Showing posts with label Beyond CHC. Show all posts
Showing posts with label Beyond CHC. Show all posts

Wednesday, May 13, 2026

AI Brief: What does Grok say about Richard Snow’s aptitude trait complexes for learning?

 The following is a Grok AI generated summary when prompted (by Dr. Kevin McGrew) to explain Richard Snow’s aptitude complexes on March 7, 2026).

(Grok refers to a generative artificial intelligence developed by xAI, an Elon Musk company, as well as a foundational term in science fiction for deep understanding. Several editorial changes were made to insure accuracy, and select links added, by McGrew—to the Grok summary).

 


Richard E. Snow’s aptitude complexes (introduced in the 1980s–1990s, with key publications in 1987, 1992, and especially the 1996 chapter with Lyn Corno and Douglas Jackson) represent a major shift in how educational psychologists think about aptitude—moving far beyond the traditional narrow view of aptitude as “just cognitive ability” (e.g., IQ or a single test score).

 

Core Definition

Snow redefined aptitude as:

“the degree of readiness to learn and to perform well in a particular situation or in a fixed domain.”

It is a predisposition or propensity—a latent quality that enables more advanced performance under specific conditions. Aptitudes are situational and domain-specific: what makes someone ready to succeed in math class may be different from what works in a history seminar or a hands-on lab.  


Aptitude Complexes (the key innovation)

Snow argued that single constructs (like “fluid reasoning” or “achievement motivation”) are insufficient. Instead, success in learning comes from aptitude complexes—dynamic constellations or critical combinations of variables that work together as a coordinated system.

These complexes draw from the classic “trilogy of the mind”:

•  Cognition — abilities and processes for analyzing, interpreting, and solving (e.g., reasoning, knowledge, strategies, cognitive style, CHC abilities).

•  Affect — emotions, anxiety, self-concept, emotion regulation, personality traits.

•  Conation — motivation, volition, goal-setting, effort, persistence, will (the “want to” and “stick with it” aspects).

An aptitude complex is not just a list of traits—it is how these elements assemble and coordinate in real time within a specific task and context. They are amalgams of cognitive, conative, and affective characteristics.

 

The Two Pathways That Build Aptitude Complexes

Snow (and later Corno et al., 2002) described aptitudes developing through two parallel, interacting pathways (sometimes called the commitment pathway and the performance/action pathway):

1.  Commitment Pathway (motivational/affective/volitional)

     •  Assembles motivational resources that energize effort.

     •  Affective and volitional processes modulate how the work proceeds (e.g., regulating anxiety, sustaining intention).

     •  Outcome: Propensity (how likely the person is to engage and persist).

2.  Performance (Action) Pathway (cognitive)

     •  Assembles and deploys cognitive resources (abilities, strategies, knowledge) to do the task.

     •  Outcome: Ability/accuracy in execution.

When the two pathways coordinate effectively in a given “problem space” (the task + the broader situation/context), successful performance occurs. Over repeated experiences, these coordinated processes coalesce into stable aptitude complexes. The learner’s perception of the situation’s constraints and affordances is crucial—aptitudes are dynamic and transactional (person ↔ environment). 

Aptitudes are both input (what the student brings to learning) and product (they develop and change through education).


Snow Academic Aptitude Model (SAAM)

Snow synthesized decades of research into a provisional taxonomy (called the Snow Academic Aptitude Model or SAAM in an unpublished working white paper [6-15-04; Increasing the Chance of No Child Being Left Behind: Beyond Cognitive and Achievement Abilities, by Kevin McGrew, David Johnson, Anna Casio, Jeffrey Evans]) which is now available for download here. It treats academic aptitudes as a “multivariate repertoire” of readiness for general and domain-specific learning. It explicitly includes affect (personality and social-emotional skills) and conative related skills and traits (e.g., achievement motivation, goal orientation, freedom from debilitating anxiety, positive self-concept, self-efficacy, interests) alongside cognitive abilities. The model emphasizes that “there is more to knowing about an individual’s propensity for academic learning than simply knowing their IQ scores!” 

 

Why This Mattered (and Still Matters)

Snow’s work grew out of his famous Aptitude-Treatment Interaction (ATI) research with Lee Cronbach. He showed that simple aptitude scores rarely predict learning outcomes well because real-world performance depends on these richer, situation-specific complexes.

