Variability is a key concept in statistics. The Greek letter Sigma has such importance, that it is probably associated more closely with statistics than with Greek. Yet, if you have a chance to examine the bookshelf of introductory statistics textbooks in a bookstore or the library you will notice that the variability between the zillions of textbooks, whether in engineering, business, or the social sciences, is nearly zero. And I am not only referring to price. I can close my eyes and place a bet on the topics that will show up in the table of contents of any textbook (summaries and graphs; basic probability; random variables; expected value and variance; conditional probability; the central limit theorem and sampling distributions; confidence intervals for the mean, proportion, two-groups, etc; hypothesis tests for one mean, comparing groups, etc.; linear regression) . I can also predict the order of those topics quite accurately, although there might be a tiny bit of diversity in terms of introducing regression up front and then returning to it at the end.
You may say: if it works, then why break it? Well, my answer is: no, it doesn’t work. What is the goal of an introductory statistics course taken by non-statistics majors? Is it to familiarize them with buzzwords in statistics? If so, then maybe this textbook approach works. But in my eyes the goal is very different: give them a taste of how statistics can really be useful! Teach 2-3 major concepts that will stick in their minds; give them a coherent picture of when the statistics toolkit (or “technology”, as David Hand calls it) can be useful.
I was recently asked by a company to develop for their managers a module on modeling input-output relationships. I chose to focus on using linear/logistic regression, with an emphasis on how it can be used for predicting new records or for explaining input-output relationships (in a different way, of course); on defining the analysis goal clearly; on the use of quantitative and qualitative inputs and output; on how to use standard errors to quantify sampling variability in the coefficients; on how to interpret the coefficients and relate them to the problem (for explanatory purposes); on how to trouble-shoot; on how to report results effectively. The reaction was “oh, we don’t need all that, just teach them R-squares and p-values”.
We’ve created monsters: the one-time students of statistics courses remember just buzzwords such as R-square and p-values, yet they have no real clue what those are and how limited they are in almost any sense.
I keep checking on the latest in statistics intro textbooks and see exercpts from the publishers. New books have this bell or that whistle (some new software, others nicer examples), but they almost always revolve around the same mishmash of topics with no clear big story to remember.
A few textbook have tried going the case-study avenue. One nice example is A Casebook for a First Course in Statistics and Data Analysis (by Chatterjee, Handcock, and Simonoff). It presents multiple “stories” with data, and how statistical methods are used to derive some insight. However, the authors suggest to use this book as an addendum to the ordinary teaching method: “The most effective way to use these cases is to study them concurrently with the statistical methodology being learned”.
I’ve taught a “core” statistics course to audiences of engineers of different sorts and to MBAs. I had to work very hard to make the sequence of seemingly unrelated topics appear coherent, which in retrospect I do not think is possible in a single statistics course. Yes, you can show how cool and useful the concepts of expected value and variance are in the context of risk and portfolio management, or how the distribution of the mean is used effectively in control charts for monitoring industrial proceses, but then you must move on to the next chapter (usually sampling variance and the normal distribution), thereby erasing the point by piling on it totally different information. A first taste of statistics should be more pointed, more coherent, and more useful. Forget the details, focus on the big picture.
Bring on the revolution!