Arnold Kling has forgotten more about statistics than I’ll ever know. He teaches the subject in school.
In his latest Tech Central Station column he applies statistical analysis to both the infamous Florida recount and regime-change in Iraq. I’m not even sure what this has to do with statistics in the first place, which shows you how much I know about it. But still this discussion is pretty interesting. Here’s a novel way (to me) of looking at the problem:
In the case of Iraq, the unknown quantity is whether, if left alone, Saddam Hussein’s regime would have eventually killed Americans or blackmailed our leaders with weapons of mass destruction (WMD). Ultimately, that is the unknown parameter about which we are concerned.
Next, let us describe Type I and Type II errors. A Type I error would be to back down from confronting Iraq and subsequently suffer a WMD attack. A type II error would be to invade Iraq when in fact we would not have been hit with WMD even if we left the regime alone.
The consequences of a Type I error — an attack on Americans using WMD — would go beyond even the death and destruction that would be involved. The response, in terms of military action and domestic security, would be very costly, both in terms of lives and in terms of compromises to our freedom and privacy.
The consequences of a Type II error would include loss of lives during the war and its aftermath. Also, we are left with a significant responsibility in helping Iraqis rebuild their state. By the same token, one could argue that a Type II error has benefits, such as ending the mass murders committed by the Hussein regime and giving Iraqis an opportunity to establish a better government.
We will never know the unknown parameter — what the Hussein regime would have done vis-a-vis weapons of mass destruction had we not invaded. However, the failure to find weapons stockpiles increases the probability that we committed a Type II error and reduces the probability that by backing down we would have committed a Type I error.
The short version, of course, is that it’s better to overestimate danger than underestimate it . Underestimation can lead to another 9-11 or worse. At least overestimation can lead to a net positive — the removal of a filthy regime.