December 25, 2010 § Leave a comment
Gerd Gigerenzer has produced the most challenging response to Kahneman and Tversky’s work on (quote-unquote) rationality as it relates to human judgement of uncertainty. In this series, I’ll work through Gigerenzer’s pop-sci books Calculated Risks and Gut Feelings and pick out bits I can apply to my thinking and teaching.
I’m not an absolutist who holds that nothing in the future is certain. It’s certain that the sun will rise tomorrow. Pedantic spiritualists and/or quantumists may argue that there is some non-zero probability that in the next few hours the sun will turn into a supermassive slice of cheesecake. Yet if the concept of certainty is to have any use, complement probabilities of the order of 10^(10^10) should be considered negligible. Certainty is best employed as an approximate concept—like approximately everything else.
Yet problem zero in statistical thinking is not understatement but overstatement of uncertainty. It’s not just undergrads that make this mistake. We pros know that our estimates are almost surely wrong, and append uncertainties to them. Yet we have a habit of assuming our quantification of uncertainty is exact, when in all but the simplest real-world problems, our chance model will be wrong. We should be more concerned with teaching students how the real world can deviate from our models that with teaching them when to divide by n and when to divide by n-1.