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Hall, Retardation, and the 95% Rule of Thumb

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Today the Supreme Court heard oral argument in Hall v. Florida, regarding when a murderer is deemed mentally retarded so as to be exempt from execution regardless of how heinous, callous, premeditated, or sadistic his actual crime really was.

In the course of this discussion, there was much talk about the 95% confidence interval in statistics.  Contrary to myth, this 95% number is nothing but a conventionally adopted rule of thumb.  There is nothing magic about it, and there is no compelling reason to use 95% in every circumstance, rather than some other number tailored to the needs of a particular situation.

The rule of thumb goes back to the period between the two world wars and the work of R. A. Fisher.  A common problem in studies is that we find that two things, call them A and B, tend to go together, and we want to get a handle on whether this is coincidence or a true correlation.  The rule of thumb is that we "reject the null hypothesis" and say it's not just a coincidence if the correlation between A and B is strong enough that the chance of it being a coincidence is less than 5%.  This is expressed in journals as p < .05.  A result meeting that criterion is pronounced "statistically significant" and given the coveted asterisk, as if there were a big difference between p = 0.051 and p = 0.049.  (There isn't.)

The quasi-religious devotion to this arbitrary criterion was skewered by the famed psychological statistician Jacob Cohen in a classic article:

The atmosphere that characterizes statistics as applied in the social and biomedical sciences is that of a secular religion [citation], apparently of Judeo-Christian derivation, as it employs as its most powerful icon a six-pointed cross, often presented multiply for enhanced authority.
Things I Have Learned (So Far), 45 Am. Psychologist 1304, 1306-1307 (1990).  (The humor in the title lies in the fact that it was written near the end of Cohen's long and distinguished career.)

Part of the problem with this arbitrary criterion is that it reduced to a yes-or-no question an issue that is really very much a matter of degree.  Again from Cohen:

Take, for example, the yes-or-no decision feature.  It was quite appropriate to agronomy, which was where Fisher came from.  The outcome of an experiment can quite properly be the decision to use this rather than that amount of manure or to plant this or that variety of wheat.  But we do not deal in manure, at least not knowingly.
Id., at 1307.

Hall's attorney says that the State of Florida cannot use a cutoff of 70 for IQ scores, but he concedes it can use a cutoff of 76.  (Transcript page 9.)  An IQ score of 76 is above 70 by more than twice the standard error of measurement for most IQ tests, and thus it is outside the 95% confidence interval for anyone with a "true" IQ of 70 or lower, the standard definition of the first prong of the test for retardation.

But is the 95% confidence interval magic?  If a state must give some consideration to the possibility of measurement error, could it use a narrower interval?  No, it is not magic.  It is just a conventional rule of thumb.

Several justices question the 95% convention.  See pages 10-11 (Chief Justice Roberts), 19-20 (Justice Kagan), 39 (Justice Alito).  They are right to question it.

Most of the chance that the true score varies from the test score occurs in a narrower band close to the test score.  The probabilities drop off rapidly in the "tails" as explained in CJLF's brief in this case.  Instead of two standard errors, one might use one standard error.  The chance that a true score lies outside the plus-or-minus one standard error interval is only about 1 in 3, and the chance that it lies in the low-end tail, the only one of concern here, is only about 1 in 6.

For the Wechsler Adult Intelligence Scale--Fourth Edition (WAIS-IV), the standard error of measurement is 2.16.  (See APA Brief at p. 23.)  The chance of a person with a true IQ of 70 scoring 73 or above on the WAIS-IV simply due to measurement error is a mere 8.2%.  (See CJLF Brief 13-15.)  The chance that a person with that test score (as Hall has) has a true IQ of 70 or below is approximately the same.

Is that an acceptable risk in an Atkins case?  Sure.  The only consequence of a "not retarded" finding in an Atkins hearing is that the defendant gets the individualized weighing of aggravating against mitigating circumstances (including mental impairment however labeled) that was found to be constitutionally proper before Atkins in Penry v. Lynaugh.  What's wrong with that?  The claim of the Atkins opinion that persons with retardation are categorically less culpable than persons without it, including those just marginally above the line, is patent nonsense when applied to persons just below the line. 