This framework directly inspired later theories (including Kevin McGrew’s 2022 CAMML model, which updates Snow’s complexes with contemporary CHC cognitive theory, Big Five personality, and self-regulated learning mechanisms while retaining the commitment/action pathway structure).

In short, Snow’s aptitude complexes gave us a whole-person, dynamic, domain-specific way to understand why two students with the same IQ can have dramatically different learning outcomes: their aptitude complexes (the coordinated cognitive + affective + conative “package” or “amalgam”) fit the demands of the task and context differently.

Snow’s legacy is summarized in the 2002 book Remaking the Concept of Aptitude (Corno et al.), which remains the definitive extension of his ideas.

 


Friday, November 15, 2024

#WJIV Geometric-Quantoid (#geoquant) #intelligence art: A geoquant interpretation of #cognitive tests is worth a 1000 words—some similar “art parts” will be in #WJV technical manual


(You will need to click on image to enlarge figure to read)

I frequently complete data analyses that never see the light-of-day in a journal article. The results are all I need (at the time) to answer intriguing questions for me, and I then move on…or tantalize psychologists during a workshop or conference presentation.  Thus, this is non-peer reviewed information.  Below is one of my geoquant figures from a series of 2016 analyses (later updated in 2020) I completed on a portion of the WJ IV norm data.  To interpret you should have knowledge of the WJ IV tests—so you can understand the test variable abbbreviation names.  This MDS figure includes numerous interesting cognitive psychology constructs and theoretical principles based on multiple methodological lenses and supporting theory/research.  This was completed before I was introduced to psychometric network analysis methods as yet another visual means to understand intelligence test data.  You can play “where’s Waldo” and look for the following

  • CHC broad cognitive factors
  • Cognitive complexity information re WJ IV tests
  • Kahneman’s two systems of cognition (System I/II thinking)
  • Berlin BIS ability x content facet framework
  • Two of Ackerman’s intelligence dimensions as per PPIK theory (intelligence-as-process; intelligence-as-knowledge)
  • Cattell’s general fluid (gf) and general crystallized (gc) abilities, the two major domains in his five domain triadic theory of intelligence.…..lower case gf/gc notation is deliberate and indicates more “general” capacities (akin, in breadth, to Spearman’s g, who was Cattell’s mentor) and not the Horn and Carroll-like broad Gf and Gc
  • Newlands process and product dominant distinction of cognitive abilities.
Enjoy.  MDS analyses and figures will also be in the forthcoming (Q1 2025)  WJ V technical manual (LaForte, Dailey, & McGrew, 2025, in preparation) but not in the form of these mutiple method/theory synthesis grand figures….stay tunned.  I may create such beautiful geoquant WJ V masterpieces once the WJ V is launched in Q1 2025.  We shall see.  I find these grand synthesis figures particularly useful when interpreting test rests…all critical information in one single figure…would you?

Friday, January 15, 2021

The McGrew Model of Achievement Competence Model (MACM)--Standing on the shoulders of giants: CJSP article supplementary materials

The Model of Achievement Competence Motivation (MACM) has been  under development since the early 2000's by Dr. Kevin S. McGrew.   The work is (has) been formally presented in an invited article--"The Model of Achievement Competence Motivation (MACM)--Standing on the shoulders of giants" (McGrew, in press, 2021), for a forthcoming special issue on motivation in the Canadian Journal of School Psychology). 

Due to the page length constraints of the journal, significant background and explanatory information could not be presented in the article.  Thus, I have "off-loaded" this material for supplementary viewing via on-line PPT slide shows and downloadable PDF files.

Five MACM PPT modules have been posted at SlideShare and can be viewed and downloaded from that site.  For those who would prefer to directly download PDF versions of the PPT modules from one page...here it is.  Below are the titles of the five modules and associated download links.  In addition, the paper includes, in a table footnote, definitions for 16 self-regulatory constructs from a recent article by Sitzman and Ely (2011).  That PDF file is also available from download below.

Enjoy.



The Model of Achievement Competence Motivation (MACM)

Saturday, March 17, 2018

The importance of differential psychology for school learning: 90% of school achievement variance is due to student characteristics

This is why the study of individual differences/differential psychology is so important. If you don’t want to read the article you can watch a video of Dr. Detterman where he summarizes his thinking and this paper.

Education and Intelligence: Pity the Poor Teacher because Student Characteristics are more Significant than Teachers or Schools. Article link.

