Dr. Kevin S. McGrewInstitute for Applied Psychometrics (IAP)
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
CHC introduction & history:
From g to CHC
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
g
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4
G1 G2 G3
g ?
Classification is arguably one of the most central and generic of all our conceptual exercises … without classification, there could be no advanced conceptualization, reasoning, language, data analysis, or for that matter, social science research.
(K.D. Bailey, 1994)
The importance of taxonomies and classification in science
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
A specialized science of classification of empirical entities known as taxonomy (Bailey, 1994; Prentky, 1994) is ubiquitous in all fields of study because it guides our search for information or truth.
The importance of taxonomies and classification in science
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Bloom's Revised Taxonomy of Learning Objectives
...most disciplines have a common set of termsand definitions (i.e., a standard nomenclature)that facilitates communication among professionalsand guards against misinterpretations. In chemistry,this standard nomenclature is reflected in the Tableof Periodic Elements. Carroll (1993a) has providedan analogous table for intelligence…..
(Flanagan & McGrew, 1998)
The importance of taxonomies and classification in science
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
A Good Taxonomy:
Psychometric approach is the dominant approach, has inspired the most research, is used most widely in practical settings. (p. 77)
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
John Horn, compared the process of classifying and categorizing human abilities and
intelligence to “slicing smoke”. (Horn, 1991)
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
GfGc Gwm
Glr
Gv
Ga
Gs
GqGrw
g
I am going to be your guide for a “walk in the clouds” of human cognitive abilities.
CHC theory will be our map.
Gs
Ga GvGfGq
GrwGlr
GwmGc
abilityconstruct
Human cognitive abilities
are hypothetical constructs
• Hidden attributes• Unseen phenomena• Not visible• Not directly observable• Latent• Are used to explain behavior
Intelligence scholars have been trying to discover/define a valid “Rosetta Stone” for describing human cognitive abilities since the early 1900’s.
© Institute for Applied Psychometrics (IAP) Dr. Kevin
McGrew 4-11-14
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Figure 1. The Evolution of CHC Intelligence Theory and Assessment Methods
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
g
Spearman’s general factor model
(T# = designates different test measures)
Latent, hidden, unobservableability construct
Factor loadings of tests on latent g ability factor
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Thurston’s Multiple Factor (Primary Mental Abilities) Model
(T# = designates different test measures)(PMA# = different “primary mental ability”)
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
Correlations between latent ability constructs
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
G1 G2 G3 …etc
Cattell-Horn Gf-Gc Hierarchical (no g) Model
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
…etc
…etc
PMA2 PMA3 PMA4
G2G1
g
Arrows from g to each test(rectangle) have been omitted for readability
Stratum I
Stratum II
Stratum III
Carroll’s Schmid-Leiman Hierarchical Three-Stratum Model
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Carroll and Cattell-Horn Model Comparison
Gq
Qua
ntita
tive
Know
ledg
e
Grw
Read
ing/
Writi
ng
Catt
ell-H
orn
Carr
oll
Gf
Flui
d In
telli
genc
eFl
uid
Inte
llige
nce
Gf
Gsm
Shor
t-Te
rmM
emor
yG
en. M
emor
y&
Lea
rnin
g
Gy
GvVi
sual
Pr
oces
sing
Broa
d Vi
sual
Perc
eptio
n
Gv
Gs
Proc
essi
ngSp
eed
Broa
d Co
gniti
veSp
eedi
ness
Gs
CDS
Corr
ect
Dec
isio
n Sp
eed
Dec/
Reac
tion
Tim
e/Sp
eed
Gt
Glr
Long
-Ter
mRe
trie
val
Broa
d Re
trie
val
Abili
ty
Gr
GaAu
dito
ryPr
oces
sing
Broa
d Au
dito
ryPe
rcep
tion
Gu
Gc
Crys
talli
zed
Inte
llige
nce
Crys
talli
zed
Inte
llige
nce
Gc
g
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Consensus Cattell-Horn-Carroll (CHC) Hierarchical Three-Stratum Model
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
G1 G2 G3
…etc
g?
Stratum I
Stratum II
Stratum III
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
g
(1a) Spearman’s general Factor model
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
…etc
…etc
…etc
PMA2 PMA3 PMA4
G2G1
g
Arrows from g to each test(rectangle) have been omitted for readability
Stratum I
Stratum II
Stratum III
(1d) Carroll’s Schmid-Leiman Hierarchical Three-Stratum Model
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
G1 G2 G3 …etc
(1c) Cattell-Horn Gf-Gc Hierarchical Model
Figure 1: Major stages in the evolution of psychometric theories from Spearman’s g to Cattell-Horn-Carroll (CHC) theory
Note: Circles representlatent factors. Squares represent manifest measures (tests; T1..). Single-headed path arrows designate factor loadings. Double headed arrows designate latent factor correlations
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
G1 G2 G3
…etc
g ?
