Chapter 14 Getting started in your classroom

To start incorporating the Compact approach to your class, you might:

  1. Start the course in the usual way.
    1. Move through the topics you like up through the confidence interval on a mean and proportion.
    2. DON’T do hypothesis testing yet.
    3. Additional topic: Try to introduce the variance along with the standard deviation. There’s a nice explanation in Chapter 3 that you might find helpful.
    4. Additional topic: Demonstrate that calculating a proportion is the same as calculating the mean of an indicator variable.
  2. Use models rather than “two sample” or “differences.”
    1. Present actual data in a response variable vs explanatory variable format.
    2. Use the Point Plot Little App to make graphics with both categorical and quantitative response and explanatory variables.
    3. Project such plots on the board or print them on paper. Have students practice drawing models. Don’t worry about exact calculations yet. If you want exact, you can use the Proportions and Point Plot Little Apps.

Bateson, W., E. R. Saunders, and R. C. Punnett. 1905. “Experimental Studies in the Physiology of Heredity.” Reports to the Evolution Committee of the Royal Society 2: 1–55, 80–99.

Diez, David, Christopher Barr, and Mine Çetinkaya-Rundel. 2014. Introductory Statistics with Randomization and Simulation. OpenIntro.org. https://www.openintro.org/download.php?file=isrs1_tablet&referrer=/stat/textbook.php.

Ismay, Chester, and Albert Y. Kim. 2019. Statistical Inference via Data Science: A Moderndive into R and the Tidyverse. CRC Press. https://moderndive.com.

Kahane, CJ. 2017. “Fatality Reduction by Seat Belts in the Center Rear Seat and Comparison of Occupants’ Relative Fatality Risk at Various Seating Positions.” DOT HS 812 369. US National Highway Traffic Safety Administration. https://crashstats.nhtsa.dot.gov/Api/Public/ViewPublication/812369.pdf.

Lock, Robin H., Patti Frazer Lock, Kari Lock Morgan, Eric F. Lock, and Dennis F. Lock. 2017. Statistics: Unlocking the Power of Data. 2nd ed. Wiley.

Tintle, Nathan, Beth L. Chance, Soma Roy, George W. Cobb, Allan J. Rossman, Todd Swanson, and Jill VanderStoep. 2016. Introduction to Statistical Investigations. Wiley.

  1. Fisher (1934) p.6↩︎

  2. Technically, the function form has to include an intercept.↩︎

  3. for the conventionally-trained reader, I acknowledge that the term linear regression is conventionally applied only to setting 2. But there is no good reason for this: all four settings can be handled with exactly the same modeling process. In some situations, setting 4 cannot be handled with linear regression. The problem with using linear regression to build a model with an indicator response variable is that a straight-line function, if not exactly level, will eventually extend outside the range zero to one. But it’s not meaningful to talk about probabilities greater than one or less than zero. A simple workaround is to treat any value greater than one as 1, and any value less than zero as 0. A refinement to this brusque treatment is accomplished by a technique called logistic regression which effectively turns the sharp bend into a gradual curve. See Figure 5.7 for an example.↩︎

  4. If you are reading this book in conjunction with a conventional text, remember that such texts frame inference in terms of the degrees of freedom, df. The relationship is \(\mbox{df} \equiv n - (\flex + 1)\).↩︎

  5. Here is a more precise statement about the 95%. Imagine a world in which you know the “true” value of the effect size. In that world, you generate data, fit a model, and calculate an effect size from the model and data. Chances are, the effect size you calculate will not be exactly the “true” value, since the data are sampled at random. But you expect the value you calculate to be “close” to the “true” value. Confidence intervals are calculated according to a certain procedure. A proper procedure for a 95% confidence interval will be such that the confidence interval includes the “true” value 95% of the time. You could test out whether a proposed procedure is proper by generating many data sets and checking whether the many corresponding calculated confidence intervals on the effect sizes really do include zero 95% of the time.↩︎

  6. https://www.webmd.com/cholesterol-management/features/when-your-doctor-orders-cholesterol-lowering-medications#1↩︎

  7. The statement attributed to Einstein might be relevant: “Nobody believes a theory except the person who made it. Everybody believes an experiment except the person who made it.”↩︎

  8. Smoking is a human behavior presumably somewhat under the control of the person him or herself. Similarly, cancer can have many causes.↩︎