By Bobby Neal Winters
“Hey, Doc,” I heard the voice from across the restaurant. I thought the voice was familiar, but as I looked up from my barbecue ribs to the direction whence it came, I didn’t recognize it. I must have looked confused because I heard the voice again, and this time I saw who was speaking.
“Hey, don’t you recognize me?” the woman in her mid-thirties said. “I must have really gotten old.”
It is always so cute to hear 35-year-olds say that. But after subtracting a minor amount of gray from her hair and an inch or two of width from her face, I did know her.
One of the great joys that a teacher has is keeping in contact with former students. Not all of them, you understand, but certain ones do bring us a great deal of joy. Such is the case with my former student Marge Anovarra.
Marge was not a math major. She was a Communication major from Krebs, Oklahoma. She was a proud Italian and a proud Okie. Pride isn’t rare in either of those races, but it is rare to see the Italian and the Okie combined. The reason it is combined in her case is the same reason that she chose to come to my university: mining.
It is little known that there has been coal mining in both Southeastern Kansas and Eastern Oklahoma. The Italians immigrated to both places to take part in that. Marge came to my university because it allowed her to take part in her Italian cultural it a place that was not home but like home and not terribly far from home. And, as one might expect, after she finished her university degree, she moved back home.
She now practices her talents as a journalist and free-lance writer throughout the region and is successful.
She first caught my attention in class when I was calling roll on the first day. With a name like Anovarra, I assumed she was a local and started joking with her. I told her that we would learn more about her during class when we started talking about confidence intervals and the margin of error. The class laughed, but afterwards she approached me an explained in very serious tones.
I was informed that her last name had been changed when her ancestors came to this country. The folks who’d registered them had been in a hurry and when her great grandfather was asked his last name, he’d stuttered.
Thus the last name preserved that error from that time onward.
When we did get to margin of error, Marge—and that was her first name, not Margaret—did like it. She liked the entire practical turn of statistics. It’s based on the idea that even if you can’t know something for sure that shouldn’t keep you from trying your best.
The concept of margin of error first occurs in the calculation of confidence intervals of the mean. The idea is that you want to know the average of some number associated to a group of objects, such as the average shoe size of everyone on our campus. This is not information that our admissions people ask for, so if we really want to know this, we would either
1) phone everyone on campus and ask, “What’s your shoe size?” and listen to approximately 7000 phones slam in our ears, or
2) take a sample and use the sample to find an estimate.
The latter course is simpler and less expensive. The idea is that a random sample of a group—a population being the technical term—models that group. The average on that sample should be close to the average of the whole group. There are ways this could go badly wrong. You could choose only to sample from the men’s basketball team who would have larger feet than the typical folks on campus; or you could choose to sample only the female gymnasts, who would tend to be smaller than typical. But the idea is that a randomly chosen sample will, for the most part, yield an average closer to that of the group.
It needs to be noted that the average of the sample will tend to be close to the average of the population, but it will almost certainly be wrong. It is for this reason that statisticians give themselves some leeway: the Margin of Error.
So you start with the average of the sample and you know that you are wrong. Your average might be too big, so you subtract the margin of error from the sample average; your average might be too small, you add the margin of error to the average of the sample. After all this, you still might be wrong, but the probability that you are correct is called the level of confidence.
You calculate the margin of error with this level of confidence in mind. So estimating the average shoe size of campus won’t give you a single number. It will give you an interval of numbers and you still have a small chance of being wrong.
That appealed to Marge’s practical nature, and it all came back to me in a flash, a microscopic fraction of the time it has taken me to relate it to the reader.
“Marge,” I said, not disguising the joy I felt in seeing her after an interval of 15 or 20 years. (I have to leave myself a margin of error you understand.) I invited her to join our table when we were sampling not only ribs but brisket and pulled port.
“It’s great to see you,” I said after she placed her order. “I understand you are a journalist now.”
“That’s right,” she said. “I write for a few papers and do some freelance work. Right now I am working on a piece for the Morning Ritual. The Morning Ritual is the house publication of a health food company that encourages the consumption of bran. The company is a sole proprietorship, owned by a militant vegan.”
After she ordered burnt ends, she then went on to explain that she’d been approached to do an expose of the barbeque restaurants in the region. The editor had approached her with shocking news.
“Almost half of the barbecue places in the region serve road kill,” he’d said in serious tones.
The research she’d done in preparation for her article didn’t bear that out. Out of a sample of 143 restaurateurs, 51 of them said that they had served road kill. She’d done the calculation and that had only worked out to 35.7 percent.
“That seems awfully high, but it’s not close to half,” she said. “I remember you teaching about margin of error, but I’ve forgotten how to apply it here.”
My family looked strangely at their plates.
I, on the other hand, took out my pen and did a little figuring on the napkin. Then I called the waiter over to borrow a calculator. I figured that the margin of error was 7.8 percent. This meant that the fraction of restaurants serving road kill was between 27.9 and 43.5 percent with 95 percent confidence.
“What might’ve happened,” I said, “was that someone looked only at that upper part of the estimate and rounded it to 44 and from there it’s not so hard to say almost half.”
This isn’t a very ethical way to present that particular data, but looking at the other end of the confidence interval is awfully disturbing too. It is saying that over one-fourth of the barbecue restaurants serve road-kill.
“Where was this survey taken?” I asked.
“It was at a barbecue festival,” she said. “But I see where you are going. I will do a little more digging to find the particulars. Thanks.”
She then finished up her burnt ends and excused herself. I gave her my business card with my e-mail address on it as she left, asking her to keep me filled in. It was a week before I got an e-mail from her.
It turns out that it wasn’t clear these people were restaurant owners at all. They were simply people that attended a barbecue festival catering to people who cooked wild game. The survey was administered at a workshop entitled “Using a dark sauce to cover tire tracks.”
“That kind of explains it,” she wrote. “I wasn’t able to use the data, but digging to get to the bottom opened up a whole new subculture that I was able to write about.”