1 human mental abilities lecture 2 leonardo gabales
TRANSCRIPT
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Human Mental Abilities
Lecture 2
Leonardo Gabales
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Lecture 2
Psychometric models of intelligence I:
Spearman’s g-Theory
Thurstone’s Primary Mental Abilities
Horn & Cattell’s Gf-Gc Theory
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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)
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Spearman’s ‘g’ Theory Charles SPEARMAN (1904): proposed a theory
of intelligence that has many supporters 100+ years later!
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)
Charles Spearman1863-1945
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Positive: as scores on one variable increase, scores on the other variable also tend to increase
Negative: as scores on one variable increase, scores on the other variable tend to decrease
Zero: no systematic relationship between scores on the two variables
X
Y
X
Y
X
Y
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Correlations between tests
Tests 1 … x x+1 … y
1 + + + + + +
… + + + + + +
x + + + + + +
x+1+ + + + + +
… + + + + + +y + + + + + +
Reasoning Tests
Reasoning Tests
Knowledge Tests
Knowledge Tests
POSITIV
E MANIF
OLD
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Spearman’s ‘g’ Theory Positive manifold: virtually all correlations among
cognitive measures are positive
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
Total variance = ‘g-variance’ + ‘s-variance’ + error
S1 S2
SxSy
g
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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 Different FA procedures will result in different solutions FA provides ‘suggestions’ for a taxonomy of tests / tasks
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‘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’
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Testing ‘g’ Tests differ in the amount of ‘g’ that they
measure - some are better measures of ‘g’ than others 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’
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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 _____?
Series completion tasks:
A C E G _ _
f1 <-- r (?) --> f2f1 <-- r (?) --> f2
f1 <-- r (?) --> f2f1 <-- r (?) --> f2
f1 <-- r --> f2 (?)f1 <-- r --> f2 (?)
f1 <-- r (?) --> f2f1 <-- 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: 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
Transformation & manipulation of information
Speed in working through a task
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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
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Thurstone & Primary Mental Abilities Thurstone accepted positive manifold – BUT noted the
existence of clusters of high correlations for subsets of variables
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)
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t11
t2 + 1
t3 + + 1
t4+ + + 1
t5+ + + + 1
t6+ + + + + 1
t7+ + + + + + 1
t8+ + + + + + + 1
t9+ + + + + + + + 1
t1 t2 t3 t4 t5 t6 t7 t8 t9
Verbal Comprehension
Inductive Reasoning
Spatial Ability
VerbalComprehension
InductiveReasoning
SpatialAbility
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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
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: 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
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
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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
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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) Abstract reasoning (‘knowledge independent mechanics’)
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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
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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
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
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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
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)
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Broad Abilities The most recent formulations of Gf/Gc theory postulate
the existence of 9 broad abilities:
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
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“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)
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Two-stratum Gf/Gc model The elaborated Gf/Gc Theory is a two-stratum model
of cognitive abilities
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
Gf Gc Gv Ga Gs GqSAR TSR CDS 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
See e.g., Horn (1998)
Time/Age
Per
form
ance
Gc
Gf
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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)