Right Wing Nation

Periodically, the topic of teaching statistics in the primary and secondary schools comes up at Kitchen Table Math. I’m torn on the issue. If you’re going to teach something, then do it — that’s the general way I feel about teaching anything. And that’s exactly what they’re not doing in the primary and secondary schools (statistics is more than means, medians, modes, and graphs). On the other hand, kids are coming out of schools without basic arithmetic knowledge, so why waste time on statistics, whether you really are teaching it or not?

However, there are times when something makes me feel nobody should be allowed to graduate from high school without statistics. The new Colgate ad campaign is one of those things.

If you haven’t seen it, they claim on their ads that dental health has been linked to cardiac health (and something else), implying that if you buy Colgate and brush your teeth with it, you won’t keel over dead from a heart attack at age fifty.

That’s crap — and let me show you why.

Let’s say we’ve got this study of 100 test subjects, and two variables for each: dental health index and cardiac health index. The first problem is that both variables are actually groups of related variables. How many times you brush your teeth each day and for how long, whether you floss or not, how many cavities you’ve had, these and other things comprise the dental health index; family history of heart disease, what you eat, how much you exercise and how, these and other things comprise the cardiac health index.

So our data look something like this:

Subject	Dental Index	Cardiac Health Index
1	63	56
2	31	25
3	35	27
97	52	47
98	15	7
99	19	18
100	64	57

We calculate Pearson correlations, and see this:

	Dental Index	Cardiac Health Index
Dental Index	1
Cardiac Health Index	0.99347832	1

Wow, look at that correlation coefficient! There has to be a relationship! Obviously, if you brush your teeth a lot you won’t get a heart attack!

Er, wrong. Because researchers are often academics, and because that old adage about academics’ lacking common sense is more than just a little true, and here because Colgate wants to sell you toothpaste, research sometimes draws bizarre and unwarranted conclusions. Forget statistics. Step back for a minute and ask yourself this: If there is a relationship between dental health and cardiac health, does it make sense to say that brushing your teeth will stop heart attacks?

Of course not, unless there is some dental health gene and some cardiac health gene and the two are somehow linked. So what common sense reason is there for this correlation?

Well, there’s a third variable: How many loads of laundry you do a week. Here is the correlation matrix:

	Loads Laundry per Month	Dental Index	Cardiac Health Index
Loads Laundry per Month	1
Dental Index	0.982919963	1
Cardiac Health Index	0.985634829	0.99347832	1

And fancy that! The correlations between how many loads of laundry you do a week and the dental and cardiac health indices are almost as high as the correlation between the two health indices! Do more laundry and you won’t die of a heart attack!

Ask yourself this: What do people with good dental health, good cardiac health, and who wear clean clothes have in common?

They take care of themselves.

So the next time you see some article or commerical about a study, before you swallow it undigested, step back and apply a little common sense.

I can hear you now. That’s ridiculous. Nobody would make such a claim. Really? How about this, then?

Chew on this next time you’re idling in the drive-thru line: Cars on U.S. roads must burn nearly on billion additional gallons of gas a year because of overweight drivers and passengers. That was the conclusion of University of Illinois computer science professor Sheldon Jacobson, who, with colleague Laura McLay, used a mathematical model to combine federal data on gas consumption and weight gain from 1960 to 2002. They found that the average American’s weight jumped by more than 24 pounds over the period and that as a group, we now pump at least 938 million more gallons a year than we did in 1960. A relative drop in the gas bucket (about three days’ worth of passenger car consumption), but it’s unnecessary. Want to do something today to boost fuel economy? Eat fewer cookies.

Apply common sense liberally. Thanks.