Math Geek Mom: How to Li[v]e with Statistics
There is a commercial for some over the counter medicine that talks about “Dr. Mom.” Already being “Dr. Mom”, in the sense of “Mama, Ph.D.”, it is interesting to stop and realize that we are as mothers also asked to assemble information and make decisions on medical issues on a daily basis. From the initial weighing-in of an infant that is given in percentiles to the lawyer voice at the end of many drug commercials, we quickly realize that taking care of a family’s health is no simple matter. To do this often requires a working knowledge of statistics as they relate to medical issues.
There is a commercial for some over the counter medicine that talks about “Dr. Mom.” Already being “Dr. Mom”, in the sense of “Mama, Ph.D.”, it is interesting to stop and realize that we are as mothers also asked to assemble information and make decisions on medical issues on a daily basis. From the initial weighing-in of an infant that is given in percentiles to the lawyer voice at the end of many drug commercials, we quickly realize that taking care of a family’s health is no simple matter. To do this often requires a working knowledge of statistics as they relate to medical issues. Just what these statistics say is not always clear, bringing back memories of a 1954 classic book called How to Lie with Statistics (Huff, 1954).
A colleague recently forwarded an article to me about statistical literacy in the U.S. and the importance of having a public who understands statistics when they deal with medical issues (Gigerenzer, et al, 2008). This article suggests several changes in how health statistics are presented so that they may be better understood by the public. These include asking the medical community to use frequency statements (of 10 children vaccinated, 8 showed some sort of reaction within two days) rather than single event probabilities (there is a 80% chance of having some reaction to the vaccine), moving from survival rates to mortality rates and requiring more education for physicians in communicating about statistics to patients and their caregivers.
I teach statistics every semester and at least once a summer, and I constantly have students who resist the idea of learning statistics. They come in calling it “sadistics” and saying that other people have told them that it is the WORST class they will ever take. Right from the beginning, I need to fight this attitude and engage them in learning. I will begin a new section of this class in only a few days, so I am once again thinking of how to encourage students to study this subject.
One way I try to do this is to point out how statistics and probability can help us see the world in a different way. For example, probability tells us that, in a group of 23 people, there is more than a 50% chance of having two people who share the same birthday. This is because all of the people in the world share only 365 birthdays. Therefore, the chance that two people who just meet share the same birthday is 1/365. When that same person meets many people, the chance that one of them will share their birthday becomes larger. Put a bunch of people in a room all searching for a “birthday buddy” and the odds of having at least one match will reach more than 50%.
If you teach a class with 23 or more students in it, you might want to test this for yourself. Take a minute and ask each one for the month and day of their birthday, and see if you have any matches. In about fifteen years of doing this, I have found matches most of the time, and that is not even including the times I have had twins in my classes.
Because of the rather large probability of a match in the group of 23, I usually bet against there being no matches when I do this with my classes. I tell them that if there is no match, then there will be no homework that evening. I then proceed to see if there are any matches in January, February, etc. Yes, our students are honest about this, although a few have noted that there is an incentive to lie, which sometimes gets me off topic with a short discussion about game theory.
One year, there were no matches in a class of more than 25 students, and I left perplexed. I went on to my next class, a small, upper division class of only five students. Before class, I mentioned to them that I was surprised that there were no matches in my previous class. One student suggested we see if there were any matches among the five of them. Sure enough, in that group of only five students, there was a match!
I often tell my students in my introductory classes that they should take a course in statistics, no matter what their intended major. If that major is nursing or pre-med, I am all the more persuasive. This is more than just me advertising for my elective classes. No matter what we do with our lives, a knowledge of statistics will help us to become more educated voters, more productive employees, and, of course, better “Dr. Moms”.
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