Human Mental Abilities
Lecture 2
Leonardo Gabales
1
Lecture 2

Psychometric models of intelligence I:

Spearman’s g-Theory

Thurstone’s Primary Mental Abilities

Horn & Cattell’s Gf-Gc Theory
2
The Psychometric Approach

… is based on utilization of psychological
tests that generate scores on quantitative
scales that are analyzed by correlative &
factor-analytic methods to identify ability
dimensions that are considered to form the
structure of individual differences in cognitive
abilities.
(Gustafsson & Undheim, 1996)
3
Spearman’s ‘g’ Theory

Charles SPEARMAN (1904): proposed a theory
of intelligence that has many supporters 100+
years later!


Charles Spearman
1863-1945
An attempt to understand relationships displayed across a
number of correlation coefficients
Correlations indicate the degree of linear association
(i.e., relationship) between two variables


Can be either positive or negative
Range from -1.00 to 1.00 (zero correlation = no relation)
4

Positive: as scores on
one variable increase,
scores on the other
variable also tend to
increase
X
Y

Negative: as scores
on one variable
increase, scores on
the other variable tend
to decrease
X
Y

Zero: no systematic
relationship between
scores on the two
variables
X
Y
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Correlations between tests
Reasoning Tests
Tests
1
Reasoning Tests
…
x
x+1 …
y
+ + +
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x+1
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…
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y
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…
x
Knowledge Tests
1
Knowledge Tests
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Spearman’s ‘g’ Theory

Positive manifold: virtually all correlations among
cognitive measures are positive


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According to Spearman this is due
to a common cause affecting
performance on all cognitive tasks
– i.e., ‘g’ or general intelligence
As correlations are never perfect,
Spearman suggested two further
causes of individual differences
unique to every task - 'error'
variance & a specific factor
S2
S1
g
Sy
Sx
Total variance = ‘g-variance’ + ‘s-variance’ + error
7
Spearman & Factor Analysis

Realising difficulties in interpreting large correlational
matrices, Spearman developed a new statistical
procedure: Factor Analysis



Based on a correlation matrix, factor analytic techniques
extract a small number of basic components or ‘factors’,
which account for the interrelationships in the data
Spearman claimed that factor analysis reflected the
basic properties of psychological functioning
However … FA is (only) a statistical procedure

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Different FA procedures will result in different solutions
FA provides ‘suggestions’ for a taxonomy of tests / tasks
8
‘g’ Theory: A Two-factor Theory

‘g’ reflects overall cognitive functioning:


Psychological processes generating 'g' reflect
physiological processes from a large part of
the CNS
‘Specifics’ ('s') reflect localised functioning:

Specific factors are machines (i.e., more
localised functions of the CNS)
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Spearman’s ‘g’ Theory

‘g’: the essence of intelligence


Highly intelligent people do all cognitive tasks
better than persons of low intelligence
As ‘g’ is present in all cognitive tasks it
appears to reflect a form of general ‘mental
energy’
10
Testing ‘g’

Tests differ in the amount of ‘g’ that they
measure - some are better measures of ‘g’ than
others

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Much work has been conducted to discover principles
that allow for the construction of good measures of ‘g’
According to Spearman, intelligent behaviour
involves working with the relationships between
fundaments

Spearman formulated 2 ‘noegenetic laws’ which he
claimed were involved in the best measures of ‘g’ 11
The Noegenetic Laws

Eduction of Relations

Given 2 fundaments (f1 & f2) find a relationship
between them:
f1 <-------- r (?) --------> f2

Eduction of Correlates

Given f1 & a relation (r) find a fundament (f2) in a
given relation to f1:
f1 <-------- r --------> f2 (?)
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The Noegenetic Laws

These principles underpin performance on
many psychometric tests:

Analogical reasoning tasks:
MOTHER is to CHILD as MARE is to _____?
f1 <-- r (?) --> f2
f1 <-- r (?) --> f2

Series completion tasks:
A C E G _ _
f1 <-- r --> f2 (?)
f1 <-- r (?) --> f2
f1 <-- r --> f2 (?)
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Raven’s Progressive Matrices


The RPM – one of the most widely used
psychometric tests available – was explicitly
developed to test both noegenetic laws
Three different instruments:

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
Coloured Progressive Matrices (5-11 years)
Standard Progressive Matrices (6 years – adult)
Advanced Progressive Matrices (superior intellect)
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General Intelligence- ‘g’

Thus, good measures of ‘g’ seem to require:

Good reasoning skills

The ability to cope with novelty

Knowledge of properties of fundaments
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Transformation & manipulation of information

Speed in working through a task
15
Louis Thurstone

Louis THURSTONE (1887-1955) challenged
Spearman’s ‘g’-factor model on both conceptual
& methodological grounds

Thurstone argued that ‘g’ was based on wholly false
premises & could not provide a valid representation of the
structure of human mental abilities

The ‘g’ factor extracted from one battery of tests was distinct
from the ‘g’ factor extracted from another battery of (different)
tests
16
Thurstone & Primary Mental Abilities

Thurstone accepted positive manifold – BUT noted
the existence of clusters of high correlations for
subsets of variables

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i.e., Despite the overall positive manifold within the
correlations from a battery of tests, there are clusters of
relatively high (& low) correlations amongst subsets of the
tests included
Clusters indicated the need to distinguish different
types of abilities

The mind consists of a number of relatively independent
‘faculties’ rather than some unitary trait – Primary Mental
Abilities (PMAs)
17
Verbal
Comprehension
t1
1
t2
+ 1
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1
t4
t5
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t6
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+ 1
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1
t7
t8
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1
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t9
+
+
+
+
+
+
+ 1
+ +
1
t1
t2
t3
t4
t5
t6
t7
t9
t3
Inductive
Reasoning
Spatial
Ability
Verbal
Comprehension
Inductive
Reasoning
t8
Spatial
Ability
18
Thurstone & Factor Analysis

