When I was in medical school many years ago I learned a lot and I have probably forgotten even more, but a few things have stuck with me over the years. One was the ice cream study.
In a class on statistics, we were all asked to conduct a statistical study on heat stroke. Being aspiring doctors, we figured it would be appropriate to begin our assignment by looking at how often people are treated in the emergency department for heat stroke.
It was not long before we noted the obvious: Heat stroke was primarily a problem only in the summer. Further, as we dug a little deeper, we noticed that the sale of ice cream seemed to be related to the occurrence of heat stroke — vanilla ice cream in particular. We were on to something.
Eventually, armed with all the data we collected — from the Library, the local emergency room and many Dairy Queens — we rushed back to dutifully apply something we had recently learned in class. It’s one of the top gadgets in the statistician’s tool box: the formula for determining the Correlation Coefficient.
In a nutshell, you fold two variables into the Correlation Coefficient hopper, and out pops a number — called an “r-value” — between zero and one. Anything close to a 1 indicates a pretty serious relationship.
Well, we were delighted. Our data yielded a value of almost 0.9.
“Eureka!” we thought. “Eating ice cream, vanilla ice cream in particular, causes heat stroke!”
We couldn’t wait to get back to class and share this with the professor who, of course, enjoyed the exercise (and the ice cream).
This was a great practical lesson in correlation and causation. Even if one thing correlates to another, this does not mean it is the cause.
To a statistician, the Correlation Coefficient is important, but, when misinterpreted, it can bring misleading results. In our little study, it is the obvious third independent variable — heat — that drives both the incidence of heat stroke and the sale of ice cream on any given day.
Oh, and by the way, vanilla just happens to be the most popular ice cream flavor.
Based on statistics very similar to our Ice Cream Study around the dawn of the new millennium, doctors began prescribing estrogen replacement therapy (ERT) to women approaching menopause to prevent heart disease, stroke, Alzheimer’s and a variety of other conditions. Based on initial studies, the r-value seemed very high between the ERT and prevention of these diseases.
It took about another decade for a more precise study to be completed. The new study revealed that ERT actually can cause many of the problems it was originally prescribed to prevent. Yet, women who took ERT were still healthier in spite of this.
Stumped, researchers concluded that a woman who would make the effort to schedule an appointment with her doctor to discuss any kind of therapy is likely to be an individual who takes better care of herself and is likely to stay healthier as a result (in spite of ERT).
The moral of this tale: High correlation does not point to a cause any more than eating ice cream causes heat stroke.
Remember this the next time you read or hear a news item suggesting that coffee consumption, or vitamins or anything else is correlated with something. Statistical correlation is merely a beginning to a better understanding which, if pursued correctly, can lead to something approaching the truth.
Dr. William Wood is vice president of medical affairs at St. Joseph Healthcare.
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