by Lynne B. Hare
The thing about uncertainty is you just never know.
Almost 30 years ago, the local chapter of the Institute of Food Technologists invited me, a statistician of all people, to speak at its annual guest night dinner. The plan was to have a brief business meeting followed by dinner and a speaker (moi) followed by an evening at a nearby racetrack.
A statistician after-dinner speaker could be as lethal as botulinum toxin, I thought. Clearly, the incentive to attend the meeting was the trip to the track. What could I do to keep it brief, entertaining and maybe even a little informative?
I went to my friend Joe, who lived near the track and had the look of an experienced bettor. “How does horse racing work?” I asked. “I mean, I know they run around a big oval, but how do you bet? What’s a daily double? A trifecta? What’s this about win, place and show?”
“Where have you been all your life? You’ve got a lot to learn,” he said and proceeded to fill me in.
Armed with Joe’s information, I put together a talk on the odds of winning with selected combinations of bets based on a full field of horses. (You might notice from that last sentence I was starting to feel confident with my use of track terminology.)
At the dinner, I pointed out that if a few horses could be eliminated from the field of true contenders, the odds of making some serious bucks increased substantially, or at least a whole lot. “Using the design of experiments in food product development works a lot like that,” I said. “It increases your odds of developing a winning product.”
The audience, 18 strong, was very polite and listened eagerly for my last words. Then chairs and tables were knocked over as they beat it out the door to the track. At least I didn’t disappoint the people who told me I was going to bomb.
Polly’s Winning Strategy
My wife, Polly, and I had no money, but we were given free passes to the track, so we sat in the stands and watched the ponies. (Notice how I got progressively better with racetrack jargon.) The first race was a source of excitement for many; it ended in joy for a few and disappointment for most. Just as I thought it would.
Right before the second race began, Polly said, “Number five is going to win.” Yeah, sure.
Five won. Must be beginner’s luck, I thought. Then, before the third race, she declared number seven would win, and it did. I said, “Do that again,” and she did.
Not being of yesterday’s litter, I got up and borrowed five bucks (see, more jargon) from my friend Pete. It’s too late to make a long story short, but Polly and I left there with 35 bucks. Not bad, considering we even gave Pete his five bucks back.
At first, I felt bad about focusing my after-dinner speech on the odds and reducing the field as a means of increasing the chances of winning. Clearly, Polly had it all over me and my silly probabilities. Then it occur-red to me that she was actually doing something very similar but from a positive perspective.
She watched the horses during their warmups. “You can tell when one has better athletic abilities than the rest. Just look at the way they move. It’s just like watching the Olympics,” she explained. Rather than eliminating those who were clearly not going to win, she was focusing on the few she thought were most likely to win.
“You can observe a lot just by watching,” said Yogi Berra. That is exactly what Polly was doing. She was watching for something that would not happen just by chance alone. That idea is at the very root of statistical decision making.
Now how could I incorporate that principle into statistical education?
Listen to Your Gut
I often talk to operations people about process variation reduction. They come to the education sessions with the same feelings I have when I’m on my way to the dentist. To ease the pain, I start by showing them they know more about statistical decision making than they think they do.
I choose a volunteer from the audience, usually someone who looks especially timid. “Here’s a quarter,” I say. “Does that look like a normal quarter to you?”
“Ummm … yes.”
“Now, we’ve never met before? And there’s nothing up either sleeve?”
“No” and “no.”
“OK. I’m going to toss this quarter, and while it is in the air I’d like you to guess if it will come up heads or tails. Are you ready?”
“Ummm … yes.”
“You don’t sound like you’re ready. Are you sure you’re ready?”
I toss the quarter and, invariably, my volunteer says nothing. “What part of ‘heads or tails’ don’t you understand?” I ask. Laughter erupts from those who are not on the spot. “Let’s try again.”
I toss the quarter again. The volunteer says, “Heads,” and I say, “You’re right!”
I toss it again. The volunteer says, “Tails,” and I say, “You’re right.”
There’s a murmur in the audience, but I ignore it.
I toss the quarter a third time. The volunteer says, “Heads,” and I say, “You’re right!”
People in the audience start talking about going to Vegas with the volunteer. (Tough talkers never say Las Vegas.)
I toss the quarter a fourth time. The volunteer says, “Heads,” and I say, “You’re right!”
More Vegas talk mixed with a little Atlantic City talk. No racetrack talk, though.
On the fifth toss, I say, “You’re right!” again, and the chatter gets much louder.
“What’s going on?” I ask the audience. “Are you calling this volunteer a liar?”
“No,” they say in unison. “We’re calling you a liar!”
“That’s the point! You know in your gut when something isn’t right. Did you actually calculate the probabilities?” I ask.
“Let’s,” I say. “The chance she guessed right the first time is what?”
“A half,” they all say.
“Right. Now—careful—what’s the chance she’ll guess right on the second toss?”
“A quarter … no, no, a half.”
“Right again. Now tell me what’s the chance she’ll get it right twice in a row?”
“A quarter,” they say with smiles on their faces.
“Three times in a row?”
“Four times in a row? One in 16. Five times in a row? One in 32 and so on. Now some of you are real risk takers; you were ready to act after my second lie, with one time in four that it could have happened by chance alone,” I say.
“None of you actually calculated the probabilities as we went along, yet you knew in your gut something was up,” I continue. “That’s the principle of statistical decision making. You look at something and determine if it could have happened by chance alone. If not, you say, ‘That dog don’t hunt!’ and take appropriate action.”
They always get it.
In statistics, the math is a bit more sophisticated, but the principle is the same. It helps you cut through ever present uncertainty to make sound decisions. And, of course, as I said at the beginning, the thing about uncertainty is you just never know. For sure.
LYNNE B. HARE is program director of applied statistics at Kraft Foods Research in East Hanover, NJ. He received a doctorate in statistics from Rutgers University, New Brunswick, NJ. Hare is a past chairman of ASQ’s Statistics Division and a Fellow of both ASQ and the American Statistical Assn.