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Suppose that two tests have a correlation of 0.6. On both tests an individual obtained an index score of 130, which is 2 standard deviations above the mean. If both tests are combined, what is the composite score?
Our intuition is that if both tests are 130, the composite score is also 130. Unfortunately, taking the average is incorrect. In this example, the composite score is actually 134. How is it possible that the composite is higher than both of the scores?
If I measure the length of a board twice or if I take the temperature of a sick child twice, the average of the results is probably the best estimate of the quantity I am measuring. Why can't I do this with standard scores?
Standard scores do not behave like many of our most familiar units of measurement. Degrees Celsius have meaning in reference to a standard, the temperature at which water freezes at sea level. In contrast, standard scores do not have meaning compared to some absolute standard. Instead, the meaning of a standard score derives from its position in the population distribution. One way to describe the position of a score is its distance from the population mean. The size of this distance is then compared to the standard deviation, which is how far scores typically are from the population mean (more precisely, the standard deviation is the square root of the average squared distance from the mean). Thus, the "standard" to which standard scores are compared are the mean and standard deviation.
The average of two imperfectly correlated index scores is not an index score. Its standard deviation is smaller than 15 and thus our sense of what index scores mean does not apply to the average to two index scores. To make sense of the composite score, we must convert it into an index score that has a standard deviation of 15.
How is this possible. It is unusual for someone to score 130. It is even more unusual for someone to score 130 on two tests that are imperfectly correlated. The less correlated the tests, the more unusual it is to score high on both tests.
Below is a geometric representation of this phenomenon. Correlated tests can be graphed with oblique axes (as is done in factor analyses with oblique rotations). The cosine of the correlation is the angle between the axes. As seen below, the lower the correlation, the more extreme the composite. As the correlation approaches 1, the composite approaches the average of the scores.
In a previous post, I presented this material in greater detail.
I found "Revisiting intellectual disability and the death penalty" in Monitor - April 2014
Monitor - April 2014
I thought you would enjoy "Revisiting intellectual disability and the death penalty" from Monitor - April 2014
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- Argument analysis: When simplicity won't do
- In wake of secret videos, security tweaks evident at the Court
- Breaking News
- Court grants five cases (UPDATED)
- Monday round-up
- Today at the Court | March 3, 2014
- This week at the Court
Posted: 03 Mar 2014 11:29 AM PST
If a state, trying to make it simple to decide who can be given a death sentence, opts for a choice that looks arbitrary, it is likely to have a difficult time in a Supreme Court that worries about the chances of error. That was demonstrated anew on Monday, when Florida found itself in deep Eighth Amendment trouble with a rule that anyone with an IQ above 70 can be executed if convicted of murder.
A quite definite majority of the Justices — perhaps, notably, including Justice Anthony M. Kennedy — left little doubt that Florida and six other states will not be allowed to maintain an automatic test-score-based cutoff for those who could qualify as mentally retarded and thus can escape the death penalty.
Kennedy's role is central because he has most often led the Court in narrowing the category of those eligible to be executed, to take account of reduced capacity to be held responsible for their criminal behavior. He was among the most active in questioning Florida's approach to mental retardation among those on death row. And, on Monday, he added in some strongly implied criticism of a system that allows some inmates to remain on death row for decades — an issue that is not directly involved in the new case of Hall v. Florida.
Justice Antonin Scalia expended considerable effort to buttress Florida's basic argument that the scientific community cannot be trusted to make the rules for eligibility for capital punishment, but except for some supportive hints from Justice Samuel A. Alito, Jr., this seemed to be a largely forlorn endeavor.
Most of the other Justices joined in the pursuit of an Eighth Amendment rule that would assure that the mental retardation inquiry was sophisticated and nuanced, so that the risk of error was taken fully into account. While such a rule might not definitely hand over the details to the judgment of scientists and doctors, it apparently would not tolerate an approach designed simply to assure that fewer death-row inmates get off with a claim of mental disability. That appeared to be Florida's main objective.
