Statistics You Can't Trust

I have borrowed this book, Statistics You Can't Trust by Steve Campbell, PhD and found this chapter quite similar to our daily encounters and would like to extract part of it here. The chapter title is Jumping To Conclusions.

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"Once we suspect that a phenomenon exists, we generally have little trouble explaining why it exists and what it means. ... To live, it seems, is to explain, to justify, and to find coherence among diverse outcomes, characteristics, and causes. - Thomas Gilovich"

Sometimes we humans make mistakes not because we are deficient at something but because we are too good at something. The "something" to which I refer is our inclination to find order in things and to explain observed phenomena. When order exists and when explanations are actually attainable, this trait can bring enormous benefits.

On the other hand, when order is absent and the concept of "explanation" meaningless, chances are we will still find order and construct plausible explanations anyway. It seems to be the human thing to do. Moreover, once order - real or imaginary- has been found, we have little trouble coming up with reasonable explanations for its existence. For example, in the following series, would you expect a plus sign or a minus sign to occur next?

- - - - + + - - - -

Some people would say minus is next because fully 80 percent of the observed signs are minus; thus, any new observation has a .8 probability of being minus. Such people would have a plausible justification for their choice. Others would say that plus is next because the series begins with four minuses, changes to two pluses, and then returns to four minuses; thus a pair of pluses is to be expected next. These people too would have a plausible justification for their choice. The choices in this case are exact opposites, but both rest on sensible-sounding foundations. Perhaps there are people who could find within this set of pluses and minuses still different clues about the nature of the next sign. If so, their explanations might also impress us as plausible.

In view of my introductory paragraph, you might have had the good sense to say, "I can't determine what sign is next because I suspect that this is a random series." If that is the way you called it, you are right. I flipped a coin ten times and called a head "plus" and a tail "minus." The above series reveals nothing more than the observed sequence of heads and tails. (If you suspect my coin of being biased, you might be interested to know that the next ten flips yielded + - + - + + + + - -, a result with a slight preponderance of pluses.)

Notice: Those guessing that plus would be next were correct, though for no good reason, and are probably right now congratulating themselves on their cleverness. If you hadn't been in on the joke, do you think you would have searched for some kind of ordering system in these random data? I would bet on it. At any rate, doing so seems to be a very strong human inclination.

Now this chapter isn't about analyzing random events, or anything of the kind. However, one of its purposes is to alert you to our tendency to overexplain, to come up with explanations no matter what, and the tendency for journalists, politicians, lawyers, and others to do the same. My aim is to encourage you to be a little slower - and insist that others be a little slower - to impose explanations on phenomena which might either defy explanation or be explainable, but not necessarily by the first cause-and-effect theory that pops into your mind. Unlike gunfighting in the Old West, being a little slow on the draw is not necessarily a bad thing for one facing off with statistical evidence.

Let us return briefly to two examples from Chapter 7. Do you recall the one about how sharks tend to attack more men than women? It is difficult to chastise too harshly the journalist who guessed that there is something about the chemistry of men that attracts sharks and something about the chemistry of women that repels them. Nevertheless, wouldn't it have made better sense to first determine whether men have greater exposure to this particular risk? And why attribute superior physiological advantages to boys because collectively they have fewer injuries than girls in ballet classes? Off-the-cut explanations are a dime of dozen. Be extremely wary of them. -END

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Aren't these too familiar scenarios to you as they are to me? We always spend lots of time trying to explain something, which is not wrong, but how many times do we really realise that the explanation, at the end of the day, doesn't mean too much? Sometimes, we may not even know what is the real answer.

Nevertheless, these happen everywhere - at home, at work, as you walk, when you read the newspapers, listen to news on TV, etc...If you would be a little more observant.

Worse still, people argue and fight over their own set of explanations, that their explanation makes more sense over the other. They end up being unhappy.

At work, we are questioned by bosses, peers, etc on why this and that happens and we are 'cornered' into trying to find some sort of explanations to get our way through. How do you think they will react if we simply tell them, "well, comrade, things happen and I don't have an explanation!" Won't they freak out or give you a BIG D on your next performance review?!

Sometimes, I also wonder why I waste time trying to guess or argue on matters like why is there a traffic jam today (and most of the times, I don't see any accidents or breakdown), where did I catch my flu from, why did someone get diarrhoea and not the other when both had the same meal?

Well, perhaps that adds some colours to our boring life and provide topics of interest in the kopi-tiam talk. Isn't not so?

10 May 2008 (10.00am)