Douglas K. Detterman

Case Western Reserve University (USA)

Abstract

Education has not changed from the beginning of recorded history. The problem is that focus has been on schools and teachers and not students. Here is a simple thought experiment with two conditions: 1) 50 teachers are assigned by their teaching quality to randomly composed classes of 20 students, 2) 50 classes of 20 each are composed by selecting the most able students to fill each class in order and teachers are assigned randomly to classes. In condition 1, teaching ability of each teacher and in condition 2, mean ability level of students in each class is correlated with average gain over the course of instruction. Educational gain will be best predicted by student abilities (up to r = 0.95) and much less by teachers' skill (up to r = 0.32). I argue that seemingly immutable education will not change until we fully understand students and particularly human intelligence. Over the last 50 years in developed countries, evidence has accumulated that only about 10% of school achievement can be attributed to schools and teachers while the remaining 90% is due to characteristics associated with students. Teachers account for from 1% to 7% of total variance at every level of education. For students, intelligence accounts for much of the 90% of variance associated with learning gains. This evidence is reviewed


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Monday, March 12, 2018

CHC theory update: Live chat or later YouTube viewing from #psychedpodcast

I am looking forward to talking about the Cattell-Horn-Carroll (CHC) model of intelligence on the #psychedpodcast this sunday evening.

I will present material largely based on the forthcoming CHC chapter coauthored with Dr. Joel Schneider.  Tune it....it shall be fun. Or, watch the discussion later on YouTube, and eventually as an audio podcast on iTunes





Sunday, January 14, 2018

Research Byte: Cognitive Mediators of Reading Comprehension in Early Development

Cognitive Mediators of Reading Comprehension in Early Development

Scott L. Decker & Julia Englund Strait & Alycia M. Roberts & Emma Kate Wright.

Contemp School Psychol DOI 10.1007/s40688-017-0127-0

Abstract

Although the empirical relationship between general intelligence and academic achievement is well established, that between specific cognitive abilities and achievement is less so. This study investigated the rela-tionships between specific Cattell-Horn-Carroll (CHC) cognitive abilities and reading comprehension across a large sample of children (N = 835) at different periods of reading development (grades 1–5). Results suggest se-lect cognitive variables predict reading comprehension above and beyond basic reading skills. However, the rel-ative importance of specific cognitive abilities in predicting reading comprehension differs across grade levels. Further analyses using mediation models found specific cognitive abilities mediated the effects of basic reading skills on reading comprehension. Implications for the important and dynamic role of cognitive abilities in predicting reading comprehension across development are discussed.

From discussion

The results from this study supported our general hypothesis that specific cognitive abilities are important for reading com-prehension and the predictors change across grade. Specifically, measures of fluid reasoning (Gf) and auditory processing (Ga) appear to be most important for predicting reading comprehension performance (as measured by the pas-sage comprehension subtest) in the early elementary grades, while long-term retrieval (Glr) appears as a significant predic-tor in grades 3–4. Crystallized knowledge (Gc) appears to be important across all five early grade levels, consistent with previous studies (e.g., Floyd et al. 2007; Hajovsky et al. 2014). Reading decoding skills (as measured by the Letter-Word ID subtest) predicted reading comprehension across all elementary grade levels, also consistent with previous studies (e.g., Floyd et al. 2012), and reading fluency (reading fluency subtest) predicted reading comprehension in grades 2–5.

Click on images to enlarge.
















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Monday, October 23, 2017

The Evolution of the Cattell-Horn-Carroll (CHC) Theory of Intelligence: Schneider & McGrew 2018 summary


The Evolution of the Cattell-Horn-Carroll (CHC) Theory of Intelligence: Schneider & McGrew 2018 summary from Kevin McGrew

This presentation includes a portion of key material to be published in a forthcoming CHC update/revision chapter--In D. P. Flanagan & Erin M .McDonough (Eds.), Contemporary intellectual assessment: Theories, tests and issues (4thed.,) New York: Guilford Press.

This is only a small amount of the chapter. Also, I have inserted some new material related to test interpretation that is not included in the to-be-published chapter. The tentative date for publication of the Flanagan book is spring 2018. The majority, but not all, of this SlideShare presentation was originally presented at the 2017 NYASP conference October 19,2017.

Tuesday, August 18, 2015

New and emerging models of human intelligence (Conway and Kovacs): Comments and elaboration

A nice article that provides an overview of contemporary intelligence research. More importantly, the authors summarize and contrast the psychometric and information processing approaches to understanding human intelligence.

