Monday, June 9, 2008

The Consolations of Probability

There's little doubt that many people find comfort in the presence of an all-powerful, all-knowing being watching over them, in knowing that everything happens for a reason, even if they don't know what those reasons might be. People who don't believe in such things cannot have such consolation. After all, what consolation is there if things just happen?

I'm not just talking about the fact that there's a lot of random stuff that happens that we aren't responsible for, or that we're incredibly lucky to be here. Those pieces of understanding are major consolations, no doubt (or at least they are to me). Greta Christina has touched on these, and similar issues several times, and written about them better than I could.

Probability and statistics, or at least an understanding of them, are incredibly useful things to have. I make a living out of them, so they're obviously useful in that sense, but I am talking here about ordinary everyday getting-through-life stuff.

For example, they're essential tools when responding to the news, because they help you identify the difference between a real issue and a likely manufacturoversy.

The tale of the traffic blackspot

Some time ago I saw a headline about how a particular busy intersection had become a pedestrian "black-spot" because there had been a "50 percent increase" in pedestrian deaths and serious injuries last year; it was suggested that it may have been caused by increased traffic from changes several intersections back along the same road. The relevant state minister was grilled about his "lack of action" and induced to promise some very expensive changes at the intersection.

My initial, emotional response was the one the journalist was doubtless trying to induce - horror at an apparently huge increase in deaths and injuries. But that nice round "50 percent" figure worried me. Was that number so rounded off from say 48 or 52 percent, or was it exactly 50, suggesting the numbers were very small? So I looked through the story for the figures. The number of deaths and serious inuries had gone from 8 the previous year to 12 in the last year. A quick calculation in my head showed that, even if the underlying probability of incidents had not changed, such a change in actual numbers could easily have happened. The fuss over the change from 8 to 12 may well be a big fuss over nothing but randomness. It could well be that the figure of 8 was itself too high - maybe something should have been done years ago - but the controversy highlighted by the article was misplaced; there was no particular reason to believe anything had changed. The journalist had managed to induce the minister to reallocate funds that may well have been much better left where they had been before.

[Since the details of the mathematics is not the point of this post, I haven't included them - in another post at a later time, I may explore a little of the specific calculations in these (real) examples. ]

If you're watching for it, this kind of thing comes up a lot. H.G. Wells once wrote "Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write". Is he overselling the case? When government policy is increasingly driven by media attention to unimportant detail rather than substantive policy, I do think it's become increasingly important. We need to be able to understand the flood of information, and if necessary, debunk the nonsense it contains. Can the broader awareness suggested by Wells' comment come to pass?

It seems that educators are responding.

In the part of the world where I live, statistics and probability are now taught throughout school (K-12). My six-year-old has already learned to record data and produce simple graphs of it on the computer. My nine-year-old has learned some basic probability. By the end of year 12, they will have a pretty solid grounding in the basic ideas. They might not end up with all the tools to do the calculations I used, but they will at least be able to ask the right questions.

While important, this sort of understanding of what's going on in the world - certainly a form of comfort - is perhaps a relatively abstract one. However, the comforts can also be much more personal.

The tale of the overtested driver

Some years ago, a fellow was asking a group of statistically-minded people (of which I was one) whether he was being victimized at work. His employer, who owned a business that had many employees driving trucks, had instituted random drug testing. Every week a small number of employees were selected and tested.

This particular driver felt he was being targetted, because he had been tested seven times in 18 months, while he knew of several others who had not been tested at all. He was worried that someone must have it in for him; he thought that maybe another employee he'd had a falling out with may have said that he was taking drugs in order to make trouble for him. He was wondering if he should confront that person.

I pointed out that for it to be an effective deterrent, drug testing had to be done at random - you can't test someone once and then not again until everyone else had been done, because if someone were inclined to take drugs while driving trucks, once they'd been tested, they'd know they were "safe" for a while. There always had to be a risk you would be tested next month. Random testing in turn meant that there would always be some people tested substantially more than others. Since he was asking, rather than someone else, it was likely that he was one of the most heavily tested people in that company, probably the most heavily tested - but someone had to be the most tested person.

The question was - if testing really was being done randomly, would seven tests in 18 months be an unusually high number for the most-tested person? Of course, you need to look at the number of people in the company and the number being tested each week. You'd also want to ask whether you'd really expect to find some people still untested at the same time.

It turned out that after 18 months, it was reasonably likely someone at the company was going to be tested seven times (around a 20% chance - a higher chance than picking up a die and rolling a six), and at the same time there would be a fair number of still-untested people (enough so that he'd likely know several). So there was no particular reason to think he was being targetted. No reason, based on the numbers so far, to expect the person he was worried about was making trouble for him.

Such knowledge was indeed, a consolation. Sure, the drug testing was a nuisance, but there wasn't any reason to think it was personal, or that anybody had it in for him. A significant source of stress in his life was lifted.

And understanding not just that things can happen at random, but of the specific consequences of how randomness works can show us that nobody may be to blame. It can show us that we are not a victim.

Probability can be a consolation, sometimes quite a personal one.


Anonymous said...

Came for the humanist carnival.

Probability is so interesting, but what passes these days for statistics is infuriating.

Can I ask what you do?

Efrique said...

christopher said Probability is so interesting, but what passes these days for statistics is infuriating.

Can I ask what you do?

Sure you can ask! I may even answer.

[I assume you mean what I do for a job - because I do all sorts of other things besides that.]

I am what passes for an infuriating statistican [ ;) ], though I work in a particular application area (one where, I must say, I am also frequently an infuriated statistician).