Justice Kennedy waited to get involved in the argument until Washington attorney Seth P. Waxman, representing Florida inmate Freddie Lee Hall, was about halfway through his argument. The Justice then began exploring whether the Court should defer to "the psychiatric profession" and why it should pay attention to psychiatric theories any more than it does to economic theories, when it must make a legal judgment.
Waxman answered that what the Court was dealing with in this case was a question of a "clinical condition," and how best to determine whether that condition existed. It cannot be done, he contended, just by using a raw IQ test score, without allowing for the inevitable chance of error in all such testing.
Kennedy held off for the rest of Waxman's argument, having raised some doubt about whether he was comfortable with turning the Eighth Amendment inquiry into one to be left to the scientists.
But, when Florida's state solicitor general Allen Winsor went to the lectern, Kennedy quickly rejoined the questioning, and promptly suggested that Florida was arbitrarily refusing to take account of the standard error in IQ testing, which the Justices said had been acknowledged by "people who design and administer" IQ tests.
Soon, Justice Elena Kagan reminded Winsor that, throughout its death penalty jurisprudence, the Court has always allowed those facing that potential sentence to make the best case they could to try to avoid it, and yet Florida had adopted a flat rule that cut off the plea for anyone who had measured above 70 on an IQ test. Some of those, she suggested, may actually be mentally retarded — and thus entitled to the protection the Supreme Court had previously given to those in that category.
Kennedy, apparently not satisfied with Winsor's responses, commented that Justice Kagan had asked a "very important question," and commented that the Florida rule prevents courts from gaining "a better understanding" of the mental condition of an individual on death row because it short-circuits a full inquiry.
Several times after that, Kennedy, sounding genuinely puzzled, wondered whether Florida really did stop the inquiry into mental retardation once a death-row inmate had an IQ above 70. But Winsor kept reaffirming the hard-and-fast cutoff for inmates who measured higher than that.
Late in the argument, Kennedy brought up something that he and his clerks must have turned up in preparing for this case. The last ten people Florida had executed, Kennedy said, had been on death row for an average of 24.9 years. He wondered if that was consistent with the Constitution and with the orderly administration of a death-sentencing scheme. Winsor seemed caught off-guard, saying only that he thought this was consistent with death penalty law.
Justice Scalia intervened to try to help out Winsor, noting that most of the delays for people on death row had resulted from the complexity that the Supreme Court itself had caused in the process.
Justice Kagan used a final thrust against Florida's scheme by asking, simply, why Florida would have adopted its flat IQ rule. Florida, Winsor said, had an interest in making sure that people do not evade execution by claiming mental retardation, and the challenge being made by Hall had the prospect of doubling the number who could do so successfully.
Kennedy's skepticism was entirely shared by Justices Kagan, Stephen G. Breyer, Ruth Bader Ginsburg, and Sonia Sotomayor. Chief Justice John G. Roberts, Jr., played only a minor role in the hearing. Justice Clarence Thomas, as is his custom, remained silent.
[Note: Although the preferred clinical term for the condition at issue in this case is "intellectual disability," and earlier posts on the case on this blog use that term, both the lawyers and the Justices used the term "mental retardation" at today's oral argument. For that reason, this post uses the latter term as well.]
In association with Bloomberg Law
Posted: 03 Mar 2014 09:43 AM PST
Several apparent tweaks to Supreme Court security procedures were evident today in the first oral argument since last week's release of surreptitious recordings of courtroom sessions.
Visitors approaching the courtroom for their second security check – the first is at the entrance to the building – were greeted with a more brightly lighted table for the Court's police officers to examine personal effects. The checkpoint just outside the courtroom is in the Great Hall, which has relatively dark ambient lighting. Visitors, as always, walk through a magnetometer, while Supreme Court police officers examine purses, notebooks, and other small personal items allowed inside the courtroom. All electronic devices, such as cellphones, are prohibited from the courtroom, as are larger bags and briefcases.