(1e) Consensus Cattell-Horn-Carroll Hierarchical Three-Stratum Model
Stratum I
Stratum II
Stratum III
PMA1
T2 T3 T4 T5 T6 T7 T8 T9T1 T12T10 T11
PMA2 PMA3 PMA4 …etc
…etc
(1b) Thurston’s Multiple Factor (Primary Mental Abilities) Model
© Institute for Applied
Psychometrics (IAP) Dr. Kevin
McGrew 4-11-14
CHC Theory Summary
• Combination of research by Raymond Cattell, John Horn, and John Carroll
• The most empirically-supported, psychometric-based, contemporary description of the structure of human cognitive abilities
• Based on the analyses of hundreds of data sets that were not restricted to a particular test battery
• The theory describes cognitive abilities as a function of degree of breadth/generality
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Richard Snow (1993): “John Carroll has done a magnificent thing. He has reviewed and reanalyzed the world’s literature on individual differences in cognitive abilities…no one else could have done it… it defines the taxonomy of cognitive differential psychology for many years to come.”
Burns (1994): Carroll’s book “is simply the finest work of research and scholarship I have read and is destined to be the classic study and reference work on human abilities for decades to come” (p. 35).
John Horn (1998):
A “tour de force summary and integration” that is the “definitive foundation for current theory” (p. 58). Horn compared Carroll’s summary to “Mendelyev’s first presentation of a periodic table of elements in chemistry” (p. 58).
Arthur Jensen (2004): “…on my first reading this tome, in 1993, I was reminded of the conductor Hans von Bülow’s exclamation on first reading the full orchestral score of Wagner’s Die Meistersinger, ‘‘It’s impossible, but there it is!’’
“Carroll’s magnum opus thus distills and synthesizes the results of a century of factor analyses of mental tests. It is virtually the grand finale of the era of psychometric description and taxonomy of human cognitive abilities. It is unlikely that his monumental feat will ever be attempted again by anyone, or that it could be much improved on. It will long be the key reference point and a solid foundation for the explanatory era of differential psychology that we now see burgeoning in genetics and the brain sciences” (p. 5).
The verdict is unanimous re: the importance of Carroll’s (1993) work
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
g
Gf GqGcSARGsm
Gv GaTSRGlm
Gs CDS Grw
Gkn Gh Gk Go
Gf Gc Gy Gv Gu Gr Gs Gt
Gp Gps
A. Carroll Three-Stratum Model
B. Cattell-Horn Extended Gf-Gc Model
D. Tentatively identified Stratum II (broad) domains 1
Carroll and Cattell-Horn Broad Ability Correspondence (vertically-aligned ovals represent similar broad domains)
Gf GqGc Gsm Gv Ga Glr Gs Gt Grw
C. Cattell-Horn-Carroll (CHC) Integrated Model
g
Stratum III (general)
Stratum II (broad)
Notes. Broad ability factor codes based on Carroll (1993) and Horn and Blankson (2005). See Table 1 for additional explanation.
80+ Stratum I (narrow) abilities have been identified under the Stratum II broad abilities. They are not listed here due to space limitations (see Table 1).
Placement of g to the left-side of the Carroll Three-Stratum Model (A) is consistent with Carroll's (1993) published figures, a placement reflecting his finding that the broad abilities towards the left (e.g, Gf, Gc) had the highest loadings on the g-factor. The placement of the Grw and Gq factors in the Cattell-Horn Extended Gf-Gc Model (B) is not consistent with this g-broad ability representation as Grw and Gq typically demonstrate high g-loadings. Grw and Gq are placed to the right in B to reflect their absence in model A.
