Combining multiple intelligence test scores (IQs) into a grand psychometrically sound estimate. Joel Schneider’s free on-line web app.

In an earlier post in March, I alerted readers to a new journal publication that presented a psychometrically sound rational and method for combining multiple intelligence test scores into a single grand estimate.  Below is the formal APA reference:  Go to link above for more info.

Schneider, W. J., Reynolds, C. R., McGrew, K. S., & Salekin, K. L. (2026). Life-and-death psychometrics: Generalizable best methods for combining scores in intellectual disability and other diagnostic assessments. Journal of Pediatric Neuropsychology, 12(2), 47–65.

I’m pleased to report that Dr. Joel Schneider has developed a free on-line web app that allows users to implement the recommended method.  Thanks to Joel.

Click on image to enlarge for easy reading

Breaking legal and research news: SCOTUS (US Supreme Court) decision re multiple IQ scores in intellectual disability (ID) death penalty case (Hamm v Smith) - A DIG decision upholding the lower court decision

Today SCOTUS ruled on the Hamm v Smith multiple IQ score Atkins intellectual disability (ID) case that was argued before SCOTUS last December. This important decision, with all concurring and dissenting opinions, is available here.  Interested parties should read all the opinions. 

All documents and the history of the case can be found in a prior IQs Corner post.  As noted in the prior lengthy post, APA submitted an Amicus brief that, based on the reading of some of the justices opinions, suggests it (together with a AAIDD Amicus Brief) played an important role in the decision.

Briefly, when SCOTUS dismisses the writ of certiorari as improvidently granted it means the justices recognized that they made a mistake in agreeing to hear the case and decided to dismiss it without issuing a ruling on the merits. In legal shorthand, this is often referred to as a "DIG" (Dismissed as Improvidently Granted). This typically happens after the Court has accepted the case, reviewed the briefs, and sometimes even heard oral arguments. 

In practice, this means that the lower court decision—which is consistent with APA’s Amicus brief—that argued that multiple IQ scores should be viewed holistically  augmented by clinical judgement—stands. This means Mr. Smith will not be executed and, more importantly, the ruling does not upset the status of prior Atkins case law.  Given the recent direction and flavor of SCOTUS, there was a fear that SCOTUS might render a formal decision that would set back prior SCOTUS Atkins ID decisions.  So, this is a win for maintaining the principles of clinical judgement, the opinions and standards established by the established medical communities (both APA’s, AAIDD), and the need for a holistic approach to the interpretation of multiple IQ scores together with adaptive behavior.

A reading of the concurring opinions indicates that APA’s brief, as well as several key APA and AAIDD ID-related publications referenced in their decisions, were influential in the decision.  Several of the dissenting opinions reveal some troubling thinking by several justices. 

As a potential conflict of interest (COI) notice, I (Dr. Kevin McGrew), together with Dr. Joel Schneider and Dr. Cecil Reynolds (as noted on page three the APA amicus brief), were consultants to APA in the drafting of that brief.

It should be noted that as a result of the work of APA Amicus brief working committee, a peer-reviewed paper outlining a psychometrically sound approach (developed by Dr. Joel Schneider) for integrating multiple IQ scores was started during the deliberations and was recently published (Schneider, Reynolds, McGrew & Salekin, 2026) after the oral argument's.  This issue will likely to be revisited in future state cases, with Schneider et al. (2026) now elevated to a scientifically sound multiple IQ composite score method.

AI Brief: Is the Intellectual Functioning Component of AAIDD’s 12th Manual Satisficing?

AI Brief:  Is the Intellectual Functioning Component of AAIDD's 12th Manual Satisficing?

 (McGrew, 2021)

 

Dr. Kevin McGrew with assist from Google NotebookLM

 

In a commentary published in Intellectual and Developmental Disabilities, Kevin S. McGrew  evaluated the intellectual functioning section (prong 1) of the AAIDD’s 12th edition manual (2021) for diagnosing intellectual disabilities (ID). He commends the organization for finally adopting the Cattell-Horn-Carroll (CHC) theory, which aligns the manual with modern scientific consensus on cognitive abilities. However, the author expresses significant concern about the manual’s contradictory guidance on part scores, arguing that its ambiguous stance could lead to legal and diagnostic confusion. McGrew also highlights various technical measurement issues and numerous copyediting errors that he believes undermine the manual's status as an authoritative resource. He suggests that while the manual is satisfactory in its theoretical shift, it does not provide the precise clarity needed for high-stakes clinical and judicial settings.