A few comments.  Also, click on any image to enlarge and make more readable.

First.  The CHC figure presented in the article is not a 100% accurate representation of the CHC model.  The figure in the article is most consistent with Jack Carroll's 1993 model.  His model was integrated with Cattell and Horn's models as the CHC model.  A recent chapter by Schneider and McGrew (2012)  provides the best summary of the "CHC" model.



Second. I have been a huge fan of Conway and Engle's executive attention model of working memory and love the figure explaining working memory and the focus of attention.  In fact, in a recent IM Keynote presentation I used a simpler version of this model to explain the importance of attentional control (AC; aka focus) in working memory, and in turn, it's role in understanding higher level cognition.  You can watch this material at the following YouTube video of the entire presentation.  You should start at approximately the 28 minute mark to see the relevant material.


Finally. The authors make the following statements in their "future directions"conclusion.  These points resonate to my thinking as recently outlined in a 4-level explanatory hierarchy for integrating different types of intelligence research.  That information is available in the last (brief) video (Human Intelligence Research:  Connecting the dots) at the end of this post.


Monday, February 23, 2015

The WJ IV Cognitive Battery and Beyond CHC Theory

For individuals who could not attend my NASP 2015 WJ IV mini-skills workshop, or those who did and who would like to view all slides shown (and those not shown) or others who want to know, you can now view the slides below that are posted at SlideShare. Enjoy.  If you click on the SlideShare link you can view other PPT shows I have available for review.

Monday, June 23, 2014

WJ IV Battery Revision: Brief Introduction and Overview SlideShare Show Posted

I just posted a brief introduction and overview SlideShare regarding the new WJ IV battery (that was released this month).  The slideshow does contain some of the same slides that were in three prior slideshows posted from the WJ IV NASP 2014 workshop by myself, and Dr.'s Schrank and Mather.  This module serves as a general purpose introduction and overview.   Additional slideshows will be posted in the future that deal with specific topics, features, data, etc. in greater depth.

[Conflict of interest disclosure:  I am a coauthor of the WJ III and WJ IV.]




Friday, June 13, 2014

The CHC Periodic Table of Cognitive Elements: "What are you made of?" Now available on a t-shirt

Back by popular demand, the blogmaster has created a new and improved CHC Theory Periodic Table of Human Cognitive Elements figure!  It is shown below.  Future updates will provide links to the updated definitions that go with each cognitive element code.  This new CHC periodic table represents the latest iteration of the CHC taxonomy of human cognitive abilities as summarized in the forthcoming WJ IV Technical Manual.

Even more exciting is that you can now purchase a t-shirt with the CHC Periodic Table printed on the front, with the title "The CHC Periodic Table:  What are you made of?"  You can find it here or go to the blog roll and click on IQs Corner Skreened blog badge.  More to come:)

Click on images to enlarge




Sunday, November 25, 2012

Implications of 20 Years of CHC Cognitive-Achievement Research: Back-to-the-Future and Beyond CHC

[Click image to enlarge]
 
The key slides from my presentation at the first Richard Woodcock Institute on Cognitive Assessment are now posted at SlideShare.  I thought I had posted these before, but I can't seem to find them.  So here they are for the first (or second) time.  Below is the abstract for the paper that I also submitted--to be published eventually by the WMF Press.


Much has been learned about CHC CHC COG-->ACH relations during the past 20 years (McGrew & Wendling’s, 2010).  This paper built on this extant research by first clarifying the definitions of abilities, cognitive abilities, achievement abilities, and aptitudes.  Differences between domain-general and domain-specific CHC predictors of school achievement were defined.   The promise of Kafuman’s “intelligent” intelligence testing approach was illustrated with two approaches to CHC-based selective referral-focused assessment (SRFA).  Next, a number of new intelligent test design (ITD) principles were described and demonstrated via a series of exploratory data analyses that employed a variety of data analytic tools (multiple regression, SEM causal modeling, multidimensional scaling).  The ITD principles and analyses resulted in the proposal to construct developmentally-sensitive CHC-consistent scholastic aptitude clusters, measures that can play an important role in contemporary third method (pattern of strength and weakness) approaches to SLD identification. 
The need to move beyond simplistic conceptualizations of COG COG-->ACH relations and SLD identification models was argued and demonstrated via the presentation and discussion of CHC COG-->ACH causal SEM models.  Another example was the proposal to identify and quantify cognitive-aptitude-achievement trait complexes (CAATCs).  A revision in current PSW third-method SLD models was proposed that would integrate CAATCs.  Finally, the need to incorporate the degree of cognitive complexity of tests and composite scores within CHC domains in the design and organization of intelligence test batteries (to improve the prediction of school achievement) was proposed.  The various proposals presented in this paper represented a mixture of (a) a call to return to old ideas with new methods (Back-to-the-Future) or (b) the embracing of new ideas, concepts and methods that require psychologists to move beyond the confines of the dominant CHC taxonomy of human cognitive abilities (i.e., Beyond CHC).




