Andrew Cockburn reports on an analysis of the raw Lancet data by Pierre Sprey who used a non-parametric method (so it was not necessary to exclude Falluja) and found:
"So, applying that simple notion to the death rates before and after the US invasion of Iraq, we find that the confidence intervals around the estimated 100,000 "excess deaths" not only shrink considerably but also that the numbers move significantly higher. With a distribution-free approach, a 95 per cent confidence interval thereby becomes 53,000 to 279,000. (Recall that the Gaussian approach gave a 95 per cent confidence interval of 8,000 to 194,000.) With an 80 per cent confidence interval, the lower bound is 78,000 and the upper bound is 229,000. This shift to higher excess deaths occurs because the real, as opposed to the Gaussian, distribution of the data is heavily skewed to the high side of the distribution center".
Hat tip: Donald Johnson.
Tim,
Did you actually read Sprey's drivel? Did you even read the section you quoted?
Sprey says he is calculating "confidence intervals around the estimated 100,000." In other words, he's not including Falluja, and he's using the same estimator as Roberts: based on the mean.
Perhaps you assumed that because he goes on and on about the horrors of minimizing the sum of squared deviations, Sprey would not use the mean as an estimate? I don't think Sprey is using something other than the mean. I think he's not aware that the mean is the solution to that minimization problem.
Also, Roberts does not use a gaussian estimate of the confidence interval. He uses a nonparametric estimate: notice that Roberts' confidence interval is not symetric.
So we have Roberts and Sprey claiming to do the same exact thing (calculate a nonparametric SE). Since Sprey clearly has never heard of the central limit theorem, I'm betting that Roberts is the one who's made the correct calculations.
I can't figure out at all what Sprey is talking about.
It's not clear whether Sprey included Fallujah or not--I missed the part about the 100,000 and assumed the numbers were higher because he did. Of course if he included Fallujah the mean should go way up.
I was assuming he included Fallujah, btw, because I'm one of those amateurs who assumes there's something wrong with a standard statistical approach that would throw out Fallujah because the death toll there was so incredibly high. The Fallujah outlier suggests, as Sprey says, that there are two different death rates--extremely high ones for those rare neighborhoods that have been heavily bombed, and much lower rates for neighborhoods that have only suffered the much lower postwar background levels of violent death. The fact that he said that was what made me think Fallujah might have been included. But maybe he didn't.
Correction--Sprey talks about two different death rates and so I thought he was alluding to Fallujah. But maybe not--he might have been saying nothing more than that the death rates in various locations were all different.
The page seems down now, but if they used the same mean as previously, then why isn't the confidence interval centered on 98,000 as previously?
z asked:
Nonparametric bootstrap CIs needn't be centered on the original estimate -- in fact, they usually aren't (though if you're lucky, they're centered pretty close by).
But to clarify, I'm not sure what Sprey did, or what data he used. I bootstrapped the excess mortality estimates based on cluster data here and my CI doesn't look like Sprey's.
It looks as if Cockburn has pulled it. There is still a mention of the story on Counterpunch, but the story itself has vanished.
I wonder why he pulled it? I doubt it's because, coincidentally with criticism here, someone realized there might be something wrong with the calculation. Though maybe that's the case.
What I'm guessing is that the article was only supposed to appear in the actual dead tree subscriber's only version of Counterpunch. I don't know if it's still there, but there's been a reference to this article in the ad for the paper version in the website for the past week or so.
Amazing! Robert's nonparametric confidence interval around the non-Falluja data looks like a fascist bell curve! Even though the underlying data isn't an evil bell curve! It's as if there was some kind of mathematical law pushing sample averages towards this shape!
The fascist bell curve comment was clearly a joke, Ragout. I thought it was Cockburn who used it anyway, and if so I wouldn't expect him to have heard of the central limit theorem.
I'm not so sure Cockburn was joking: he explains that the bell curve is fascist because it was beloved of 1920s eugenicists.
Anyway, the main target of my mockery is Sprey, who clearly doesn't understand the central limit theorem, or that the distribution of an estimator is different than the distribution of the underlying data. His whole discussion amounts to a basic confusion over these points.
Yeah, he does mention the eugenicists, but I'm pretty sure that was just part of the joke. Though maybe some naive Counterpunch readers might have been silly enough to go away thinking that Gauss was a founding father of the eugenics and fascist movements. BTW, I'm not sure, but weren't some of the early statisticians rather favorable towards eugenics? Galton, maybe? Not sure. Hmm, maybe it's true.
I don't know if Sprey is incompetent or not. Given his background, you wouldn't think he would be, but I don't know.
Ronald Fisher, Galton, Pearson...yikes. Better do a purge of all of orthodox statistics and reformulate the field on a foundation of strict Bayesianism. I gather some want to do this anyway, but now we've got a firm political reason for doing it.
I doubt Cockburn was any more serious about this fascist stuff than I am being.
Galton invented the term eugenics, and basically social darwinism as well. That doesn't mean his mathematics are bad, of course, but I would take a careful look at how he used them himself if I were ever to rely on his conclusions (as opposed to his methods).
My favourite eugenicist is Hans Eysenck (1916-1997), who produced rock-solid statistical evidence that blacks have poorer brains than whites.
He then went on to use the same rock-solid methods to show that astrology works. I'm not kidding!
Take a look at the wikipedia pages of these people ... there are apparently a lot of people who worship these men as heroes even today.
Article still there
http://www.counterpunch.org/andrew01092006.html