The other night after a feeble attempt at affability with a member of the opposite sex failed dreadfully, I began pondering Type 1 and Type II statistical errors. (And to think Fig often wonders why I’m single.)
It occurred to me as I stood sadly alone that when someone goes on the prowl they are implicitly conducting a sort of statistical test whereby a hypothesis is formed, data are gathered, and a conclusion to either accept or reject the hypothesis is formed. This technique is imperfect, so sometimes the hapless wooer will incorrectly reject the hypothesis when it is in fact true (Type I error), and sometimes will incorrectly accept the hypothesis when it is in fact false (Type II error).
To explain it more clearly, consider that my default hypothesis when I see a fair lass is “She’s not interested.” Having formed said hypothesis, I need to collect some data, so I saunter over and initiate a conversation. During the course of the conversation, I look for evidence in support of my hypothesis, such as:
- She immediately vacates the area when I approach
- She folds her arms and doesn’t look at me
- She keeps fingering a wedding ring
- She abruptly pulls out a Gloria Steinem book from her purse and commences to reading
But I also keep a wary eye for evidence to reject my hypothesis, such as:
- She keeps eye contact for a prolonged period of time
- She laughs readily and engages in gentle teasing
- She plays with her hair or jewelry
- She touches me lightly on the arm
- She says something like “The attractiveness of your erudition and wit is exceeded only by your HOTNESS!”
Now that I’ve gathered the data, it’s time to base a conclusion on them. Essentially there are four outcomes:
- I decide correctly to reject my hypothesis (i.e. I think she’s interested in me and this is true)
- I decide incorrectly to reject my hypothesis (i.e. I think she’s interested in me when she’s really not, a Type 1 error)
- I decide correctly to accept my hypothesis (i.e. I think she’s not interested in me and this is true)
- I decide incorrectly to accept my hypothesis (i.e. I think she’s not interested in me when she really is, a Type II error).
Personally speaking, I commit a Type I error rarely. This is not because I possess some amazing psychological insights, but rather because it takes a lot of evidence to convince me that a girl really is interested and hence cause me to reject my default hypothesis. Instead I’m predisposed to make a Type II error, which is perhaps the far more tragic kind. Because I require so much evidence to reject my default hypothesis, I’m far more likely to conclude incorrectly that the girl doesn’t like me when in fact she thinks she’s found her soul mate.
My painful tale of romantic woe illustrates nicely a trade-off that statisticians face routinely. If they set the standard of proof too high, they’ll be prone to reject a true hypothesis. If they set the standard of proof too low, however, they’ll be prone to accept a false hypothesis (which might get a guy slapped in the face in my example). The FDA behaves like I do when approving drugs, for instance. Because incorrectly approving a harmful drug would be so disastrous, the FDA sets a very high standard of proof for drug approval. This consequently makes the FDA more likely to reject beneficial drugs.
Sometimes I wonder if maybe, just maybe, the FDA has committed a Type II error and rejected a beneficial drug that would have helped me with my Type II problems, but that's probably just the Zoloft talking.