As for the first alleged error: I certainly don’t claim to be a statistics expert, but I wonder if the critics are simply misreading Alito’s point. On the matter of margin of error (or “SEM”) for IQ tests, Alito objects that the majority opinion “unjustifiably assumes a blanket (or very common) error measurement of 5.” He says that assumption is what leads to the majority’s holding that a defendant with an IQ as high as 75—five points above the cutoff for intellectual disability—must be permitted to introduce additional evidence of intellectual disability. He points out that SEMs “vary by IQ test and test-taker.” (Dissent at 17.)
According to Law Blog (evidently paraphrasing the statistics experts), the “5-point standard adopted by the majority is a margin of error based on a 95% confidence level.” But the majority doesn’t say that in the critical passage (maj. op. at 20) that Alito objects to.
The majority, much earlier in its opinion (maj. op. at 11), does state that an IQ score of 71 “is generally considered to reflect a range between 66 and 76 with 95% confidence.” But, so far as I can tell, it doesn’t incorporate that 95% confidence measure into the passage that Alito objects to.
If the majority means to condition the 5-point standard on a 95% confidence level, it would have been easy for it to say so. And, indeed, one would have expected it to say so in response to Alito.
I’m willing to bet that death-penalty opponents and disabilities activists aren’t going to read the majority opinion as conditioning the 5-point standard on a 95% confidence level. Indeed, I wonder if the IQ expert who worked on an amicus brief for the prisoner will change his tune once he realizes that his supposed “gotcha” moment, if correct, would make it more difficult for other prisoners to get relief. [Deleted as erroneous within minutes of original posting.]
The second error that Alito allegedly made was to refer to “the 66% confidence interval” for so-called 1 SEM, when the correct figure apparently is 68%. But as Law Blog states, the 66% figure “comes from a court brief”—by the highly esteemed Seth Waxman and his Wilmer Cutler team, no less—“that repeats what appears to be a misprint in a recent edition of the [American Association on Intellectual and Development Disabilities’] intellectual disability manual.” So if that’s an error, it’s strange to pin it on Alito.
Update: A Supreme Court practitioner writes in defense of Alito on the first alleged error:
I think the bloggers and so-called experts are confusing a legal dispute for a factual error. Alito is well aware that, even when the SEM is 2.16, that means a 74.32 will fall w/in a 95% confidence interval, because 95% confidence is 2 SEM’s away. He says this expressly. His point is a legal one — regardless of whether 95% confidence is the gold standard for statisticians, there’s no *constitutional* justification for requiring the state to surpass 95% confidence, because the defendant is the one who bears the burden of proof. And that’s all the more true for a 75 cut-off, which is *more* than 95% confidence on Hall’s particular test.