Thurstone developed a method of multiple-factor
analysis (based on different rotation techniques)
which allowed for the discovery of groupings of
variables

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Thurstone viewed FA not only as a means to identify PMAs,
but also as a tool to guide more sophisticated tests of them
Remember... Different factor structures can be
produced in the same data by varying the FA
procedures employed (e.g., extraction or rotation
methods)

There is an INDEFINITE number of possible factor solutions
for any given correlation matrix, & FA alone CANNOT
determine which solution should be accepted
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Thurstone’s (1938) 7 PMAs
Thurstone initially identified 7 Primary Mental Abilities:

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Verbal Comprehension
Inductive Reasoning
Numerical Fluency
Word Fluency
Spatial Ability
Memory
Perceptual Speed
Each PMA was considered to behave ‘as a functional
unity that is strongly present in some tests & almost
completely absent in many others’
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Primary Mental Abilities

Thurstone suggested that ‘g’ should be replaced by a
number of correlated PMAs – a multiple factor theory

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Note: While Thurstone’s initial formulations did not include the
general factor, his later writings provided for the possibility that
the intercorrelations of PMAs could define a general ability factor
similar to Spearman’s ‘g’
However… it was quickly realised that both general &
group factors exist

By 1960 over 20 PMAs had been identified leading to theories
outlining the organisation of mental abilities
21
Masters of the (Cognitive) Universe

Spearman's theory is sometimes described as a
‘monarchic’ conception of intelligence:


i.e., it postulates one (& only one) underlying general
factor that reigns supreme over all cognitive functions
In contrast, Thurstone's theory is described as
an ‘oligarchic’ conception of intelligence:

i.e., there is not a single monarch or a completely free
interaction of individuals, but several equally
important rulers of the cognitive domain
22
Raymond B. Cattell

Proposed the theory of fluid & crystallised
intelligence in 1941 as a ‘modification’ of
Spearman’s ‘g’-factor theory:


“g is too g”
Postulated the existence of two relatively distinct
‘second order’ factors of intelligence:

Gc (crystallised intelligence)
 Accumulated knowledge (‘knowledge-bound pragmatics’)

Gf (fluid intelligence)
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 Abstract reasoning (‘knowledge independent mechanics’)
Fluid & Crystallised Intelligence

Gf & Gc are not independent


r ≈ .50
 MOTHER is to CHILD as MARE is to _____?
Oblique factor rotation
 allows for correlated factors
24
Gf vs Gc

The main distinction between Gf & Gc is the amount
of education &/or acculturation that is implicated in
the item content, or cognitive processes engaged in
measures of these constructs

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Gf depends only minimally on education or acculturation,
whereas Gc is largely determined by these processes
Investment theory of Intelligence

Knowledge as a result of invested (fluid) intelligence
25
Gf/Gc Theory: Horn & Cattell

Gf/Gc Theory has been further elaborated by Cattell, John Horn,
& their colleagues

The original conceptualisation of Gf/Gc theory inherently
provided for the possibility that further factorially distinct
cognitive abilities would be identified


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Structure of PMAs suggest several (fairly) distinct forms of ability –
known as second order (or broad ability) factors
Each broad ability is proposed to be structurally equivalent &
contribute to intellect
Gf/Gc theory is (arguably) the most widely accepted hierarchical
model of human intelligence (Pallier et al., 2001)
26
Broad Abilities

The most recent formulations of Gf/Gc theory postulate
the existence of 9 broad abilities:
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Gf – Fluid reasoning
Gc – Acculturated knowledge
Gv – Broad visualisation
Ga – Broad auditory ability
SAR – Short-term acquisition & retention (STM)
TSR – Tertiary storage & retrieval (LTM)
Gs – Broad speediness
CDS – Correct decision speed
Gq – Quantitative reasoning (?)
See e.g., Horn (1998) or Horn & Noll (1994, 1997) for reviews
27
“If you put water into a cup, it becomes the cup. If
you put water into a bottle, it becomes the
bottle. If you put water into a teapot, it becomes
the teapot.”
(Bruce Lee)
28
Two-stratum Gf/Gc model

The elaborated Gf/Gc Theory is a two-stratum model
of cognitive abilities
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
Gf
Gc
First stratum: a large number of specific or ‘narrow abilities’
reflecting an extension of Thurstone’s PMAs
Second stratum: a limited number of ‘broad abilities’ derived
from the common variance among the first stratum abilities
Gv
Ga
Gs
SAR
TSR
CDS
Gq II: Broad Abilities
I: Narrow Abilities
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Gf/Gc Theory
Supported by:

Developmental trends

Brain damage studies

Different predictive validities

Construct validity / FA evidence
Performance

Gc
Gf
Time/Age
See e.g., Horn (1998)
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Summary

Psychometric theories of intelligence

Factor Analysis


Benefits & limitations!
Intelligence – general intelligence or multiple
abilities?!

There is still much debate in the literature (see e.g., Bowman et al.,
2002)
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“… We are taught to be “on guard” because incorrect
beliefs can become so emotionally based that it is
very difficult to accept the evidence that threatens
them. Yet this teaching can have very little influence.
We can look back at the examples from our history
and say, “My, how absurd,” but not let that lesson do
much to alter our beliefs in our own time.
The example of such a belief that I wish to bring
to your attention in this chapter is the belief in a
concept of general intelligence.”
(John Horn)
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