Monday, September 10, 2012

AP101 Brief # 16: Beyond CHC: Within-CHC Domain Complexity Optimized Measures

[Note:  This is a working draft of a larger paper (Implications of 20 years of CHC Cognitive-Achievement Research:  Back-to-the-future and Beyond CHC) that will be presented at the first Inaugural Session of the Richard Woodcock Institute for Advancement of Contemporary Cognitive Assessment at Tufts University (Sept, 29, 2012):  The Evolution of CHC Theory and Cognitive Assessment).]   Working knowledge of the WJ III test batery will make this brief easier to understand, but is not necessary.

Beyond CHC:  ITD—Within-CHC Domain Complexity Optimized Measures
            Optimizing Cognitive Complexity of CHC measures
I have recently begun to recognize the contribution that The Brunswick Symmetry derived Berlin Intelligence Structure (BIS) model can make in applied intelligence research, especially for increasing predictor-criteria relations by maximizing these relations via matching the predictor-criteria space on the dimension of cognitive complexity.  What is cognitive complexity?  Why is it important?  More important, what role should it play in designing intelligence batteries to optimize CHC COG-ACH relations?
Cognitive complexity is often operationalized by inspecting individual test loadings on the first principal component from principal component analysis (Jensen, 1998).  The high g-test rationale is that performance on tests that are more cognitively complex “invoke a wider range of elementary cognitive processes (Jensen, 1998; Stankov, 2000, 2005)” (McGrew, 2010b, p. 452).  High g-loading tests are often at the center of MDS (multidimensional scaling) radex models (click here for AP101 Brief Report #15:  Cognitive-Aptitude-Achievement Trait Complexes example)—but this isomorphism does not always hold.   David Lohman, a student of Richard Snow’s, has made extensive use of MDS methods to study intelligence and has one of the best grasps of what cognitive complexity, as represented in the hyperspace of MDS figures, contributes to understanding intelligence and intelligence tests.  According to Lohman (2011), those tests closer to the center are more cognitively complex due five possible factors—larger number of cognitive component processes; accumulation of speed component differences: more important component processes (e.g., inference); increased demands of attentional control and working memory; and/or or more demands on adaptive functions (assembly, control, and monitoring).  Schneider’s (in press) level of abstraction description of broad CHC factors is similar to cognitive complexity.  He uses the simple example of 100 meter hurdle performance.  According to Schneider (in press), one could independently measure 100 meter sprinting speed and then standing still and jumping over a hurdle (both examples of narrow abilities).  However, running a 100 meter race is not the mere sum of the two narrow abilities and as is more of a non-additive combination and integration of narrow abilities.  This analogy captures the essence of cognitively complexity—which, in the realm of cognitive measures, are tasks that have more of the five factors listed by Lohman involvedduring successful task performance.
Of critical importance is the recognition that factor or ability domain breadth (i.e., broad or narrow) is not synonymous with cognitively complexity.  More important, cognitive complexity has not always been a test design concept (as defined by the Brunswick Symmetry and BIS model) explicitly incorporated into "intelligent" intelligence test design (ITD).  A number of tests have incorporated the notion of cognitive complexity in their design plans, but I believe this type of cognitive complexity is different than the within-CHC domain cognitive complexity discussed here.
For example, according to Kaufman and Kaufman (2004), “in developing the KABC-II, the authors did not strive to develop ‘pure’ tasks for measuring the five CHC broad abilities.  In theory, Gv tasks should exclude Gf or Gs, for example, and tests of other broad abilities, like Gc or Glr, should only measure that ability and none other.  In practice, however, the goal of comprehensive tests of cognitive ability like the KABC-II is to measure problem solving in different contexts and under different conditions, with complexity being necessary to assess high-level functioning” (p. 16; italics emphasis added).  Although the Kaufman’s address the importance of cognitively complex measures in intelligence test batteries, their CHC-grounded description defines complex measures as those that are factorially complex or mixed measures of abilities from more than one broad CHC domain.  The Kaufman’s also address cognitive complexity from the non-CHC neurocognitve three-block functional Luria neurocognitive model when they indicate that it is important to provide measurement that evaluates the “dynamic integration of the three blocks” (Kaufman & Kaufman, 2004, p.13).   This emphasis on neurocognitive integration (and thus, complexity) is also an explicit design goal of the latest Wechsler batteries.  As stated in the WAIS-IV manual (Wechsler, 2008), “although there are distinct advantages to the assessment and division of more narrow domains of cognitive functioning, several issues deserve note.  First, cognitive functions are interrelated, functionally and neurologically, making it difficult to measure a pure domain of cognitive functioning” (p. 2).  Furthermore, “measuring psychometrically pure factors of discrete domains may be useful for research, but it does not necessarily result in information that is clinically rich or practical in real world applications (Zachary, 1900)” (Wechsler, p. 3).   Finally, Elliott (2007) similarly argues for the importance of recognizing neurocognitive-based “complex information processing” (p. 15; italics emphasis added) in the design of the DAS-III, which results in tests or composites measuring across CHC-described domains, as important in test design.
The ITD principle explicated and proposed here is that of striving to develop cognitively complex measures within broad CHC domains—that is, not attaining complexity via the blending of abilities across CHC broad domains and not attempting to directly link to neurocognitive network integration.[1]   The Brunswick Symmetry based BIS model provides a framework for attaining this goal via the development and analysis of test complexity by paying attention to cognitive content and operations facets. 
Figure 12 presents the results of a 2-D MDS Radex model of most all key WJ III broad and narrow CHC cognitive and achievement clusters (for all norm subjects from approximately 6 years of age thru late adulthood). [2]   The current focus of the interpretation of the results in Figure 12 is only on the degree of cognitive complexity (proximity to the center of the figure) of the broad and narrow WJ III clusters within the same domain (interpretations of the content and operations facets are not a focus of this current material).  Within a domain the broadest three-test parent clusters are designated by black circles.[3]  Two-test broad clusters are designed by gray circles.  Two test narrow offspring clusters within broad domains are designated by white circles.  All clusters within a domain are connected to the broadest parent broad cluster by lines.  The critically important information is the within-domain cognitive complexity of the respective parent and sibling clusters as represented by their relative distances from the center of the figure.  A number of interesting conclusions are apparent. [Click on image to enlarge]

