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Lesson: What’s Normal?

This lesson is about the idea of “normal.” Of course, normal has a different meaning in statistics than it does in everyday language. We’re contrasting the two in the context of a large data set on births in the US in 2014. In particular, this lesson focuses on the age of the mother at the time of the birth of her baby.

The idea for this lesson came out of the StatPREP faculty development workshop at St. Kate’s University in Saint Paul, Minnesota, held in June 2017. A group of faculty were impressed by how easy it is, with the software in the ggformula package used in StatPREP, to quickly look through a lot of data.

More of that group’s ideas will appear in future lessons. For this first one, we decided to entirely eliminate software commands from the tutorial. Instead, the students use sliders to display their own opinions about what constitutes “old” or “young” for a pregnant mother.

The distribution of ages is almost bell-shaped: it’s a little skew left corresponding to the surprisingly young age of some mothers. Students overlay the normal-distribution approximation and then answer questions about the extent to which the approximation is a good one.

Some discussion questions

  1. Where is the normal approximation poor? What does this correspond to in terms of the sociology of pregnancy.
  2. It’s conventional with the normal approximation to consider as unusual or surprising or even “abnormal” values outside of the interval plus-or-minus two standard deviations. How well does this convention match the students’ own judgement about what constitutes being unusually young or old during pregnancy?
  3. Just because the approximation is called “normal” doesn’t mean that it is a good definition of normal versus abnormal in practice. What other names are used for the distribution to avoid the implication of judgment contained in the word “normal?”
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