This is an impressive, and much needed, contribution to the CHC cognitive-math achievement relations modeling research literature. It is open access available here.
Tuesday, July 07, 2026
Research Alert: Cognitive (CHC)–Mathematics Relations: A Meta-Analysis of Norm-Referenced Standardized Test Batteries
Sunday, October 19, 2025
Extremely important (IMHO) #CHC #cognitive #reading achievement #g+specific abilities #SEM paper - #schoolpsychology #schoolpsychologists #SPED #EDPSY #LD #SLD
Extremely interesting (important/intriging) CHC cognitive-reading achievement relations meta-SEM paper. Why? Because, as far as I know, it is the first g+specific abilities paper to evaluate a model with causal relations specified within and between cognitive and reading achievement CHC constructs. Paper info below, as well as open access link to PDF. Also, this is the first time I’ve seen a meta-structural equation modeling analysis. Kudos to the authors.
Click on images to enlarge fo easy reading
Abstract
Cognitive tests measure psychological constructs that predict the development of academic skills. Research on cognitive–reading achievement relations has primarily been completed with single-test batteries and samples, resulting in inconsistencies across studies. The current study developed a consensus model of cognitive–reading achievement relations using meta-structural equation modeling (meta-SEM) through a cross-sectional analysis of subtest correlations from English-language norm-referenced tests. The full dataset used for this study included 49,959 correlations across 599 distinct correlation matrices.These included correlations among 1112 subtests extracted from 137 different cognitive and achievement test batteries. The meta-SEM approach allowed for increased sampling of cognitive and academic reading skills measured by various test batteries to better inform the validity of construct relations. The findings were generally consistent with previous research, suggesting that cognitive abilities are important predictors of reading skills and generalize across different test batteries and samples. The findings are also consistent with integrated cognitive–reading models and have implications for assessment and intervention frameworks.
Keywords: cognitive abilities; reading skills; cognitive–achievement relations; CHC theory;meta-structural equation modeling
Friday, June 06, 2025
Research Byte: General Ability (#g) Level Moderates Cognitive–#Achievement Relations for #Mathematics (#WJIV)—#WJIV #WJV #schoolpsychology #mathematics #SPED #EDPSYCH
Spearman’s Law of Diminishing Returns (SLODR) suggests general intelligence would be a stronger predictor of academic skills at lower general ability levels, and broad cognitive abilities would be stronger predictors of academic skills at higher general ability levels. Few studies have examined how cognitive–mathematics relations may vary for people with different levels of general cognitive ability. Multi-group structural equation modeling tested whether cognitive–mathematics relations differed by general ability levels for school-aged children (grades 1–5 and grades 6–12) using the Woodcock-Johnson Third Edition (n = 4470) and Fourth Edition (n = 3891) standardization samples. Results suggested that relationships between cognitive abilities and mathematics varied across general ability groups. General intelligence showed a stronger relative effect on mathematics for those with lower general ability compared to those with average or high general ability, and broad cognitive abilities showed a stronger relative effect on mathematics for those with average or high general ability compared to those with lower general ability. These findings provide a more nuanced understanding of cognitive–mathematics relations.
Tuesday, April 08, 2025
Research Byte: Conjectures and refutations in #cognitive ability #structuralvalidity research [with #WISC-V]: Insights from Bayesian structural equation modeling - #schoolpsychology #IQ #intelligence #Wechslers #WISC-V
Conjectures and refutations in cognitive ability structural validity research [with #WISC-V]: Insights from Bayesian structural equation modeling
Click here to view Journal of Psychology of School Psychology source of publication - not open access.
Sunday, November 10, 2024
Research Byte: A special contribution from #spatial ability to #math word problem solving: Evidence from #SEM and #networkanalysis
Click here to see journal page.
Abstract
Tuesday, November 06, 2018
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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Tuesday, May 27, 2014
Victory for psychometrics in Hall v Florida "bright line" (ignoring SEM) SCOTUS decision re Atkins MR/ID death penalty cases
This morning SCOTUS rectified the long standing "bright line" (ignoring SEM) problem with Atkins ID/MR cases in Florida. Click here for background information. Click here for today's decision.
Monday, March 03, 2014
Hall v Florida SCOTUS transcript from today
Here is today's transcript for the oral arguements and questioning before the US Supreme Court (SCOTUS) re the Hall v Florida Atkins case. To someone who has worked his entire career in intelligence testing, it is very interesting to hear the justices talk about IQ, SEM, etc.
Amicus briefs from APA and AAIDD (and others) have been posted previously at this blog. Prior decisions regarding Hall v Florida are available in the blogroll under Atkins decisions
Monday, December 23, 2013
SCOTUS Hall v Florida Atkins ID update: Petitioners and Amicus Briefs--major focus on IQ "bright line" and SEM
The Hall v Florida petition was filed Dec 16. Today, an Amicus Brief was filed by a number of organizations, led by the American Psychological Association.
