## How to Lie with Statistics

by Stanley Erickson

Hidden in a dark corner of each major auto insurance company is a statistician or two whose job is to make calculations about the drivers who insure with the company. One way to make profits for the company is to employ statistics in a less-than-thorough manner. This article gives an example of how statistics can mislead.

Suppose we lived in a world where all drivers were equally capable of driving and equally capable of avoiding accidents and tickets. Let's simply suppose that some drive further each month than others, for commuting, shopping, visiting relatives, or whatever. Suppose there were a few who drive as little as 3,000 miles a year, and some, like professional drivers, who drive up to 50,000 miles a year.

Suppose that a zealous insurance CEO asks his statistician if drivers with two or more tickets in a three-year period were more likely to have an accident.[1] He would soon report back that drivers with two or more tickets have almost twice [2] the chance of having an accident.

Wow! Twice the accident rate! What fools! The CEO might think that by hitting these guys with higher premiums, he might make them think about their careless driving habits. Maybe it will teach them a lesson. The company can make quite a bit more profit, as other insurers are not going to try and steal the worst drivers away. Furthermore, the state motor vehicle departments start thinking about taking away these driver's licenses. Everybody thinks that these guys have to be gotten off the road before they kill themselves or someone else. Unfortunately, they aren't careless drivers. According to the assumptions, they are equally good at driving as everybody else. The statistics lied. The difference in mileage exposure alone is enough to produce a strong correlation between tickets and accidents.

You are probably thinking that even a closeted statistician can figure out that mileage alone is the key to the connection between tickets and accidents. All he would have to do would be to look at the mileage figures that the premium payers put down and see if that explains it. Regrettably, when Customer Joe looks at that blank space for mileage on the insurance application, he likely realizes that if he is a high-mileage driver and he puts his real mileage down, the company is going to bill him more. So he shades his mileage, perhaps putting 15,000 miles where 30,000 should be. Eighty-year-old Priscilla, who hardly ever drives, doesn't want to put down 2,000 miles as she is afraid the company will think she doesn't have enough practice to keep driving safely, so she puts down 6,000. Nobody checks Joe s or Priscilla s odometers. Furthermore, most companies don't update their mileage figures annually so that someone whose driving pattern changes might not be noticed by the company at all. Simply stated, the mathematician has no chance of figuring out the mileage connection he doesn't have good data. So when he tells the CEO that he has checked out this possibility, and as far as he can tell, the connection is not all due to mileage, he's right according to his numbers, but wrong according to the world.

This is probably the simplest statistics foolery that makes tickets look like they mean something that they don't. Regrettably, both the motor vehicle departments and the insurance commissioners of the states haven't quite realized that they are dealing with a complicated situation and bad data.

1. Don't forget, all drivers are equally good, but some have more exposure to accidents and tickets because they drive more.
2. Depending on the distribution of high mileage and low mileage drivers, the actual ratio ranges from about 1.6 to 1.9 for this simple example.

Source: January/February 1995 NMA NEWS.