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# Putting Story Structure to Work (page 2)

By John Wiley & Sons, Inc.
Updated on Jan 14, 2011

Using storytelling to teach history seems easy, but can you really use a story structure in a math class? Absolutely. Here's an example of how I introduced the concept of a Z-score—a common way to transform data—when I taught introductory statistics. Begin with the simplest and most familiar example of probability—the coin flip. Suppose I have a coin that I claim is loaded—it always comes up heads. To prove it to you, I flip the coin and it does indeed come up heads. Are you convinced? College students understand that the answer should be no because there is a fifty-fifty chance that a fair coin would have come up heads. How about one hundred heads in a row? Clearly the odds are really small that a fair coin will come up heads one hundred times in a row, so you'd conclude that the coin isn't fair.

That logic—how we decide whether a coin is fishy or fair—is used to evaluate the outcome of many, if not most, scientific experiments. When we see headlines in the newspaper saying "New drug for Alzheimer's found effective" or "Older drivers less safe than younger" or "Babies who watch videos have smaller vocabularies," these conclusions rest on the same logic as the coin flip. How?

Suppose we want to know whether an advertisement is effective. We ask two hundred people, "Does Pepsodent give you sex appeal?" One hundred of these people have seen an advertisement for Pepsodent and one hundred have not. We want to know if the percentage of people in the saw-the-ad group who say it gives you sex appeal is higher than the percentage in the didn't-see-the-ad group who say it gives you sex appeal. The problem here is just like the problem with the coin-flip example. The odds of the saw-the-ad group being higher are around 50 percent. One of the two groups has to be higher. (If they happened to tie, we'd assume that the ad didn't work.)

The logic for getting around this problem is the same as it was for the coin-flip example. For the coin flip, we judged one hundred heads in a row as a highly improbable event assuming that the coin was fair. The odds of a fair coin coming up heads one hundred times in a row are very small. So if we observe that event—one hundred heads in a row—we conclude that our assumption must have been wrong. It's not a fair coin. So the saw-the-ad group being higher than the other group may also not be improbable—but what if that group was much more likely to answer yes? Just as we judged that there was something funny about the coin, so too we should judge that there is something funny about people who have seen the ad—at least funny when it comes to answering our question.

Of course funny in this context means "improbable." In the case of the coin, we knew how to calculate the "funniness," or improbability, of events because we knew the number of possible outcomes (two) and the probability of each individual outcome (.5), so it was easy to calculate the odds of successive events, as shown in Table 1. But here's our next problem: How do we calculate the "funniness," or probability, of other types of events? How much worse does the vocabulary of kids who watched videos have to be compared to that of kids who didn't watch videos before we're prompted to say, "Hey, these two groups of kids are not equal. If they were equal, their vocabularies would be equal. But their vocabularies are very unequal."