Gf Fluid reasoning Gkn General (domain-specific) knowledgeGc Comprehension-knowledge Gh Tactile abilitiesGsm Short-term memory Gk Kinesthetic abilitiesGv Visual processing Go Olfactory abilitiesGa Auditory processing Gp Psychomotor abilitiesGlr Long-term storage and retrieval Gps Psychomotor speedGs Processing speedGt Decision and reaction speed (see Table 1 for definitions)
Grw Reading and writing 1 See McGrew (2004, 2005) for literature review supporting these domains
Gq Quantitative knowledge
CHC Broad (Stratum II) Ability Domains
(Missing g-to-broad ability arrows acknowledges that Carroll and Cattell-Horn disagreed on the validity of the general factor)
© Institute for Applied Psychometrics, LLC Kevin S. McGrew 7-22-08
g
General(stratum I)
The CHC taxonomy of cognitive abilities –
The three levels (stratum)Narrow
(stratum III)Broad
(stratum II)
Gf Gc Gwm
Glr Gv Ga Gs
Gc
Note. WJ IV authors propose that Gsm be changed to Gwm (McGrew,
LaForte & Schrank, 2014)
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
g
Gf Gc Gwm
Glr Gv Ga Gs
Gc
Substantive Stage of Test Development:Develop Test Design and Specification Blueprint
• What is the theoretical domain?• How should intelligence be defined?• What intelligence theory has the best validity evidence?
Answer: Cattell-Horn-Carroll (CHC) theory of cognitive abilities
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
g
Gf Gc Gwm
Glr Gv Ga Gs
Gc
Substantive Stage of Test Development:Develop Test Design and Specification Blueprint
What broad & narrow ability domain(s) are to be measured and in what proportion?
How do we define the broad and narrow ability constructs?© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Contemporary psychometric research has converged on the Cattell-Horn-Carroll (CHC) model of cognitive
abilities as the consensus working taxonomy of human intelligence
g
Gf GqGcSARGsm Gv Ga
TSRGlm Gs CDS Grw
Gkn Gh Gk Go
Gf Gc Gy Gv Gu Gr Gs Gt
Gp Gps
A. Carroll Three-Stratum Model
B. Cattell-Horn Extended Gf-Gc Model
D. Tentatively identified Stratum II (broad) domains
Carroll and Cattell-Horn Broad Ability Correspondence (vertically-aligned ovals represent similar broad domains)
Gf GqGc Gsm Gv Ga Glr Gs Gt Grw
C. Cattell-Horn-Carroll (CHC) Integrated Model
g
Stratum III (general)
Stratum II (broad)
80+ Stratum I (narrow) abilities have been identified under the Stratum II broad abilities. They
are not listed here due to space limitations(see Table 1)
Gf Fluid reasoning Gkn General (domain-specific) knowledgeGc Comprehension-knowledge Gh Tactile abilitiesGsm Short-term memory Gk Kinesthetic abilitiesGv Visual processing Go Olfactory abilitiesGa Auditory processing Gp Psychomotor abilitiesGlr Long-term storage and retrieval Gps Psychomotor speedGs Cognitive processing speedGt Decision and reaction speed (see Table 1 for definitions)Grw Reading and writingGq Quantitative knowledge
CHC Broad (Stratum II) Ability Domains
(Missing g-to-broad ability arrows acknowledges that Carroll and Cattell-Horn disagreed on the validity of the general factor)
The CHC taxonomy of cognitive abilities:
Current status
Dr. Kevin S. McGrewInstitute for Applied Psychometrics (IAP)
GfGc Gwm
Glr
Gv
Ga
Gs
GqGrw
g
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Gf
Gc Gwm
Glr
Gv
Ga
Gs
GqGrw
g
The CHC taxonomy of cognitive abilities: Current Status
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
GfGc Gwm
Glr
Gv
Ga
Gs
GqGrw
g
Contemporary psychometric research has
converged on the Cattell-Horn-Carroll
