## Monday, September 7, 2009

### Inferences can be deceiving

Watching TV can make you act smarter. All it takes is thinking as you watch. For instance:

A car insurance company boasts that "customers who switched to [the insurance company] have saved an average of $ManyBucks." I'm sure that's true, and I'm sure many people make the wrong inference. The wrong inference to make is that [the insurance company] has lower premiums than its competitors. Significantly so, given the average savings of$ManyBucks.

The right inference is: well, duh! Switching insurance companies is effortful; only people who save a significant amount are likely to switch. Thought experiment: would you switch insurance companies for $1/yr? What about$10/yr? What about $100/yr? What about$1000?

Failing to see that the advertised savings come from a sample that self-selects on those same savings, some people infer --- incorrectly --- that [the insurance company] must be cheaper. (This is an example of what statisticians call sampling on the dependent variable.)

This works to the advertiser's advantage mostly when people are buying new insurance rather than switching. After all, the switchers will know whether it makes sense to switch, but the new buyers may just use their perceptions to base their decisions.

As I said in the title, inferences can be deceiving.