We are not talking about Lennie from Of Mice and Men here.  We are talking about people like the defendant in this case.  Let us never forget what this man did, as described by the trial judge:

On February 21, 1978, Freddie Lee Hall kidnapped Karol Lea Hurst from the parking lot of a grocery store as she was carrying her packages to her car. He drove her, in her own car, some 18 miles away into another county and into the woods a quarter of a mile off the paved road. There, in the front seat of her car, he forced her to remove her clothes and then he raped her. He listened to her cry, and he listened to her beg for her life and the life of her unborn child. He watched her write a check for him to cash in return for her life. Then he beat her--so hard that it tore the flesh of her neck and shoulders through the fabric of her denim jacket. And then he killed her by firing a bullet into the back of her head, either pulling the trigger himself or encouraging another to do it in his place. There is no evidence that has been presented to this Court that reasonably mitigates the aggravated nature of this act. The aggravating circumstances of this case clearly 'outweigh' the mitigating factors.
By no stretch of the imagination is the execution of this murderer a miscarriage of justice.

4 Comments

I know Kent has often said that you can't determine how the particular justices will rule based on oral argument, especially Justice Kennedy. But, having read the briefs and the argument transcript, I am confident that five justices will hold that a 70 cutoff with or without consideration of the SEM is unconstitutional. I believe that these justices will require that the trier of fact be given the opportunity to consider evidence that is presented on all three prongs in order to satisfy Atkins.

By the way, I was surprised at Waxman's argument. Why he would concede that a cutoff of 76 is okay is mind-boggling.

Kennedy's questions about the extraordinary delays in carrying out the dp was also interesting. I his comments can be taken two ways when it comes to the constitutionality of capital punishment?

Words cannot express my contempt for Mr. Waxman and this bit of dishonesty:

"First of all, we're talking ­­ I mean, this is a man who has a 71." No, counselor, this is a man who scored an 80, a score that if Hall's IQ were 69, would be well-nigh impossible to fake. That the Supreme Court let him get away with this facile dishonesty is telling. I think even the death penalty supporters on the Court are getting tired of the slogs toward death and are slowly conceding the field. If I were questioning Mr. Waxman, I would have pushed him hard on the near impossibility of a mentally retarded guy scoring an 80 on an IQ test. Ms. Hurst's memory deserved a better showing.

I don't know if Ms. Hurst has any near living relatives, but I imagine they would be astounded at the utter surreality of the oral argument. This case is decades old and could get much older. The guy got an 80, and now there are "experts" who are trying to prove that this animal is mentally retarded?

The Supreme Court, in my view, loses a bit of its legitimacy every time it engages in this sort of nonsense. This isn't law--this is a rigged game of mother, may I?

I think states should do everything in their power to preserve death sentences and should flout the Court when they can get away with it. How many appellate decisions flout the AEDPA standard? What's sauce for the goose is sauce for the gander. When you look at the barbarity of Hall's crime and the long march to justice (caused in large part by the Supreme Court), there is absolutely no reason for anyone to respect the decision that will force Florida to take another look at this death sentence. None.

I wish the Florida AG would have had the cojones to simply tell Kagan and Ginsburg--guys, this vicious murderer that you care so deeply about scored an 80 on an IQ test--the odds of him being able to do that if he were truly mentally retarded are astronomical. Quite frankly, your questioning has a surreal quality. This guy isn't mentally retarded, and the Florida courts were absolutely correct to reject his claim. If you want to vote to give him another chance at escaping death, there's nothing I can do about it, but it would be a miscarriage of justice, and an appalling abuse of power.


"By the way, I was surprised at Waxman's argument. Why he would concede that a cutoff of 76 is okay is mind-boggling."

It's an ever so slight concession to reality. At some point, obviously, a score on an IQ test is enough to end the inquiry. Well, if a test score shows that the guy has less of a 5% chance of being MR, certainly, the state can make a rule that he doesn't get the benefit of the Atkins decision, but can avail himself of the mitigant argument to the sentencer. Of course, Waxman's concession should end the case. Hall scored an 80--a score that would be nearly impossible for a truly mentally retarded person to get.

But you know Ginsburg and Kagan have a murderer to save, so the elephant in the room will be ignored.

federalist's comments are well taken. But I think miss an important practical point: When either party in a criminal prosecution -- defense or prosecution -- overreaches it generally backfires.

No doubt Hall should be executed for his horrendous crimes. And, if Florida hadn't overreached by using an outlier strict cutoff, I have no doubt that the trier-of-fact would have rejected Hall's MR claim and he would be that much closer to his just punishment.

Perhaps Kennedy (by his off-topic questioning) was trying to show that there was a causal connection between Florida's overreaching and the inordinate delay?

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