Causality

Drivers who switched ... saved an average of [X dollars] a year

This popular insurance commercial carries a clear subtext: if you change your insurance provider, you will save money. But is this really the same as "changing insurance saves you money?".

Causality is an import concept, which is often critical in understanding economic analysis. To give an anecdotal example, the sun rises 1 hour after I wake up, but this doesn't mean me waking up makes the sun rise. Sure, there is a correlation between two events, but that doesn't necessarily have any strong inferences about their causality.

But back to the insurance example: those who switch insurance surely save money. If they weren't about to save, they wouldn't have switch to boot. So this is more or less stating the obvious. But drivers are different, and so are the policy packages offered. Therefore picking a a number of drivers at random, and switch their insurance might provide surprising average results.

And, of course, the above slogan would be different even if the sample size of drivers who switched is just two, but then again -- advertising is often designed to be catchy and not necessarily informative.