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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?”

Comments from you

Please make comments below in the Leave a Reply box of things you liked about the lesson, things that went well or not well, what you tried, and things that could be different. Comments are visible to everyone who views this site. Your comments can help others implement the lessons and help the StatPREP team improve the lessons.

5 Comments Post a comment
  1. Joe Roith #

    I did this lesson in class last week and overall I think it was a success, but definitely had some of my own issues. First, what went well:

    I think the students really did like having the real, big dataset to think about. We certainly got into some interesting discussions about the cutoffs for too young/too old to be a mother. It really seemed to hold their attention well. They could easily see the resemblance of the real data to the classic distribution, along with the areas it doesn’t fit as well. We ended up having our cutoffs very close to the empirical rule as well. I used this strictly as an introduction to the Normal model in my class. It did not conflict at all with my “normal” lesson plans and lectures. Although, ideally, I will incorporate more real data into my lessons to start replacing my old lessons.

    Where I saw room for improvement:

    A lot of the issues or awkwardness I experienced stemmed from my own familiarity with the lesson. Having not written it myself, and not taught it yet, I stumbled with jumping the gun on key ideas or moving past something too quickly. This could have been easily remedied if I had done a better job going through the material beforehand. I also took a lot of time deciding if I wanted to let my students complete this lesson individually or to do it as a class. The structure is better set up for individual, but I was wary of the ability of everyone to grasp the concepts. I ended up doing it in more of a lecture style with students following along on their computers. It went fairly well, even with the stumbles mentioned, but I found myself skipping over some of the descriptive parts of the lesson so I wasn’t simply reading a screen. I am still wary about individual work, but am confident that I could guide my classes through it.

    Overall I thought the content was great and I love the structure of the lessons. I am working on converting some of my own worksheets into the interactive lessons and it is a lot of fun!

    February 28, 2018
  2. Mark Ahrens #

    I used this lesson with an Intro Stats class at Normandale CC. The students had already covered the Normal distribution in class and so were familiar with the Empirical Rule and unusual values.

    The value of the lesson to me, which we covered in detail in the post discussion, was the use of a theoretical Normal distribution to model real, somewhat irregular data. I think the students (and me) thought that the lesson did this very well. I also think that the topics chosen were well thought out, and the time it took to read, do and discuss, was just about right.

    By the way, I had about 30 students that day, and we kept getting disconnected from the server – often nearly all of us at once. It did become frustrating and some students simply stopped doing the lesson. Also, when I previewed the lesson I had had some difficulty with the “Next Topic” and other buttons working in Chrome ; one student (and only one) had the same problem in class. Interestingly, no one else did.

    Keep up the good work. I will be trying other lessons soon.

    March 2, 2018
  3. Anne Nelson Fisher #

    I used this lesson twice in the past couple of weeks at Central Lakes College, first with Intro to Statistics and then with a Concepts in Math (liberal arts math) class.

    I would echo many of the comments that Joe made above. I was a bit shaky with the presentation the first time through it, but it went more smoothly the second time, and in both classes we certainly had great discussions about “young” and “old” mothers. Both groups did end up choosing points that were very close to the empirical rule. As Joe also noted, the lesson is set up for more individual reading than classroom presentation, but not having used it before, I wanted to see how students reacted to it in class.

    March 7, 2018
  4. Kathryn Kozak #

    Thank you Joe, Mark, and Anne. Would it be helpful to have a webinar to talk about using this lesson in your class prior to the start of next semester? Would it help to have something written on how to best use it in your classes, or do you think each teacher may have their own style?

    April 1, 2018
  5. Kathryn Kozak #

    Thank you Joe, Mark, and Anne. Would it be helpful to have a webinar to talk about using this lesson in your class prior to the start of next semester? Would it help to have something written on how to best use it in your classes, or do you think each teacher may have their own style?

    April 1, 2018

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