First, as expected, the WJ III GIA-Ext cluster is almost perfectly centered in the figure—it is clearly the most cognitively complex WJ III cluster.   In comparison, the three WJ III Gv clusters are much weaker in cognitive complexity than all other cognitive clusters with no particular Gv cluster demonstrating a clear cognitive complexity advantage.    As expected, the measured reading and math achievement clusters are primarily cognitively complex measures.  However, those achievement clusters that deal more with basic skills (Math Calculation—MTHCAL; Basic Reading Skills—RDGBS) are less complex that the application clusters (Reading Comprehension-RDGCMP; Math Reasoning-MTHREA). 
The most intriguing findings in Figure 12 are the differential cognitive complexity patterns within CHC domains (with at least one parent and at least one offspring cluster).  For example, the narrow Perceptual Speed (Gs-P) offspring cluster is more cognitively complex than the broad parent Gs cluster.  The broad Gs cluster is comprised of the Visual Matching (Gs-P) and Decision Speed (Gs-R9; Glr-NA) tests, tests that measure different narrow abilities.  In contrast the Perceptual Speed cluster (Gs-P) is comprised of two tests that are classified as both measuring the same narrow ability (perceptual speed).  This finding appears, on first blush, counterintuitive as one would expect a cluster comprised of tests that measure different content and operations (Gs cluster) would be more complex (as per the above definition and discussion) than one comprised of two measures of the same narrow ability (Gs-P).  However, one must task analyze the two Perceptual Speed tests to realize that although both are classified as measuring the same narrow ability (perceptual speed), they differ in both stimulus content and cognitive operations.  Visual Matching requires processing of numeric stimuli.  Cross Out requires the processing of visual-figural stimuli.  These are two different content facets in the BIS model.  The Cross Out visual-figural stimuli are much more spatially challenging than the simple numerals in Visual Matching.  Furthermore, the Visual Matching test requires the examinee to quickly seek out and discover and mark two digit pairs that are identical.  In contrast, in the Cross Out test the subject is provided a target visual-figural shape and the subject must then quickly scan a row of complex visual images and mark two that are identical to the target.  Interesting, in other unpublished  analyses I have completed, the Visual Matching test often loads on or groups with quantitative achievement tests while Cross Out has frequently show to load on a Gv factor.  Thus, task analysis of the content and cognitive operations of the WJ III Perceptual Speed tests suggests that although both are classified as narrow indicators of Gs-P, they differ markedly in task requirements.  More important, the Perceptual Speed cluster tests, when combined, appear to require more cognitively complex processing than the broad Gs cluster.  This finding is consistent with Ackerman, Beier and Boyle’s (2002) research that suggests that perceptual speed has another level of factor breadth via the identification of four subtypes of perceptual speed (i.e., pattern recognition, scanning, memory and complexity; see McGrew 2005 and Schneider & McGrew, 2012 for discussion of a hierarchically organized model of speed abilities).  Based on Bruinswick Symmetry/BIS cognitive complexity principles, one would predict that a Gs-P cluster comprised of two parallel forms of the same task (e.g., two Visual Matching or two Cross Out tests) would be less cognitively complex than broad Gs.  A hint of the possible correctness of this hypothesis is present in the inspection of the Gsm-MS-MW domain results.
The WJ III Gsm cluster is the combination of the Numbers Reversed (MW) and Memory for Words (MS) tests.  In contrast, the WJ III Auditory Memory Span cluster (AUDMS; Gsm-MS) cluster is much less cognitively complex when compared to Gsm (see Figure 12).  Like the Perceptual Speed (Gs-P) cluster described in the context of the processing speed family of clusters, the Auditory Memory Span cluster is comprised of two tests with the same memory span (MS) narrow ability classification (Memory for Words; Memory for Sentences).  Why is this narrow cluster less complex than its broad parent Gsm cluster while the opposite held true for Gs-P and Gs?  Task analysis suggests that the two memory span tests are more alike than the two perceptual speed tests.  The Memory for Words and Memory Sentences tests require the same cognitive operation—simply repeating back, in order, words or sentences spoken to the subject.  This differs from the WJ III Perceptual Speed cluster as the similarly classified narrow Gs-P tests most likely invoke both common and different cognitive component operations.  Also, the Memory Span cluster tests are comprised of stimuli from the same BIS content facet (i.e., words and sentences; auditory-linguistic/verbal).  In contrast, the Gs-P Visual Matching and Cross Out tests involve two different content facets (numeric and visual-figural).
In contrast, the WJ III Working Memory cluster (Gsm-MW) is more cognitively complex than the parent Gsm cluster.  This finding is consistent with the prior WJ III Gs/Perceptual Speed and WJ III Gsm/Auditory Memory Span discussion.  The WJ III Working Memory cluster is comprised of the Numbers Reversed and Auditory Working Memory tests.  Numbers Reversed requires the processing of stimuli from one BIS content facet—numeric stimuli.  In contrast, Auditory Working Memory requires the processing of stimuli from two BIS content factors—numeric and auditory-linguistic/verbal; numbers and words).  The cognitive operations of the two tests also differ.  Both require the holding of the presented stimuli in active working memory space.  Numbers Reversed then requires the simple reproduction of the numbers in reverse order.  In contrast, the Auditory Working Memory test requires the storage of the numbers and words in separate chunks, and then the production of the forward sequence of each respective chunk (numbers or words), one chunk before the other.  Greater reliance on divided attention is most likely occurring during the Auditory Working Memory test. 
In summary, the results presented in Figure 12 suggest that it is possible to develop cluster scores that vary by degree of cognitively complexity within the same broad CHC domain.  More important is the finding that the classification of clusters as broad or narrow does not provide information on the measures cognitive complexity.  Cognitively complexity, as defined in the classification of clusters as broad or narrow does not provide information on the measures cognitive complexity.  Cognitive complexity, as in the Lohman sense, can be achieved within CHC domains without resorting to mixing abilities across CHC domains.  Finally, narrow clusters can be more cognitively complex, and thus likely better predictors of complex school achievement, than broad clusters or other narrow clusters. 

