There is a fair bit of stats knowledge in these quarters and also obviously there is quite a bit of interest in estimating the Iraqi death toll so I thought the following query might be of broad interest.
As you know, the British polling firm ORB released a poll last week conducted in Iraq on the basis of which they estimate that more than a million Iraqis have been killed since the U.S. invasion. Some of the press reports have noted that the new estimate gives some credence to the Lancet study. I want to argue something stronger: that when you take into account the passage of time between the two studies, during which many more Iraqis were killed, up to the level of precision reported by the two studies, the numbers are in fact the same. To this extent that this is true, it seems to me strong evidence that the studies are basically correct in their assessment of the magnitude of the Iraqi death toll. A slightly more precise formulation would be - if you extrapolate the confidence interval of the Lancet study, it overlaps with the confidence interval of the ORB estimate. [When I say "extrapolate," I have a particular extrapolation in mind - the Just Foreign Policy estimate, where we extrapolate from the Lancet study using the trend implied by the Iraq Body Count tally - see the link at my signature below.] One problem with this is that "extrapolating a confidence interval" doesn't create a confidence interval. Let's put that to the side for the moment. The second problem is that the ORB poll didn't report a confidence interval for its death estimate, but a margin of error, presumably on the poll responses. Here's where my query lies: creating a (rough) confidence interval from the reported information, especially a lower bound. My memory is that the margin of error in such a case is essentially an estimate of the radius of a hypersphere around the joint sample statistic. My thinking is that in order to get a rough lower bound, we can reassign one margin of error's worth of probability in the responses in a way that would maximally lower the death estimate. A rough approximation to this would be to add one margin of error to the people responding no deaths in their household, and to scale down the others so that they still add up to one. I make this argument here: http://www.dailykos.com/story/2007/9/14/15210/1864 The effect of going down one margin of error in this way would be to reduce the ORB estimate it to 1,088,625 - roughly 40,000, or 4% higher than the Just Foreign Policy estimate. If one went down 1.96 margins of error, roughly corresponding to a 95% confidence interval, it would be below the Just Foreign Policy extrapolation of the Lancet number. Thus, roughly speaking, the ORB confidence interval covers the extrapolated Lancet estimate and [I show at the above link] the extrapolated Lancet interval covers the ORB estimate. [This doesn't take into account that there is also a margin of error on the estimate of the number of households. Taking that into account would make the confidence interval wider, thus supporting the claim.] I would be interested in your collective feedback on this... -- Robert Naiman Just Foreign Policy http://www.justforeignpolicy.org Just Foreign Policy's current estimate of Iraqi deaths due to violence since the U.S. invasion - now more than a million: http://www.justforeignpolicy.org/iraq/iraqdeaths.html
