Opinion-Policy Nexus

A political Theorist Teaching Statistics: Measurement

Another post about my experiences this term as a political theorist teaching methods.

That gloss invites a question, I suppose. I guess I'm a political theorist, whatever that means. A lot of my work has been on problems of justice and legitimacy, often with an eye to how those concerns play out in and around cities, but also at grander spatial orders.

Still, I've always been fascinated with mathematics (even if I'm not especially good at it) and so I've kept my nose pressed against the glass whenever I can, watching developments in mathematical approaches to the social and behavioural sciences, especially the relationships between formal models and empirical tests.

I was lucky enough in graduate school to spend a month hanging out with some very cool people working on agent-based modeling (although I've never really done much of that myself). This year, I was given a chance to put these interests into practice and teach our MA seminar in applied statistical methods.

I began the seminar with a simple exercise from my distant past. My first undergraduate physics lab at the University of Toronto had asked us to measure the diameter of a steel ring. That was it: measure a ring. There wasn't much by way of explanation in the lab manual, and I was far from a model student. I think I went to the pub instead.

I didn't stay in physics, and eventually I wound up studying philosophy and politics. It was only a few years ago that I finally saw the simple beauty of that lab assignment as a lesson in measurement. In that spirit, I gave my students a length of string, a measuring tape, and three steel hoops. Their task: detail three methods for finding the diameter of each hoop, and demonstrate that the methods converge on the same answer for each hoop.

measurement

I had visions of elegant tables of measurements, and averages taken over them. Strictly speaking, that vision didn't materialize, but I was impressed that everyone quickly understood the intuitions at play here, and they did arrive at the three approaches I had in mind:

1. First, use the string and take the rough circumference several times, find the average, then divide that figure by $\pi$.
2. Second, use a pivot point to suspend both the hoop and a weighted length of string, then mark the opposing points and measure.
3. Third, simply take a bunch of measurements around what is roughly the diameter.

The lesson that took a while to impart here was that I didn't really care about the exact diameters, and was far more concerned that they attend to the details of the methods used for measurement, and that they explicitly report these details.

In the laboratory sciences measurement protocol is so vitally important. We perhaps don't emphasize the simple point enough in the social sciences, but we should: it matters how you measure things, and what you use to make the measurements!

Posted

Thursday, April 10, 2014 - 16:29