On Monday, before the argument in Hall v. Florida, the challenge to Florida's scheme for identifying defendants as intellectually disabled and therefore ineligible for the death penalty, those inspection tables were each lighted with triple-bulb standing lamps and were covered with white tablecloths. Many visitors, including reporters who regularly must pass through the checkpoint, were required to extend or remove their belts for inspection. A sign prominently displayed at the checkpoint reminds visitors that cameras and recording devices are not allowed in the courtroom.
Inside the courtroom, a standard security announcement delivered by a police officer about ten minutes before the start of oral arguments appears to have been tweaked. The announcement, which typically discusses the need to remain quiet and where spectators should exit, on Monday encouraged spectators to "discreetly" alert security personnel "if you see anything suspicious."
The Court's Public Information Office declined to discuss the changes, saying it does not comment on security procedures.
Last week, an activist group named 99Rise claimed credit for posting several video clips taken surreptitiously inside the courtroom and posted on YouTube. The clips include several minutes from an October argument, as well as the shaky footage capturing last week's outburst, during a patent argument, by Noah Kai Newkirk in which he urged the Court to overturn its 2010 campaign-finance decision in Citizens United v. Federal Election Commission. Newkirk has been charged with violating a law prohibiting a "harangue or oration" at the court. He has pleaded not guilty.
Court observers have speculated that the courtroom videos were made with something as small as a pen camera that evaded detection at the Court's security checkpoints.
In association with Bloomberg Law
Posted: 03 Mar 2014 07:40 AM PST
Posted: 03 Mar 2014 07:06 AM PST
UPDATED 1:15 p.m. The Court at midday issued an amended order in the Arkansas case dealing with religious objections to a prison policy banning inmates from having beards. The challenging inmate, Gregory Holt, who also uses a Muslim name, had raised six questions in his petition. The amended order limited the grant to the single question whether the policy was invalid under the federal statute "to the extent" that it barred Holt from "growing a one-half-inch beard in accordance with his beliefs." Holt had offered that as a compromise alternative to the no-beard policy. (The post below has been expanded to include other details about Monday's orders.)
The Supreme Court, beginning to shape its docket for the next Term starting in October, agreed on Monday to hear five new cases, including a constitutional challenge to a state prison system's policy barring inmates from wearing beards. The Court also asked the federal government for its view on a new dispute between Florida and Georgia over the regulation of the flow of water from rivers in Georgia into Florida's Apalachicola River (142 Original).
The Court denied review of two new cases involving the power of state or local governments to regulate housing and other opportunities for undocumented immigrants.
The Court has already rounded out the list of cases it will hear and decide during the current Term, so all new granted cases will go over to October or later.
Here, in brief, are the issues in the granted cases:
Integrity Staffing Solutions v. Busk — claim for overtime pay by workers for the after-hours screening as a measure to prevent workplace theft.
Omnicare, Inc. v. Laborers District Council – proof needed in a private lawsuit by an investor claiming that a registration statement filed with the Securities and Exchange Commission was untrue.
Warger v. Shauers — scope of a right to new trial in federal court because of alleged dishonesty by a juror during the jury selection process.
North Carolina Board of Dental Examiners v. Federal Trade Commission — definition of a state agency's right to share in the state government's immunity from federal antitrust claims.
Holt v. Hobbs — religiously based challenge, under the federal Religious Land Use and Institutionalized Persons Act, to the Arkansas prison system's ban on the wearing of beards by inmates. (This is a case filed directly by an inmate, in a hand-written petition.)