Click here for a variety of posts re: Atkins cases in Flordia, which have been problematic due to the Florida "Cherry court" establishment of a "bright line" score of 70, with no consiseration of the standard error of measurement (SEM)
Tuesday, December 25, 2012
What we've learned from 20 years of CHC COG-ACH relations research: Back to the future and Beyond CHC
Friday, August 24, 2012
IQ Score Interpretations in Atkins MR/ID Death Penalty Cases: The Good, Bad and the Ugly

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www.themindhub.com
Saturday, September 10, 2011
Research Bytes: Bi-factor item factor analysis and CFA model fit/misfit
Wednesday, May 18, 2011
Research bytes: Reliability paradox in SEM models and causal v effect indicator models

For the quantoid readers of IQs Corner. Italics emphasis added by the blog dictator.
Hancock, G. R., & Mueller, R. O. (2011). The Reliability Paradox in Assessing Structural Relations Within Covariance Structure Models. Educational and Psychological Measurement, 71(2), 306-324.
A two-step process is commonly used to evaluate data–model fit of latent variable path models, the first step addressing the measurement portion of the model and the second addressing the structural portion of the model. Unfortunately, even if the fit of the measurement portion of the model is perfect, the ability to assess the fit within the structural portion is affected by the quality of the factor–variable relations within the measurement model. The result is that models with poorer quality measurement appear to have better data–model fit, whereas models with better quality measurement appear to have worse data–model fit. The current article illustrates this phenomenon across different classes of fit indices, discusses related structural assessment problems resulting from issues of measurement quality, and endorses a supplemental modeling step evaluating the structural portion of the model in isolation from the measurement model.
Hardin, A. M., Chang, J. C. J., Fuller, M. A., & Torkzadeh, G. (2011). Formative Measurement and Academic Research: In Search of Measurement Theory. Educational and Psychological Measurement, 71(2), 281-305
The use of causal indicators to formatively measure latent constructs appears to be on the rise, despite what appears to be a troubling lack of consistency in their application. Scholars in any discipline are responsible not only for advancing theoretical knowledge in their domain of study but also for addressing methodological issues that threaten that advance. In that spirit, the current study traces causal indicators from their origins in causal modeling to their use in structural equation modeling today. Conclusions from this review suggest that unlike effect (reflective) indicators, whose application is based on classical test theory, today’s application of causal (formative) indicators is based on research demonstrating their practical application rather than on psychometric theory supporting their use. The authors suggest that this lack of theory has contributed to the confusion surrounding their implementation. Recent research has questioned the generalizability of formatively measured latent constructs. In the current study, the authors discuss how the use of fixed-weight composites may be one way to employ causal indicators so that they may be generalized to additional contexts. More specifically, they suggest the use of meta-analysis principles for identifying optimum causal indicator weights that can be used to generate fixed-weight composites. Finally, the authors explain how these fixed-weight composites can be implemented in both components-based and covariance-based statistical packages. Implications for the use of causal indicators in academic research are used to focus these discussions.
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Tuesday, April 05, 2011
Time to Stop Executing the Mentally Retarded--The Case for Applying the Standard Error of Measurement
Although this report is intended primary for readers of the ICDP blog, I am also posting it to the IQ's Corner blog as those readers may find the attempt to explain SEM in terms understandable by non-psychologists of interest.
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intelligence intelligence testing Atkins cases ICDP blog psychology school psychology neuropsychology Forensic psychology criminal psychology criminal justice death penalty capital punishment ABA IQ tests IQ scores adaptive behavior AAIDD mental retardation intellectual disability SEM standard error of measurement law review articles
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Saturday, November 27, 2010
Research byte: Are reading,listening and video comprehension tasks measuring the same comprehension construct?
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intelligence IQ tests IQ scores CHC theory Cattell-Horn-Carroll human cognitive abilities psychology school psychology individual differences cognitive psychology neuropsychology special education educational psychology psychometrics psychological assessment psychological measurement IQs Corner neuroscience neurocognitive cognitive abilities cognition Listening comprehension Reading comprehension Video comprehension
Thursday, November 25, 2010
Research byte: Relationship between working memory, memory span and fluid intelligence (Gf)

As per usual when I make a research byte/brief post, if anyone would like to read the original article, I can share via email---with the understanding that the article is provided in exchange for a brief guest post about it's contents. :) (contact me at iap@earthlink.net if interested). Also, if figure/images are included in the post, they can usually be made larger by clicking on the image.
