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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)