Another error by a SCOTUS justice? Alito's statistics questioned
Statistics experts are questioning the numbers in Justice Samuel A. Alito Jr.’s dissent this week to a decision striking down Florida’s bright-line IQ standard for determining death-penalty eligibility.
The Wall Street Journal Law Blog spoke with experts who said Alito cited an incorrect figure—a 66 percent confidence level in the reliability of an IQ test rather than a 68 percent confidence level. The incorrect figure was apparently taken from a brief that cited an apparent misprint in an intellectual disability manual. Experts also said Alito was comparing apples and oranges when he criticized the margin of error used by the majority.
The Florida law at issue barred defendants with an IQ above 70 from presenting evidence of a mental disability that would exempt them from execution. The five-justice majority said Florida’s standard failed to recognize that an IQ score is imprecise, and a score of 70 is considered to represent a zone of 65 to 75 when the margin of error (known as the standard error of measurement, or SEM) is taken into account. As a result, the court said, the defendant should be able to present additional evidence of disability for an IQ score of up to 75.
The majority assumed a plus or minus five-point margin of error, based on criteria used by medical professionals. Alito said that was too high, and said a plus or minus 2.16 margin of error was the standard used in the most recent IQ test given to the defendant challenging the Florida law.
The 2.16-point margin of error endorsed by Alito represents a 68 percent confidence level, meaning there is a 68 percent probability that the Florida defendant’s true score is within 2.16 points higher or lower than his score, experts told the Law Blog. When a 95 percent confidence level is used, the margin of error is plus or minus 4.3 points, which is closer to the five-point range used by the majority.
But Alito repeatedly refers to the “the 66 percent confidence interval” rather than a 68 percent confidence level, which is a widely accepted value. Alito’s figure apparently comes from a court brief citing what appears to be a misprint in an the intellectual-disability manual by the American Association on Intellectual and Developmental Disabilities, the Law Blog says.
AAIDD President Dr. James Thompson told the Law Blog, “I’m 99.99 percent sure that the 66 percent was a simple misprint.”
Statistics experts also said Alito was mixing apples and oranges when he criticized the majority for the five-point margin of error. “To blindly import a five-point margin of error when we know as a matter of fact that the relevant SEM is 2.16 amounts to requiring consideration of more than two SEMs,” Alito wrote.
The case is Hall v. Florida. The opinion is here (PDF).