Forecast: Hazy on Probability

There's this article at LiveScience.com under the headline "Rainy Weather Forecasts Misunderstood by Many" (here). It reports that about half of all people don't understand what the "probability of precipitation" means in a weather forecast.

If, for example, a forecast calls for a 20 percent chance of rain, many people think it means that it will rain over 20 percent of the area covered by the forecast. Others think it will rain for 20 percent of the time, said Susan Joslyn, a cognitive psychologist at the University of Washington who conducted the study.

Of course, how the article should really be titled is simply "Probability is Misunderstood by Many". I see the same -- dare I say stunning -- difficulty that enormous numbers of college students have in interpreting the most basic probability statements. Unfortunately, in the classes that I teach probability is never more than a quick two-week building-block on the way to something else (either in a survey class, fundamentals of inferential statistics, etc.). Part of me wishes we could give a whole semester course in probability (and basic game theory?) to everyone, but I know there's no room for that in the basic curriculum.

Having seen the difficulty, I've tried to emphasize the interpretation process more in later semesters, and tend to run into more and more resistance against it. Even students who are in the habit of happily crunching on formulas and churning out numerical solutions can be vaguely frustrated and unhappy at being asked what the numbers mean.

This is one where I find it really hard to empathize with the students on the issue (that being rare for me), and I almost can't begin to imagine where I need to start if I get an incredulous response as to how I knew that 75% was "a good bet" if I mention that in passing. Perhaps just growing up in an environment where I was personally steeped in games as recreation every day for decades (chess, craps, Monopoly, Risk, poker, D&D -- see here for more) marinated the fundamental idea of probability into my brain in a way that can't be shared in a class lecture.

Anyway, some people have suggested that statistics needs to be taught to everyone functioning in a modern society. Even more fundamental (after all, it's foundational to statistics) would be getting the majority of people to have a sense for probability in their gut, because most people currently do not. I'd hypothesize that psychological experiments like those at U. Washington have promise of cornering the precise way that our brains are fundamentally irrational -- that math so simple could be so bewildering in practice, suggests a deep limitation (or variant prioritization) in our cognitive abilities.

Blogging as Software Development

A core principal of open-source software development is something like this: "Release early. Release often. And listen to your customers." (See here.) The idea being, it's better to get something out to your users -- even buggy or incomplete -- so as to (a) get first-mover advantage, and (b) find out exactly what your users want fixed or improved first, because it's rarely the same as what you'd expect on your own.

I'm finding that with the advent of electronic publishing/easy blogging, I'm doing the same thing with my writing. I frequently post something and then go back -- hours or days or weeks later -- re-read it, and make minor (but occasionally numerous) changes to the grammar, sentence structure, and so forth. Sometimes I add in a new anecdote, analogy, or quote that I've come up with in the meantime.

Now, once upon a time we all had to do this the other way around. When publishing was entirely by print -- fixed and labor-intensive -- then ideally you'd write, draft, revise, edit, etc., prior to the final "official" version being published and observed by any readers. (Back when I was a high-school student working on an actual typewriter, I would personally skip the draft/revise process, but I'd take a long time mentally picturing each paragraph and sentence before I put it on the page. Excepting that time I was writing a paper in the morning, last minute, with my grandfather sitting on the stairs waiting to drive me to school.) The point being, what would our older teachers think if we told them that we could entirely reverse the process -- publish our rough draft first, and then instantly add any revisions we wanted, while people were reading and responding to what we had written?

I'm finding that it's a lot healthier for me, now that blogging software is widely available, to reverse the process in exactly this way. I get my stuff out in the world and get some kind of feedback almost immediately. I can get in the flow of the writing/thinking process without getting interrupted too much by the need to stop and pull out a dictionary or a thesaurus. I can put the draft out there and only come back to it if I truly have a really good idea to add or modify what I've written later on. It feels almost like publishing was just waiting to be done this way for the entire history of writing.

On Classroom "Contracts"

What follows is an open letter I sent to the editor of Thought & Action magazine.
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In the Fall 2008 Thought & Action magazine, professor P.M. Forni had an article called "The Civil Classroom in the Age of the Net". Within that article, he recommends a commonly-seen tactic referred to as a "contract" or "covenant" with the students in the class. Professor Forni writes (p. 21):

Read the covenant to your students on the first day of classes and ask them whether they are willing to abide by it. You can certainly make it part of the syllabus, but if you prefer a more memorable option, bring copies on separate sheets. Then, after the students' approval, you will staple the sheets to the syllabi just before distributing them to your class. Either way, it is of utmost importance that you do not change the original stipulations during the course of the term.

Personally, I think this is one of the more corrosive practices that I've seen widely used in colleges these days.

First of all, the practice is morally ambiguous in that it demands agreement to something being called a "contract" without an opportunity for fair negotiation on both sides. If a student actually does not agree to the presented covenant, what then? In truth, the point of negotiation is when the student formally registers for the class. When instructors bully a classroom of students into a signing statement on the first day of class, we're giving a terrible lesson into the gravity and consideration they should take before signing their name to any document.

Secondly, there is a message usually delivered along with these "contracts" along the lines of, "the covenant is an ironclad agreement that can never be broken". That is again a misrepresentation of how contracts are actually used in the business world. Contracts attempt to establish principles of intent, but they are routinely re-negotiated and amended all the time. When a disagreement erupts between parties, the existing contract may be used as a starting point for discussions, but if agreement cannot be reached, then arbitration or a court case may result. If this were not so, then the entire field of contract law would not exist.

Thirdly, the common usage of these so-called "covenants" causes some students in classes where this is not used (such as the classes that I teach) to believe that without a signed contract, they have no behavioral or performance requirements whatsoever. Obviously this is not the case (again, it's really the moment of course registration in which they agree to abide by the professor's classroom policies), but I have seen it argued by students confused by the practice.

The classroom "contract" or "covenant" of behavior is a confusing, frankly deceptive practice, and it should be avoided by conscientious instructors.