David Kaye on Hall v Florida-- "Deadly statistics: Quantifying an "unacceptable risk in capital punishment" - In press article in Law, Probability and Statistics

The following article is "in press" in Law, Probability and Statistics.  A preview can be found here.

 

Deadly Statistics:
Quantifying an “Unacceptable Risk” in Capital Punishment
David H. Kaye*
Law, Probability & Risk
Vol. 15, No. 4, Dec. 2016 (in press)

Abstract: In Atkins v. Virginia, the U.S. Supreme Court held that the Eighth Amendment ban on
cruel and unusual punishment precludes capital punishment for intellectually disabled offenders.
Death-penalty states responded with laws defining intellectual disability in various ways. In Hall v.
Florida, the Court narrowly struck down the use of a measured IQ of 70 to mark the upper limit of
intellectual disability because it created “an unacceptable risk that persons with intellectual disability
will be executed.” But the Court was unclear if not inconsistent in its description of an upper limit
that would be acceptable. Four dissenting Justices accused the majority not only of misconstruing
the Eighth Amendment, but also of misunderstanding elementary statistics and psychometrics. This
article uses more complete statistical reasoning to explicate the Court’s concept of unacceptable risk.
It describes better ways to control the risk of error than the Court’s confidence intervals, and it argues
that, to the extent that the Eighth Amendment allows any quantitative cut score in determining an
offender’s intellectual disability, these more technically appropriate methods are constitutionally
permissible.

Keywords: Hall v. Florida, cruel and unusual, Eighth Amendment, capital punishment, intellectual
disability, IQ, psychometrics, cut-score, measurement error, standard error, confidence interval,
shrinkage estimator, Bayesian inference, credible region, burden of persuasion

Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
I. The Intellectual Disability Trilogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
II. The Need to Allow States to Use Cut Scores and the Meaning of “Significantly Subaverage”
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
III. True Scores and Single-measurement Error Within Classical Test Theory.. . . . . . . . . . . . . . 15
A. First- and Second-order Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
B. True Scores and Measurement Error.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
C. Reliability and Standard Error of Measurement (SEM). . . . . . . . . . . . . . . . . . . . . . . . 18
D. Confidence Intervals from the SEM (SEM-IS).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
E. SEM-adjusted-maximum Score (SEM-AM).. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
F. Confidence Intervals from the Standard Error of Estimate (SEE-IS). . . . . . . . . . . . . . 27
IV. Other Statistical Issues in and Outside of Hall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
A. Multiple Scores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
B. Credible Regions (BCR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Summary and Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34