Among the cases that the Court chose to deny were two from local governments in Farmers Branch, Texas, a suburb of Dallas, and Hazleton, Pa., seeking further clarification of the authority of governments at any level to pass laws that limit what undocumented immigrant may do when living in this country. Both jurisdictions had strictly limited the occupancy of housing in the community by non-citizens illegally in the U.S. The Hazleton ordinance also had barred such individuals from working in the community. Both of the ordinances at issue had been struck down in lower courts. (The petitions were in the cases of Farmers Branch v. Villas at Parkside and City of Hazleton, PA., v. Lozano, et al.)
The Court refused to take a new look at claims that the federal government has acted unconstitutionally in using various forms of global electronic eavesdropping in its investigation of potential terrorist activity. It denied review, without comment, of a petition by the Center for Constitutional Rights, a New York City-based advocacy group, and five of its staff attorneys, attempting to revive their lawsuit against the warrantless surveillance system used by the George W. Bush Administration from shortly after the 2001 terrorist attacks on the U.S., until early 2007. The petition in CCR v. Obama did not challenge the ongoing program of the National Security Agency, which has had the approval of both Congress and of the secret Foreign Intelligence Surveillance Court. That broader program is facing several court challenges that the Court will confront later.
In association with Bloomberg Law
Posted: 03 Mar 2014 04:28 AM PST
Another day, another snowstorm here in our nation's capital. But — as usual — the Court is open and there is plenty of news coverage. This morning the Court will hear oral arguments in Hall v. Florida, the challenge to Florida's scheme for identifying defendants who are intellectually disabled and therefore ineligible for the death penalty. Lyle Denniston previewed the oral argument for this blog, and Steve Wermiel discussed the case in his column for law students. Other coverage comes from NPR's Nina Totenberg and Jess Bravin of The Wall Street Journal, while in his column for The Atlantic Andrew Cohen argues that, "[i]f the Supreme Court meant what it said in Atkins [v. Virginia], the justices must loudly declare that the execution of the mentally retarded in America will not be tolerated, either as a nod to states' rights or for any other hoary justification."
- In an op-ed for The Boston Globe, Kent Greenfield weighs in on the challenges to the Affordable Care Act's contraception mandate, arguing that a decision in the challengers' favor "could do real damage. Hobby Lobby wants to be relieved of regulatory controls because of religious views. Such relief will give it an unfair advantage in the marketplace, since Hobby Lobby would not have to provide health coverage that its competitors still must."
- At Cato At Liberty, Ilya Shapiro discusses the amicus brief that Cato recently filed in Susan B. Anthony List v. Driehaus, a case involving the right to challenge a state law prohibiting false statements in elections. Cato's fellow amicus on the brief is "legendary satirist" P.J. O'Rourke, and the brief argues – among other things – that "mocking and satire are as old as America."
- At Jost on Justice, Kenneth Jost weighs in on Justice Clarence Thomas's practice of not asking questions at oral argument.
- At more than twenty cents, Andrew Suszek criticizes what he describes as the "strong trend among journalists and judges alike in using the" Court's decision in United States v. Windsor, striking down a provision of the federal Defense of Marriage Act, "to conclude that state same-sex marriage bans are unconstitutional."
In association with Bloomberg Law
Posted: 02 Mar 2014 09:01 PM PST
This morning at 9:30 a.m. we expect orders from the February 28 Conference. We will report on the orders as soon as they become available. At 10 a.m. the Justices will hear oral arguments in Hall v. Florida Lyle Denniston previewed that argument for this blog, and Steve Wermiel discussed it in his column for law students.
In association with Bloomberg Law
Posted: 02 Mar 2014 09:00 AM PST
On Monday the Court granted five new cases and called for the views of the Solicitor General in one new case. Lyle reported on those orders. On both Tuesday and Wednesday we expect one or more opinions in argued cases; we will begin live-blogging at 9:45 a.m. each day. Tuesday's live blog will be available here. Wednesday's live blog will be available here. This is the second week of the February sitting. On Friday, the Justices will meet for their March 7 Conference. Our list of "Petitions to watch" for that Conference will be available soon.
In association with Bloomberg Law
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