 

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In his review of the 12th edition of the American Association on Intellectual and Developmental Disabilities (AAIDD) manual, McGrew (2021; link for downloading article) evaluates whether the "Intellectual Functioning Component" (aka.,prong 1 of a three-prong definition of intellectual disability—ID) provides a "satisficing"—or satisfactory and sufficient—solution for practitioners and scholars.[1] McGrew draws on over 45 years of experience in school psychology and intelligence research, theory, and test development. In addition, he draws on his expert work and consultation (since 2009) on Atkins intellectual disability (ID) death penalty cases in legal settings. McGrew provides an evaluation of the AAIDD’s manual's prong 1 (intellectual functioning) theoretical grounding, technical guidance, and professional polish. He does not evaluate the other two ID prongs (adaptive behavior and age of onset).

Advancement in Intelligence Theory

McGrew awards the manual a Grade B+ for its formal adoption of the Cattell-Horn-Carroll (CHC) theory of intelligence. This shift aligns the AAIDD manual with the contemporary consensus taxonomy of cognitive abilities, moving away from outdated models. However, McGrew notes that the manual "muddies the CHC waters" by giving preferential treatment to fluid (Gf) and crystallized (Gc) intelligence while neglecting other broad CHC abilities like learning efficiency (Gl), working memory (Gwm), retrieval fluency (Gr), auditory processing (Ga), visual-spatial processing (Gv), and processing speed (Gs). He suggests that a visual-graphic model of the CHC hierarchical model would have been a beneficial addition for users.

Measurement and Organizational Challenges

The manual receives a Grade B- for its treatment of major measurement issues. While it provides adequate coverage of such measurement issues as the standard error of measurement (SEM), confidence intervals, and the Flynn effect (aka., norm obsolescence), McGrew criticizes the lack of a topic index, which makes finding specific guidance very frustrating. For instance, practice effects are obscurely placed under "progressive error" in the glossary, and the Flynn effect is curiously categorized under "Making a Retrospective Diagnosis," despite being relevant to historical and current intellectual assessments.

The Part-Score Controversy

The most critical evaluation—a Grade C—is reserved for the manual's handling of part scores. McGrew identifies three primary failures in this area:

 

●      Inconsistency: The manual contradicts itself by advising against the use of part scores as proxies for general intelligence (psychometric g) while simultaneously suggesting that their valid use requires 3–6 subtests of Gf and Gc.

●      Variance with Other Authorities: This "just say no to part scores" stance conflicts with other major authoritative sources, such as the DSM-5, which acknowledges that highly discrepant subtest scores may invalidate an overall IQ score.

●      Scientific and Legal Tensions: McGrew argues that the manual fails to address the "General-2-individual" (G2i) legal principle which acknowledges that group-based scientific research (e.g., suggesting full-scale scores are always superior) may not apply to every unique individual case—the G2i principle conundrum is that scientists generalize; but courts must particularize to an individual. He warns that without clearer guidance; legal entities may fill the void with "remedies of dubious quality.”

Editorial Quality and Professionalism

McGrew gives the manual a Grade D for style and substance, citing at least 20 copyedit errors in the sections relevant to the intellectual functioning prong alone. These include misspellings of prominent researchers, incorrect terminology like "test e-norms," and frequent "misplaced italics.” He contends that such preventable errors tarnish the manual’s status as an "authoritative" and "definitive" source for diagnosing intellectual disabilities.

Conclusion

McGrew concludes that while the endorsement of CHC theory is a significant positive revision, the manual’s obfuscation regarding part scores and its numerous editorial flaws represent major missed opportunities. He emphasizes that practitioners cannot wait another decade for the next edition to offer more robust guidance, particularly in high-stakes legal and diagnostic settings. He concludes that while he may be a "tough grader," his critiques are intended to push AAIDD toward more robust and clearer guidance in future editions or supplements

[1] Nobel laureate Herb Simon advanced the behavioral economics concept of satisficing (Simon, 1956)—the idea that, although we may aspire to optimal solutions, real-world constraints often require us to settle on what is both satisfactory and sufficient (hence, the portmanteau term satisficing).

