Thursday, September 23, 2010

Fun with Statistics

Statistics can often be a double-edged sword. They can seem very useful in argument, as it can add an element of empiricism to the point at hand. However, statistics are VERY OFTEN misleading in the worst of ways. And opponents can certainly take advantage of that fact just as well as you can. This is exactly why it's so important for an audience to have a good intuitive understanding of how statistical facts can be manipulated to sway them.

This morning, in listening to the radio, I heard a fairly negative reaction to what I believe to be (probably) an accurate statistic. An audio clip relayed the rant of a young man who claimed that Census data showed that 70% of first-time marriages are successful. Cynical reactions ensued. I think their intuitions, in mistrusting him, were correct. But they couldn't seem to reconcile their gut-feelings with the statistical data, so they disregarded it as being false.

Now, this isn't brain-surgery. I'm certainly not the brightest person in the world, and I don't claim to be bestowing some kind of esoteric knowledge on ye lay people. But, in fact, this isn't something hard to unravel if you just take a couple of seconds to question it.

What should stick out like a sore thumb to most people is the "first-time" qualifier. Now there's nothing wrong per se with looking at things this way. But it can be misleading. We're usually fed marriage statistics in relation to all marriages (or more accurately each marriage). So we're all familiar with the statistic that over half of all marriages end in divorce. Both of these statistics could be true. Let's walk through a small example.

Let's say we have a pool of 20 men and 20 women. They all get married (that's a total of 20 marriages). Let's also say that 10 of those marriages end in divorce. And now let's say that those 10 men and 10 women each end up remarrying someone else in that smaller pool of divorced people. Those couples, later, get divorced. Now, let's try to break down the statistics on this in two different ways.

In total, there were 30 separate marriages. 20 of those marriages ended in divorce (10 in the original marriages, 10 in the second set of marriages). So, in this example, about 33% of total marriages were successful. Now let's take a look at the same group of numbers in a different way. Let's just look at "first-time" marriages. In our case, there were 20 "first-time" marriages. 10 of those marriages ended in divorce. So, looking at it this way, about 50% of these marriages were successful. Now, granted, other things (sample size, bias, etc.) may have affected the statistics in a more general fashion. But this is a great example of how a seemingly meaningless qualifier can not only give you different statistical outcomes, but can push someone towards different conclusions.

This isn't a good reason to simply ignore statistics. As much as we might hate it, they are a part of our lives, and perform countless useful functions as part of the modern world, from the theoretical all the way down to the technical. But, as with any method of relaying information, we have to constantly be aware of not only the biases of the person relaying the information, but of the determinant factors constraining the data-set. In short, don't ignore the facts...just keep your head up.

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