Back from vacation today and greeted by a Chicago Tribune headline with a beautiful example of how to badly confuse people with numbers. Now I wish I hadn’t skipped my “how to lie with statistics” lecture in 205 last quarter since this is the main trick I talk about. The short form: if somebody is explaining something to you as a percent change on a rate statistic, hold on to your wallet because you are probably being conned.

The headline was: “75% tax increase proposed” which on the online version is, “Democratic lawmakers push 75% state income tax increase” which at least makes it clear it’s about state income tax while also tipping the political-point being made by the right-leaning trib (Dems raise your taxes, beware!).

I wonder how many people read the headline and think the state is proposing a 75% income tax rate?  Nobody is used to thinking of percent change on a rate and they often confuse which rate is being affected.  If you know something about Illinois state taxes, you know the current state income tax rate is 3%.  The current proposal is to raise that to 5.25%.  Is that a 75% increase or a 2.25% increase?  Yes to both actually and how you describe it depends on how you want people to react to the statement.

You can’t really win here.  If you describe the rate increase as a 2.25% increase, most readers won’t realize that if they paid $1,000 in state tax last year, they will have to pay $1,750 this year — which is a bigger difference than “+2.25%” implies.  OTOH, a “75% increase” is going to be read as a 75% rate by a decent fraction of the readers who are probably going to think the gov’t is potentially about to confiscate virtually all their wages.

Innumeracy is a problem.  Given how many otherwise smart people either avoid math or are bad at it, it’s not at all clear how one would effectively communicate basic facts about budgetary issues, medical risk factors or other kinds of rate information.

BTW, one of the games you are playing with the rate-of-rate statement like “75% increase” is that the rate being changed isn’t in the headline.  I guessed it was the state income tax, but I actually looked at the article to see if they meant sales tax.  In IL, sales taxes can run to 11.5% and a +75% rate increase would be pretty noticeable.  Base rates are important.  “Doubling your risk of heart attack” isn’t so bad if your base rate is 1 in a million.  It’s pretty grim if it’s one in 10, though.