Hamm v Smith intellectual disability SCOTUS Atkins death penalty oral arguments (12-10-25) re multiple IQ scores: #ID #atkins #deathpenalty #IQ #intelligence

See prior post regarding Hamm v Smith Atkins ID death penalty case where central issue is how to handle multiple IQ scores.  All briefs are at that prior blog post page.

Oral arguments before the SCOTUS justices occurred this past Wednesday, 12-10-25.  One can download audio file (arguments lasted 2 hours) or transcript of arguments at this link. 

Supreme Court to consider the role of #IQ tests in ban on executing people who are #intellectually disabled (#ID)- #SCOTUSblog: #schoolpsychology #schoolpsychologists #intelligence

An email quick-blog post FYI.

 

If you want more information, including amicus briefs for the defendent from professional groups (APA, AAIDD), visit a special post at IQs Corner blog—-

 

Court to consider the role of IQ tests in ban on executing people who are intellectually disabled - SCOTUSblog 
https://www.scotusblog.com/2025/12/court-to-consider-the-role-of-iq-tests-in-ban-on-executing-people-who-are-intellectually-disabled/

Pardon typos and spelling errors-Message may be sent from iPhone and I've always had spelling problems :)
 

 

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Kevin S. McGrew, PhD
Educational & School Psychologist
Director
Institute for Applied Psychometrics (IAP)
https://www.themindhub.com
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IQs Corner. In what way are #intelligence testing (#IQ) and the US Supreme Court (#SCOTUS) alike?—SCOTUS will be hearing important case addressing #multiple IQ scores and #intellectualdisability #Dx in fall 2025 term

This fall 2025, the Supreme Court of the United States (SCOTUS) will be hearing a case related to intelligence testing in the context of Atkins intellectual disability (ID) death penalty cases. The case is Hamm v Smith.

The question before SCOTUS is :  Whether and how courts may consider the cumulative effect of multiple IQ scores in assessing Atkins claims (in the context of diagnosis ID in death penalty cases)?

Note.  In order to save space and time, instead of writing “general intelligence” or “general intellectual functioning” every time, I use the abbreviation “IQ”.

The respondent (Joseph Smith) has five IQ test scores from comprehensive IQ tests.  He obtained two scores of 75 and 74 during the developmental period (before age 22), and three scores of 72, 78, and 74 between the ages of 28 and 46.  

This case is important for assessment professionals who conduct intelligence testing in general, and potential ID diagnostic cases (Atkins cases in particular).  I find this SCOTUS case particularly interesting given that in 2021, after the 2021 release of the latest official AAIDD manual (Intellectual disability: Definition, diagnosis, classification, and systems of supports), I published a critique where I specifically stated, as one weakness of the new AAIDD manual that “…many high-stakes ID cases often include case files that include multiple IQ scores across time or from different IQ tests. Some form of guidance, at minimum in a passing reference, to the issues of the convergence of indicators and IQ score exchangeability would have been useful. Users will need to go beyond the AAIDD manual for guidance (see Floyd et al., 2021; McGrew, 2015; and Watson, 2015)” (click here to download and read this critique).

All official petitioner and respondent legal briefs (and amicus briefs) have now been published at the SCOTUS blog as of yesterday.  The number of documents posted on the SCOTUS docket are many.  To help the reader better determine which documents are most critical (the final briefs), instead of clicking away on the various links at the SCOUTUS blog, I’ve organized the petitioner and respondent brief links below.

If you prefer to not wade through all the briefs (it is not for everyone), I would encourage practicing assessment professionals read the three respondent-related briefs.  The points made are relevant to all who conduct intellectual assessments.  As a potential conflict of interest notice, I (Dr. Kevin McGrew), together with Dr. Joel Schneider and Dr. Cecil Reynolds (as noted on page three for the APA amicus brief), were consultants to APA in the drafting of that brief.  This work was performed pro bono. I, at a minimum, suggest reading all the respondent briefs.  If time permits, I would also suggest reading the petitioner’s Alabama brief and the US Justice Department Solicitor General’s brief to better understand the petitioner and respondent positions re Hamm v Smith. 