(CHC) model of cognitive abilities as
the consensus working taxonomy of human intelligence
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
From
CHC model is analogous to the Periodic Table of Elements in Chemistry
Gh
Go OM
Ga PC US UM U8 UR U1U9 UP UL
Gv Vz SR MV CS SS CF IM PI LE IL PN
Sens
ory-
Mot
or D
omai
n-Sp
ecifi
c Ab
ilitie
s
Sensory
The CHC Periodic Table of Human
AbilitiesAdapted from Schneider & McGrew (2012) and McGrew, LaForte and Schrank (2014)
Gf I RG RQ
Gwm WM MS AC
Gps R3 PT MT
Gs P N R9
Gt R1 R2 R4 R7 IT
Glr MA MM M6 FI FA FE SP F0 NA FW LA FF FX
Ideas Words Figures
Dom
ain-
Inde
pend
ent
Capa
citie
s
Glr-Learning efficiency
Glr-Retrieval fluency
Broad ability
Narrow ability
© Institute for Applied Psychometrics (IAP)Dr. Kevin McGrew 3-28-14
Gq KM A3
Gc LD VL K0 LS CM MY
Gkn KL K1 A5 MK KF LP BC
Grw V RD RC RS WA SG EU WS
Acqu
ired
Know
ledg
eSy
stem
s
K2
Gk
Gp PI P2 P3 P4 P6 P7 A1
U1U9 UP UL
Motor
Gh
Go OM
Ga PC US UM U8 UR U1U9 UP UL
Gv Vz SR MV CS SS CF IM PI LE IL PN
Sens
ory-
Mot
or D
omai
n-Sp
ecifi
c Ab
ilitie
s
Sensory
The CHC Periodic Table of Human
AbilitiesAdapted from Schneider & McGrew (2012) and McGrew, LaForte and Schrank (2014)
Gf I RG RQ
Gwm WM MS AC
Gps R3 PT MT
Gs P N R9
Gt R1 R2 R4 R7 IT
Glr MA MM M6 FI FA FE SP F0 NA FW LA FF FX
Ideas Words Figures
Dom
ain-
Inde
pend
ent
Capa
citie
s
Glr-Learning efficiency
Glr-Retrieval fluency
Broad ability
Narrow ability
© Institute for Applied Psychometrics (IAP)Dr. Kevin McGrew 4-17-14
Gq KM A3
Gc LD VL K0 LS CM MY
Gkn KL K1 A5 MK KF LP BC
Grw V RD RC RS WA SG EU WS
Acqu
ired
Know
ledg
eSy
stem
s
K2
Gk
Gp PI P2 P3 P4 P6 P7 P8
U1U9 UP UL
Motor
A1
See handouts
or provided PDF copy to
read
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
See handouts
or provided PDF copy to
read
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
See handouts
or provided PDF copy to
read
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14
Gh
Go OM
Ga PC US UM U8 UR U1U9 UP UL
Gv Vz SR MV CS SS CF IM PI LE IL PN
Sens
ory-
Mot
or D
omai
n-Sp
ecifi
c Ab
ilitie
s
Sensory
The CHC Periodic Table of Human
AbilitiesAdapted from Schneider & McGrew (2012) and McGrew, LaForte and Schrank (2014)
Gf I RG RQ
Gwm WM MS AC
Gps R3 PT MT
Gs P N R9
Gt R1 R2 R4 R7 IT
Glr MA MM M6 FI FA FE SP F0 NA FW LA FF FX
Ideas Words Figures
Dom
ain-
Inde
pend
ent
Capa
citie
s
Glr-Learning efficiency
Glr-Retrieval fluency
Broad ability
Narrow ability
© Institute for Applied Psychometrics (IAP)Dr. Kevin McGrew 3-28-14
Gq KM A3
Gc LD VL K0 LS CM MY
Gkn KL K1 A5 MK KF LP BC
Grw V RD RC RS WA SG EU WS
Acqu
ired
Know
ledg
eSy
stem
s
K2
U1U9 UP UL
GkMotor
Gp PI P2 P3 P4 P6 P7 A1P8
Gq KM A3
Gc LD VL K0 LS CM MY
Gkn K1 A5
Grw V RD RC RS WA SG EU WS
Ga PC US UM U8 UR U1U9 UP UL
Gv Vz SR MV CS SS CF IM PI LE IL PN
Acqu
ired
Know
ledg
eSy
stem
sSe
nsor
y-M
otor
Dom
ain-
Spec
ific
Abili
ties
Gf I RG RQ
Gwm WM MS AC
Gs P N R9
Glr MA MM M6 FI FA FE SP F0 NA FW LA FF FX
Ideas Words Figures
Dom
ain-
Inde
pend
ent
Capa
citie
s
K2
Broad and Narrow Abilities Most Relevant to the Development of Measures of Cognitive and Achievement Abilities
Gq KM A3
Gc LD VL K0 LS
Gkn K1 A5
Grw V RD RC RS WA SG EU WS
Ga PC UM
Gv Vz MV SS
Acqu
ired
Know
ledg
eSy
stem
sSe
nsor
y-M
otor
Dom
ain-
Spec
ific
Abili
ties
Gf I RG RQ
Gwm WM MS AC
Gs P N
Glr MA MM NA FW LA
Ideas Words Figures
Dom
ain-
Inde
pend
ent
Capa
citie
s
K2
Broad and Narrow Abilities Measured by the WJ IV COG, OL and ACH
FI
© Institute for Applied Psychometrics (IAP) Dr. Kevin McGrew 4-11-14