Pascale M.J. Engel de Abreu, Andrew R.A. Conway, Susan E. Gathercole. Working memory and fluid intelligence in young children. Intelligence 38 (2010) 552–561
Abstract
The present study investigates how working memory and fluid intelligence are related in young children and how these links develop over time. The major aim is to determine which aspect of the working memory system—short-term storage or cognitive control—drives the relationship with fluid intelligence. A sample of 119 children was followed from kindergarten to second grade and completed multiple assessments of working memory, short-term memory, and fluid intelligence. The data showed that working memory, short-term memory, and fluid intelligence were highly related but separate constructs in young children. The results further showed that when the common variance between working memory and short-term memory was controlled, the residual working memory factor manifested significant links with fluid intelligence whereas the residual short-term memory factor did not. These findings suggest that in young children cognitive control mechanisms rather than the storage component of working memory span tasks are the source of their link with fluid intelligence.


The findings of this study are very similar to a series of SEM models I ran with indicators from the WJ III. The WJ III CHC-based models also showed that memory span (Gms-MS) was a causal factor for working memory (Gsm-MW) which in turn had a significant causal effect on g (and not just Gf). The primary difference was that these WJ III based analyses also included processing speed (Gs) as a causal influence on MS and MW but, consistent with the developmental cascade hypothesis Gs did not have a direct causal effect on Gf (it was mediated thru Gsm-MS-MW). In addition, these models included a much broader array of indicators of g, inclusive of Gc, Gv, Ga, Glr, and Gf.
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intelligence IQ tests IQ scores CHC theory Cattell-Horn-Carroll human cognitive abilities psychology school psychology individual differences cognitive psychology neuropsychology special education educational psychology psychometrics psychological assessment psychological measurement IQs Corner neuroscience neurocognitive cognitive abilities cognition Gv Ga Glr Gf Gc Gsm working memory developmental cascade hypothesis cognitive control fluid intelligence general intelligence WJ III
Saturday, April 10, 2010
Tiger Woods Masters Ability IQ scores within his "zone" (band): Real world example of SEM
If you are intrigued and want to learn more about SEM and its importance in psychological testing (using Masters golf performance as a real world example), click here to visit prior blog post and be sure to read the entire report that is mentioned (click on the report URL).
Technorati Tags: psychology, forensic psychology, forensic psychiatry, neuropsychology, intelligence, school psychology, psychometrics, educational psychology, IQ, IQ tests, IQ scores, adaptive behavior, adaptive functioning, intellectual disability, mental retardation, MR, ID, criminal psychology, criminal defense, criminal justice, ABA, American Bar Association, Atkins cases, death penalty, capital punishment, AAIDD, Atkins MR/ID listserv, ICDP blog, statistics and law, SEM, standard error of measurement, Tiger Woods
Wednesday, December 23, 2009
Research Byte 12-23-09: Shared and unshared genetic factors in timed and untimed reading and math abilities
Abstract
The present study examined the phenotypic and genetic relationship between fluency and non-fluency-based measures of reading and mathematics performance. Participants were drawn from the Western Reserve Reading and Math Project, an ongoing longitudinal twin project of same-sex MZ and DZ twins from Ohio. The present analyses are based on tester-administered measures available from 228 twin pairs (age M = 9.86 years). Measurement models suggested that four factors represent the data, namely Decoding, Fluency, Comprehension, and Math. Subsequent quantitative genetic analyses of these latent factors suggested that a single genetic factor accounted for the covariance among these four latent factors. However, there were also unique genetic effects on Fluency and Math, independent from the common genetic factor. Thus, although there is a significant genetic overlap among different reading and math skills, there may be independent genetic sources of variation related to measures of decoding fluency and mathematics.
Comments extracted from article
Results suggested a four-factor model including reading Decoding, reading Fluency, reading Comprehension, and Math. Further quantitative genetic analysis suggested that a common genetic factor is important to the covariance among phenotypically distinct latent factors (e.g., Plomin & Kovas, 2005). However, Fluency and Math factors were also influenced by unique genetic influences, independent from the general genetic factor.
Interestingly, the two factors with unique genetic in fluences are the only ones to contain measures of timed performance, or fluency. Previous work has suggested that there are large and significant effects due to heritability on measures of reading fluency (h² = .65–.67; Harlaar, Spinath, Dale, & Plomin, 2005), and mathematics fluency (h² = .63; Hart et al., 2009). It is possible that the fluency components in each of these factors are important for explaining the unique genetic effects on both.
Notably, there is no genetic overlap between the factors which contain fluency-based measures, outside of the general genetic overlap among all the latent factors. That, as well as the comparison of phenotypic models 4 and 5 in Table 3, suggests that the genetic influences of reading fluency are not the same as the genetic influences of mathematics fluency, although both are strongly independently influenced by genes.