Petitioner briefs

• The state of Alabama brief.  Alabama is the petitioner.  That is, if you want to read why the State of Alabama asked SCOTUS to hear this case, click on the link provided.
• The Alabama brief also includes a very long appendix for those who want to read the prior courts related testimony from the state and various experts. This is a very long read and is not necessary for readers who only want to understand the legal and professional issues. 
• Supporting amicus brief from the US Justice Department Solicitor General.
• Two supporting briefs from legal groups—the American Legal Foundation and the Criminal Justice Legal Foundation.
• Supporting amicus briefs from other states (Idaho et al.; Kentucky)

Respondent briefs

• Smiths respondent brief.
• Supporting amicus brief from American Psychological Association (APA), American Psychiatric Assocation (ApA), and Alabama APA.
• Supporting amicus brief from AAIDD et al.

Final comment.  Those from school psychology should make note that we three consultants involved in drafting the APA/ApA,AL-APA brief all had our original educational roots in the profession of school psychology.  Furthermore, SP professionals should note the significant number of authoritative references to publications authored by school psychologists in the respondents briefs, as well as in some of the petitioners briefs.  I’ve been doing expert consultation, writing declarations, and testifying in court re: Atkins ID cases since 2009.  Joel Schneider and Cecil Reynolds have also been active in a similar capacity.  There are more psychologists who come from, or are affiliated with, the field of school psychology who have been prominent consultants/experts to lawyers and the courts re Atkins cases.  

Perhaps some of these briefs should be assigned readings (in intellectual assessment courses or special topic seminars) for graduate students being trained in the art and science of intelligence testing and interpretation.

Law Review Article: Evaluating Intellectual Disability: Clinical Assessments in Atkins Cases (Ellis et al., 2018)

This new law review article is, IMHO, the best overview article regarding the history of ID, the legal issues in Atkins cases, and good discussion of the major conceptual and measurement issues found in many Atkins cases. An excellent introduction to ID issues in Atkins cases.

EVALUATING INTELLECTUAL DISABILITY: CLINICAL ASSESSMENTS IN ATKINS CASES

James W. Ellis, Caroline Everington, Ann M. Delpha

ABSTRACT

The intersection of intellectual disability and the death penalty is now clearly established. Both under the U.S. Supreme Court's constitutional decisions and under the terms of many state statutes, individual defendants who have that disability cannot be sentenced to death or executed. It now falls to trial, appellate, and post-conviction courts to determine which individual criminal defendants are entitled to the law's protection. This Article attempts to assist judges in performing that task. After a brief discussion of the Supreme Court's decisions in Atkins v. Virginia, Hall v. Florida, and Moore v. Texas, it analyzes the component parts and terminology of the clinical definition of intellectual disability. It then offers more detailed discussion of a number of the clinical issues that arise frequently in adjudicating these cases. For each of these issues, the Article's text and the accompanying notes attempt to provide judges with a thorough survey of the relevant clinical literature, and an explanation of the terminology used by clinical professionals. Our purpose is to help those judges to become more knowledgeable consumers of the clinical reports and expert testimony presented to them in individual cases, and to help them reach decisions that are consistent with what the clinical literature reveals about the nature of intellectual disability and best professional practices in the diagnostic process.

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Sixth Circuit Court of Appeals rules (Black v Carpenter, 2017) against norm obsolescence (Flynn effect) adjustment of IQ scores in Atkins death penalty cases

A newly published 6th Circuit opinion (Black v Carpenter, 2017) rules against norm obsolescence (the Flynn effect) in the evaluation of IQ test scores in Atkins ID death penalty cases.  I obviously disagree with this decision as outlined in my 2015 chapter in the AAIDD "The Death Penalty and Intellectual Disability" (Polloway, 2015).

I have no further comment at this time as my expert opinion is clearly articulated in the AAIDD publication and I will continue my efforts to educate the courts.  This decision is at variance with the official positions of American Association on Intellectual and Developmental Disabilities (AAIDD) and the American Psychiatric Association (DSM-5), the two professional associations with official  guidance regarding  the diagnosis of ID. 

This looks like another issue that might need the attention of SCOTUS.

The following section is extracted from the complete ruling.


