Monday, March 26, 2007

Errors: Type I and II

Writing about mistakes is not the most positive thing one can do on Monday morning. However, all through this weekend, I have been thinking about the liberal sprinkling of errors that I have made all through my life, and find that they fit a particular pattern.

First, a quick refresher: Type I errors occur when a suitable object is declared defected (i.e. an innocent person is sentenced to jail for some crime, or the rightly coded software is declared buggy). A type II error, on the other hand, occurs when a wrong object is declared suitable (i.e. a defected light bulb is declared fit for sale after testing, or a guilty defendant is declared innocent).

Ideally, one would want to minimize both types of errors, however, it turns out that prevention of these types of errors is mutually exclusive - it cannot be done! Lets take an example - if I was a bank and wanted to make sure that I do not give loans to any potential defaulters (i.e. do not make any type II errors) then the only way of ensuring that would be to not give any loans at all - in which case I would be making TONS of type I errors by declaring perfectly good prospects as unfit for loans.

As I look back, I find that my life has been spent in preventing type II errors - i.e. I usually feel worse at having missed out on rising stocks (i.e. made type II errors) than at having lost money on falling ones (i.e. type I errors). This is contrary to good sense - when I met a friend recently who invests for a living, he told me that their motto was not to make the maximum possible money, but to make money on each deal they did i.e. a conservative approach which ensures that even though you may forgo the best deals (make type II errors), you ensure that you do not do any bad ones (no type I errors).

I agree that making type II errors to ensure you do not make type I errors is risky and sub-optimal. But being congenitally optimistic (and this could be my biggest flaw!!), I feel that it still makes sense to hope for the rainmaking deal, the last-ball six, the perfect answer, even if you lose a few matches or money on the way.

But at the end, its a personal choice!! For more info on error types visit this site.

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