Implications for Test Battery Design and Assessment Strategies
The recognition of cognitive complexity as an important ITD principle suggests that the push to feature broad CHC clusters in contemporary test batteries, or in the construction of cross-battery assessments, fails to recognize the importance of cognitive complexity.  I plead guilty to contributing to this focus via my role in the design of the WJ III which focused extensively on broad CHC domain construct representation—most WJ III narrow CHC clusters require the use of the third WJ III cognitive book (the Diagnostic Supplement; Woodcock, McGrew, Mather & Schrank, 2003).  Similarly, guilty as charged in the dominance of broad CHC factor representation in the development of the original cross-battery assessment principles (Flanagan & McGrew, 1997; McGrew & Flanagan, 1998). 
It is also my conclusion that the narrow is better conclusion of McGrew and Wendling (2010) may need modification.   Revisiting the McGrew and Wendling (2010) results suggest that the narrow CHC clusters that were more predictive of academic achievement likely may have been so not necessarily because they are narrow, but because they are more cognitively complex.  I offer the hypothesis that a more correct principle is that “cognitively complex measures” are better.   I welcome new research focused on testing this principle.
In retrospect, given the universe of WJ III clusters, a broad+narrow hybrid approach to intelligence battery configuration (or cross-battery assessment) may be more appropriate.  Based exclusively on the results presented in Figure 12, the following clusters would appear those that might better be featured in the “front end” of the WJ III or a selective testing constructed assessment—those clusters that examiners should consider first within each CHC broad domain:  Fluid Reasoning (Gf)[4], Comprehension-Knowledge (Gc), Long-term Retrieval (Glr), Working Memory (Gsm-MW), Phonemic Awareness 3 (Ga-PC), and Perceptual Speed (Gs-P).  No clear winner is apparent for Gv, although the narrow Visualization cluster is slightly more cognitively complex than the Gv and Gv3 clusters.  The above suggests that if broad clusters are desired for the domains of Gs, Gsm and Gv, then additional testing beyond the “front end” or featured tests and clusters would require administration of the necessary Gs (Decision Speed), Gsm (Memory for Words) and Gv (Picture Recognition) tests.