E. Implications of the Flynn Effect

There is good reason to have pause before retroactively adjusting IQ scores downward to offset the Flynn Effect. As we noted above, see n.1, supra, the Flynn Effect describes the apparent rise in IQ scores generated by a given IQ test as time elapses from the date of that specific test’s standardization. The reported increase is an average of approximately three points per decade, meaning that for an IQ test normed in 1995, an individual who took that test in 1995 and scored 100 would be expected to score 103 on that same test if taken in 2005, and would be expected to score 106 on that same test in 2015. This does not imply that the individual is “gaining intelligence”: after all, if the same individual, in 2015, took an IQ test that was normed in 2015, we would expect him to score 100, and we would consider him to be of the same “average” intelligence that he demonstrated when he scored 100 on the 1995-normed test in 1995. Rather, the Flynn Effect implies that the longer a test has been on the market after initially being normed, the higher (on average) an individual should perform, as compared with how that individual would perform on a more recently normed IQ test.

At first glance, of course, the Flynn Effect is troubling: if scoring 70 on an IQ test in 1995 would have been sufficient to avoid execution, then why shouldn’t a score of 76 on that same test administered in 2015 (which would produce a “Flynn-adjusted” score of 70) likewise suffice to avoid execution? Further, even if IQ tests were routinely restandardized every year or two to reset the mean score to 100, and even if old IQ tests were taken off the market so as to avoid the Flynn Effect “inflation” of scores that is visible when an IQ test continues to be administered long after its initial standardization, that would only mask, but not change, the fact that IQ scores are said to be rising.

Indeed, perhaps the most puzzling aspect of the Flynn Effect is that it is true. As Dr. Tassé states in his declaration, “[t]he so-called ‘Flynn Effect’ is NOT a theory. It is a wellestablished scientific fact that the US population is gaining an average of 3 full-scale IQ points per decade.” The implications of the Flynn Effect over a longer period of time are jarring: consider a cohort of individuals who, in 1917, took an IQ test that was normed in 1917 and received “normal” scores (say, 100, on average). If we could transport that same cohort of individuals to the present day, we would expect their average score today on an IQ test normed in 2017—a century later—to be thirty points lower: 70, making them mentally retarded, on average.

Alternatively, consider a cohort of individuals who, in 2017, took an IQ test that was normed in 2017 and received “normal” scores (of 100, on average). If we could transport that same cohort of individuals to a century ago, we would expect that their average score on a test normed in 1917 would be thirty points higher: 130, making them geniuses, on average.

It thus makes little sense to use Flynn-adjusted IQ scores to determine whether a criminal is sufficiently intellectually disabled to be exempt from the death penalty. After all, if Atkins stands for the proposition that someone with an IQ score of 70 or lower in 2002 (when Atkins was decided) is exempt from the death penalty, then the use of Flynn-adjusted IQ scores would conceivably lead to the conclusion that, within the next few decades, almost no one with borderline or merely below-average IQ scores should be executed, because their scores when adjusted downward to 2002 levels would be below 70. Indeed, the Supreme Court did not amplify just what moral or medical theory led to the highly general language that it used in Atkins when it prohibited the imposition of a death sentence for criminals who are “so impaired as to fall within the range of mentally retarded offenders about whom there is a national consensus,” 536 U.S. at 317. If Atkins had been a 1917 case, the majority of the population now living—if we were to apply downward adjustments to their IQ scores to offset the Flynn Effect from 1917 until now—would be too mentally retarded to be executed; and until the Supreme Court tells us that it is committed to making such downward adjustments, we decline to do so.

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COLE, Chief Judge, concurring in the opinion except for Section II.E. I concur with the majority opinion except as to the section discussing the implications of the Flynn Effect. In holding that Black did not prove that he had significantly subaverage general intellectual functioning, we concluded that Black’s childhood IQ scores would be above 70 even if we adjusted those scores to account for both the SEM and the Flynn Effect. Accordingly, I would not address the question of whether we should apply a Flynn Effect adjustment in cases generally because it is unnecessary to the resolution of Black’s appeal. Regardless, courts, including our own in Black I, have regarded the Flynn Effect as an important consideration in determining who qualifies as intellectually disabled. See, e.g., Black v. Bell, 664 F.3d 81, 95–96 (6th Cir. 2011); Walker v. True, 399 F.3d 315, 322–23 (4th Cir. 2005).

Breaking News: SCOTUS vacates Moore v Texas Atkins decision: Briseno adaptive behavior standards not consistent with medical consensus

SCOTUS has vacated Moore v Texas which had as the central issue the inappropriate use of the state of Texas's unusual Briseno adaptive behavior standards.

Prior posts regarding this case can be found here. The history of the case before SCOTUS is available at the SCOTUS blog. A copy of the decision can be accessed here.

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