As I leafed through information about
a medical treatment a while back, I was astounded to read that one out of every two thousand patients
with no prior history of heart disease dropped dead while undergoing the treatment, killed by a side-effect
that caused heart complications.
The literature I was reading called this a "rare event." Personally, I firmly
subscribe to the belief that anything "extremely rare" happens
about as often as a meteorite blasting through my roof. But I'm a statistician, not a physician.
So when I read that 1 out of 2000 people died from the treatment itself, those sounded like
scary odds. Then I realized that maybe the odds weren't so scary, if the treatment
was curing something that already was or would soon become life-threatening.
So it made me ask myself: Is something that happens, on average,
1 out of 2000 times a rare event?
It really depends on your perspective.
Statistical "odds" are actually pretty hard to
understand and put into perspective. What does "one in two thousand" really mean? Just how
rare is it? It does sound "rare," doesn't it?
We're expected to make decisions that may profoundly impact our lives
based on our rather fuzzy understanding of what statistical odds mean. So here's a way to
think about these kinds of "odds" that might help when you face situations where someone tells
you that the chances of something happening are "rare."
Let's start with someone saying, "oh, that only happens one time out
of a hundred," or, "there's only a one percent chance of that happening"
(those are the same things, although they can sound very different).
Now, let's translate that into something that makes sense.
We'll use raisins--and rabbits--to help out.
Suppose you have one of those little 1.5 ounce snack-size boxes of raisins.
Those little boxes contain somewhere between 83 and 85 raisins. Yes, I had a friend help me count
them out. I'm a statistician. I do things like that. For our purposes here, sneak about 15
additional raisins out of another box (about a teaspoon's worth) and add them to your snack box.
Now it's nice and full, and contains approximately 100 raisins.
Would you eat that first raisin from a freshly-opened snack box, without
looking, if you knew that one of the raisins inside the box was really a rabbit poop--or,
as an acquaintance calls them, a "rabbit raisin?"
That's what one out of a hundred means. In your unopened little
box of snack raisins ninety-nine of them are real raisins and one is a rabbit raisin.
But let's go back now to that medical treatment warning which led me
to think about all this. The treatment had a "rare" side effect: on average, 1 in 2000 patients
who received the treatment dropped dead. How rare is something that happens only one in two thousand
times? Sounds pretty unlikely, doesn't it?
Well, let's do it with rabbit raisin stats. A smidge less than three
of the standard sized boxes of raisins sitting on the shelf at the grocery store (about two and a half
pounds worth of raisins) contains two thousand raisins. So, doing the math (you don't have
to--I've done it for you), there is one big ol' rabbit raisin lurking in every two and a half
boxes of yummy real raisins.
So the next time someone tells you that "the chances of that happening
are really rare" think about it in terms of rabbit raisins.
It puts it in a whole different light, doesn't it?
By the way, rest assurred that there aren't any rabbit raisins really
lurking inside of boxes of raisins. I'm just using that as an illustration.
Why would I pick rabbits, and raisins and rabbit raisins?
Well, those of us who have raised bunnies or have bunny friends know that
rabbit raisins really
can look very much like real raisins. So it became real easy to imagine an evil rabbit raisin
lurking inside of a bunch of real raisins when I started thinking about this. However, if you've
never seen a real rabbit raisin, you'll have to just trust me on this--they really do look like
raisins. Sort of. OK. Squint.