teachin’ (math?) stat…
Arthur Charpentier (from the awesome Freakonometrics) pointed out to me those two blogs about teaching statistics. One by Meg Dillon about the joy of teaching statistics in France, of all places!, and entitled Statistics à la Mode. And another one by Douglas Andrews commenting on the first one, entitled the Big Mistake: teaching stat as though it was math… (It appeared on an ASA community blog/forum I did not know about.)
“…there is almost invariably a peculiar pair of caveats presented as from on high: Never accept the alternative hypothesis, and ever say the probability is 0.95 that the mean lies in a 95% confidence interval for the mean.” Meg Dillon, After Math
Both blogs managed to bemuse me (this is not going to be a very coherent post, I am afraid!): the first one because it has this condescending tone of pure mathematicians about statistics or at least statistics course (i.e. “anyone can teach statistics!” mixed with “I hate teaching statistics!”) that I meet too often, esp. this side of the pond. Plus it seemed to miss the fundamental distinction between probability and statistics (check the above quote). And it did not say why the contents of the French course was much nicer than the equivalent designed by Meg Dillon at her university (except for the fact that she could use measure theory from the start). Maybe the French idiosyncrasy the author basks in is the fact that statistics is not recognised as a field in French universities (there is no stat department for instance) but is instead a subfield of mathematics…
“…stat is a different intellectual discipline. She longs for a so-called stat course based on sigma-algebras and probability spaces. Well, that has been tried many times over many years, and it fails miserably at helping students understand the important stat concepts.” Douglas Andrews, ASA Blog Viewer
The second post is making sense in stressing that stat is not math. (Or rather, as it should have been stated, it is not only math.) And that (non-statistician) mathematicians should get some preliminary training or exposure to real data when teaching statistics courses. I can certainly remember a few of my (French) stat teachers who had never approached data in their whole life! However, the comment that “foundation of stat is in empirical science and in learning from observed data, not in math” seems to go overboard. As it echoes in negative the complaint from the math teacher that intro statistics courses were “a hodgepodge of recipes” with no mathematical backbone. My feeling there is that, while we certainly do not need measure theory for the earliest statistics courses (Riemann integration is good enough for my second and third year students), we have to anchor statistical techniques into a mathematical bed to avoid them looking as a bag of tricks. I remember after my first (mathematical) statistics course on being puzzled by the lack of direction and/or the multiplicity, when compared with a standard math course. I was missing the decision-theoretic part that was to come later! Had I been exposed to a non-mathematical intro stat course, I do not think I would have persevered in this field! (And I would have moved to differential geometry instead…)
Xi'an's Og 
January 24, 2012 at 11:56 pm
I think it is hard to draw clear conclusions without knowing the type of students that make up your audience. I teach part of a course that targets mostly non-math people, so drowning the concepts in math would not be a very useful exercise. Of course if you are a highly-motivated, mathematically-aware student you would struggle to find the course interesting, even when I provide additional material for those students.
I don’t like the idea of providing just recipes, although many students that can see they will use stats in their dissertations want to have some recipes. Emphasizing the concepts with example applications seem to make most sense to students.
January 24, 2012 at 6:09 pm
Differential geometry? Really?
January 24, 2012 at 7:49 pm
Really!
January 24, 2012 at 12:58 pm
I did a non-mathematical intro stats course. I became a numerical analyst.
Most of the people I know who did that course who became researchers in stats actually did something else and sort of “fell into” statistics almost by accident (be it through needing more classes and accidentally taking a fun stats course, or by job opportunity).
I became a statistician because my functional analysis (at the time) wasn’t up to developing mesh-free methods for systems of reaction-diffusion equations and statistics seemed like a nice excuse to compute matrix functions.
I had to re-learn all of the content of the intro course, which, for my purposes was completely useless.
That being said, it’s a question of target audience. At least where I did my study (QUT), the 101 stats course is a large “service teaching” course not strictly aimed at mathematicians. I am told that those who were never likely to become a research statistician quite like the “recipe-based” approach.