It’s over. Two solid weeks of 9 to 5 to 9 and beyond statistics. Plus a few cocktails and cookouts and camaraderie. I’m exhausted.
The students are mostly later early career: union leaders, personnel managers, directors of this and that. The degree is a Master of Professional Studies. Think of it as an MBA with the focus on people not profit (no, neither is bad). As such, the bulk of students have had no contact with math for years—just like most people.
But all of them use and see statistics daily. I should add “and misunderstand statistics.” Most do. About half have had a statistics class before and, with one or two rare exceptions, all of them hated it. Dry memorization of meaningless formulas is the biggest complaint, along with too many concepts.
One student reported taking a class from a colleague who regularly read from his $400+ book (it came with software). Now that’s boring. I always ask and the only thing anybody can ever remember, if they remember anything, is that small p-values are “good”. Strangely, only one person ever remembered the value of the magic number.
Here’s what I did wrong:
I’ve already stripped away most of the math usually found in stats courses—statistics is not a branch of mathematics—but I can never resist teaching how to count. You know, factorials and combinatorials and the like. Lets students learn to compute lottery probabilities and so forth. There’s always amazement at how improbable the Mega Millions (for example) is.
In other words, dry memorization of meaningless formulas. Do students really need to understand “n choose k”? I’m now thinking not. The binomial distribution can be just as easily taught with pictures (maybe). (I only cover two distributions, the binomial and normal.)
I’m wavering on teaching Bayes’s formula, and think I’ll stick with it. The probability of having (say) cancer with a positive mammogram is always a surprise. But I don’t believe anybody remembers the formula. I mean, remembers two weeks after the class, let alone a year after.
Not enough time spent on understanding the results from regression. Even professional statisticians forget that regression models the central parameter of a normal distribution as a function of various observables. The model is correlative, not causative, but everybody—as in everybody—forgets this.
That’s why “hypothesis testing” is such a crock (regression “model selection”, of course, relies on it). Everybody thinks it’s used to prove or disprove some causal theory. And—raise your hands—how many of you know, really know, why it is “fail to reject” and not “accept” the “null”? Sheesh. What a philosophical boondoggle. Though I do introduce Fisher’s infatuation with falsification and “objectivity”, I need to spend more time demonstrating this.
Here’s what I did right:
Emphasizing probability is deductive: given a set of premises and a proposition, the probability is deduced from those premises. Change the premises (a different model, say), change the probability.
Requiring students collect their own data. Canned examples, which work out beautifully in textbooks, are of little use. Problem with them is that the student must first understand this new data, the terms, limitations, situation, and so on, all before they can get to the statistics. In other words, you have to learn two things, not one. And then, like I said, the canned examples always “work.” Unlike data in the real world, which is plagued by uncertainties, mistakes, missingness, and so forth.
I use R, and it works out fine. Even for folks who’ve never opened a spreadsheet before (one student). I emphasize it’s not a computer course, and that any mistakes in the code I’ll fix. Nobody is graded on computer skills—only on understanding. This relieves a lot of stress, and I’ve never had a complaint. Plus, nearly all of the MPS students pay their own tuition. I can’t bear making them pay for some point-and-click software.
Using R also lets me do statistics the right way. Which is this. You have some “y”, some outcome, of which you are uncertain. You quantify that uncertainty using a probability distribution, usually a normal. You want to know how your uncertainty of “y” varies if you know the value of some “x”s.
The central parameter of that normal is given as a function of the “x”s. Now, we do not care about any parameter, but only how the “x”s influence our uncertainty of the “y”. That’s what software should compute, which is easy in R. This is what hardly anybody does.
Focusing on parameters confuses, badly confuses, causation and correlation, and leads to vast over-certainties. And is what accounts for the majority of published errors.
To prove that, we scan the headlines for “New study shows” headlines, read the reports, find the papers, and discover the statistical abuses are just a bad as predicted. Always fun, too. Need to do more of this.