded on a 0/1 scale; everyone who makes an effort and turns it in gets full credit. If there was a difference of opinion, maybe we could have a class discussion about it. I suppose that I will quietly take solace in the statistic that young people tend not to vote.