It is also interesting to note the shared environmental overlap among all the factors. Instruction in this age-group is typically for the skills represented by these factors (e.g., Chall, 1983). This would serve to influence these processes through the shared environment, especially given that for most students in the early elementary years, academic skill exposure and learning are a function of what is taught in school. Moreover, in the case of twins, they also share the same rearing environment. This overlap is of note as it is shared between all mathematics and reading factors, suggesting that whether it is school- and/or family-level influences, there is a common environmental etiology underlying academic difficulties. This can have ramifications in how academic skill-based interventions are conceptualized.
The math literature sometimes separates math into components of computation and problem solving. Our findings in the current study and others (Petrill & Hart, 2009) suggest that the data were best represented by one latent factor. However, all measures of math are based on the Woodcock–Johnson, which may be serving to make them more similar.
Related to this issue, although the shared environmental influences on math are higher than those on reading, this difference cannot be directly tested statistically.Authors conclusion
In sum, the results suggest that there are some common genetic and environmental factors that connect reading and mathematics performance. At the same time, there also appear to be independent genetic effects for reading fluency and for mathematics. Although requiring further study, these findings may suggest that the overlap in reading and mathematics performance may be due to both genes and the shared environment whereas the discrepancy between math and reading may be genetically mediated. This has ramifications for our understanding of math and reading difficulties. Independent genetic effects may be serving to make math disability and reading disability distinct, and differentially prevalent. On the other hand, the extent to which they are comorbid in some children, common genes and environments may be affecting the outcomes.
Technorati Tags: psychology, educational psychology, school psychology, cognition, neuropsychology, behavioral genetics, genetics, reading, math, LD, special education, reading fluency, math fluency, Gs, Gq, Grw, intelligence, twin studies

Tuesday, December 22, 2009
State special education definitions of MR/ID
Bergeron, R., Floyd, R., & Shands, E. (2008). States’ Eligibility Guidelines for Mental Retardation: An Update and Consideration of Part Scores and Unreliability of IQs. Education and Training in Developmental Disabilities, 43(1), 123–131. (click here to view)
Abstract
Mental retardation (MR) has traditionally been defined as a disorder in intellectual and adaptive functioning beginning in the developmental period. Guided by a federal definition of MR described in the Individuals with Disabilities Education Act, it is the responsibility of each of the United States to describe eligibility guidelines for special education services. The purpose of this study was to examine eligibility guidelines for MR for the 50 states and the District of Columbia. This study examined the terms used to describe MR, the use of classification levels, the cutoff scores, and the adaptive behavior considerations for each state. In addition, this study examined guidelines for consideration of intelligence test part scores and consideration of the unreliability of IQs through consideration of the standard error of measurement (SEM) or an IQ range. As found in previous studies, results revealed great variation in the specific eligibility guidelines for MR from state to state. The greatest variation appeared to be across the adaptive behavior considerations. Approximately 20% of states (10) recommend consideration of intelligence test part scores, and approximately 39% of states (20) recommend attention to unreliability of IQs through consideration of the SEM or an IQ range.
Technorati Tags: psychology, school psychology, educational psychology, special education, forensic psychology, neuropsychology, criminal psychology, ID, MR, IQ, intellectual disability, mental retardation, AAIDD, intelligence, IQ tests, reliabilitypsychometrics, SEM

Monday, December 14, 2009
New IAP Applied Psychometrics 101 Report: IQ scores and SEM
A new IAP Applied Psychometrics 101 report (#5) is now available. The title of the report and abstract is below. The report can be downloaded by clicking here.
Applied Psychometrics 101 #4: The Standard Error of Measurement (SEM): An Explanation and Facts for "Fact Finders" in Atkins MR/ID death penalty proceedings.
Abstract
The standard error of measurement (SEM) is a professionally accepted and scientifically based measurement concept that allows users of psychological test scores to account for the known degree of imprecision in the scores. Atkins MR/ID cases almost always involve standardized psychological testing in the domains of intelligence (IQ tests) and adaptive behavior (AB). Scores from IQ and AB measures are fallible—not perfectly reliable. This report provides an easy to understand explanation of the psychometric concept of SEM augmented by an example based on real-world data. The report concludes with 8 SEM facts that “fact finders” should understand and internalize when evaluating psychological test data during legal proceedings--Atkins MR/ID death penalty proceedings in particular.Here is a visual treat/tease from the report:
All prior IAP AP101 reports can be accessed via the Applied Psychometrics 101 (AP101) Reports section of the blog--on the blog sidebar.
Technorati Tags: psychology, forensice psychology, criminal psychology, school psychology, educational psychology, neuropsychology, developmental disabilities, MR, ID, mental retardation, intlellectual disability, AAIDD, Joint Test Standards, psychometrics, psychological measures, applied psychometrics, SEM, standard error or measurement, reliability, measurement error, Atins cases, death penalty, capital punishment, adpative behavior, intelligence, IQ, IQ tests, IQ scores, ICDP

















