You may have heard of the bedbugs epidemic in New York. So the other day, a friend relayed the story at her workplace. Bedbugs were found. Dogs were sent in to sniff out the creepy insects. If the dogs detected something in an office, the room is closed off until cleaning is completed. The dogs did not find anything suspicious in her office.
We had a little dialogue. How safe should she feel about the situation? That's when a little statistical thinking could help. The dogs are essentially a detection system like a steroids test or a lie detector test (discussed in Chapter 4), and all such systems are subject to errors. There are two types of errors: false positives and false negatives; and any given system trades off the two errors. The designer of the system calibrates the sensitivity, which in effect is setting the trade-off level between the two errors.
To understand how such a system is calibrated, we need to know who makes the decision and what incentives do the decision maker has. My guess is that the dogs are sent in by the exterminators for a diagnosis of the problem. Exterminators make money if there is a problem. I wouldn't be surprised that these dogs generate a lot of false positives, which means not many false negatives.
In this case, if you are the employee, you would also like the test to generate false positives and not false negatives. The "cost" of the false positive to you is minimal but a false negative might mean you will bring some bugs home. The only people who might not like this calibration are the ones footing the bill for the cleanup, that is, the employer. It is apparently quite expensive. (But perhaps the employer too may favor false positives because there may be legal exposure if a worker thinking her room is clean brings some bedbugs home. If so, I'm not sure why the dogs are needed at all; if everyone agrees on the precautionary principle, then just send in the exterminators!)
On balance, I feel that those declared clean are pretty safe, and many if not most of those declared positive are probably not infected either. (Whether the bedbugs crawl from one room to another is another matter.)
PS. It is possible that for a detection system to generate a lot of errors of both types. Lie detectors is an example of such.
PS. This is a situation where the uncertainty / fear will drive a "market" to over-diagnose and over-spend on a problem. If you run an exterminator business, it is in your interest to drum up as much hysteria as possible over the problem, with the press feeding on sensationalist stories.