Utilization of the ITD test design principle of optimizing within-CHC cognitively complexity of clusters suggests that a different emphasis and configuration of WJ III tests might be more appropriate.  It is proposed that the above WJ III cluster complexity priority or feature model would likely allow practitioners to administer the best predictors of school achievement.  I further hypothesize that this cognitive complexity based broad+narrow test design principle most likely applies to other intelligence test batteries that have adhered to the primary focus on featuring tests that are the purest indicators of two or more narrow abilities within the provided broad CHC interpretation scheme.  Of course, this is an empirical question that begs research with other batteries.  More useful with be similar MDS Radex cognitive complexity analysis of cross-battery intelligence data sets.[5]

References (not included in this post.  The complete paper will be announced and made available for reading and download in the near future)



[1] This does not mean that cognitive complexity may not be related to the integrity of the human connectome or different brain networks. I am excited about contemporary brain network research (Bressler & Menon, 2010; Cole, Yarkoni, Repovs, Anticevic & Braver, 2012; Toga, Clark, Thompson, Shattuck, & Van Horn, 2012; van den Heuvel & Sporns, 2011), particularly that which has demonstrated links between neural network efficiency and working memory, controlled attention and clinical disorders such as ADHD (Brewer, Worunsky, Gray, Tang, Weber & Kober, 2011; Lutz, Slagter, Dunne, & Davidson, 2008; McVay & Kane, 2012). The Parietal-Frontal Integration (P-FIT) theory of intelligence is particularly intriguing as it has been linked to CHC psychometric measures (Colom, Haier, Head, Álvarez-Linera, Quiroga, Shih, & Jung, 2009; Deary, Penke, & Johnson, 2010; Haier, 2009; Jung & Haier, 2007) and could be linked to CHC cognitively-optimized psychometric measures.
[2] Only reading and math clusters were included to simplify the presentation of the results and the fact, as reported previously, that reading and writing measures typically do not differentiate well in multivariate analysis—and thus the Grw domain in CHC theory.
[3] GIA-Ext is also represented by a black circle.
[4] Although the WJ III Fluid Reasoning 3 cluster (Gf3) is slightly closer to the center of the figure, the difference from Fluid Reasoning (Gf) is not large and time efficiency would argue for the two-test Gf cluster.
[5] It is important to note that the cognitive complexity analysis and interpretation discussed here is specific to within the WJ III battery only. The degree of cognitive complexity in the WJ III cognitive clusters in comparison to composite scores from other intelligence batteries can only be ascertained by cross-battery MDS complexity analysis.