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Chapter 5 – Topic 5A – Theories and Individual Tests of Intelligence and Achievement
Definitions of Intelligence
An operational definition defines a concept in terms of the way it is measured – this is different
than “real” definition. Operational definitions of intelligence suffer from two dangerous short comings –
1) they are circular (intelligence tests were invented to measure intelligence, not measure it) 2) operation
definitions block further progress in understanding the nature of intelligence (they foreclose discussion on
the adequacy of theories and intelligence. Operational definitions leave much to be desired. In contrast, a
real definition is one that seeks to tell us the true nature of the thing being defined.
Expert Definitions of Intelligence
Read page 153 for the different expert definitions. In spite of the diversity in viewpoints of
intelligence, two themes recur again and again in expert definitions – experts tend to agree that
intelligence is 1) the capacity to learn from experience and 2) the capacity to adapt to one’s environment.
One concern is that very few contemporary intelligence tests appear to require the examinee to learn
something new or to adapt to a new situation as part and parcel of the examination process.
Layperson and Expert Conceptions of Intelligence
Another approach to understanding a construct is to study its popular meaning and this is much
more scientific than it appears.
In an experiment where both laypersons and experts rated the importance of behaviours to their
concept of an “ideally intelligent” person, answers turned out to be very similar. In order of importance,
experts saw verbal intelligence, problem-solving ability, and practical intelligence as crucial to
intelligence. In their conception of intelligence, experts and laypersons alike consider verbal ability and
problem solving to be essential aspects of intelligence. Some disagree also occurred – experts believed
that practical intelligence was an essential component while laypersons felt social competence as a third
component (these two nominations share one property in common: contemporary tests generally make no
attempt to measure either of these – main reason is inertia)
A Primer of Factor Analysis
There are two forms of factor analysis: confirmatory and exploratory. In confirmatory factor
analysis, the goal is to conform that test scores and variables fit a certain pattern predicted by theory. The
central purpose of exploratory factor analysis is to summarize the interrelationships among a large
number of variables in a concise and accurate manner as an aid in conceptualization (the underlying
variables are then called factors).
The Correlation Matrix
The beginning point for every factor analysis is the correlation matrix, a complete table of
intercorrelations among all the variables. There are just too many intercorrelations for the viewer to
discern the underlying patterns for all the variables by just looking at it intuitively.
The Factor Matrix and Factor Loadings
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The factor matrix consists of a table of correlations called factor loadings. The factor loadings
(values from -1.00 to +1.00) indicate the weighting of each variable on each factor. A factor is nothing
more than a weighted linear sum of the variables; that is, each factor is a precise statistical combination of
tests used in the analysis. In a sense, a factor is produced by “adding in” carefully determined portions of
some tests and perhaps “subtracting out” fractions of other tests. Factor loadings are nothing more than
correlation coefficients between variables and factors.
Geometric Representation of Factor Loadings
It is customary to represent the first two or three factors as reference axes in two or three
dimensional space – the factor ladings can then be plotted for examination.
The Rotated Factor Matrix
An important point is that the position of the reference axes is arbitrary and can be rotated around
if it produces a more sensible fit with the factor loadings. In a rotation to positive manifold, the computer
program seeks to eliminate as many of the negative factor loadings as possible. In a rotation to simple
structure, the computer program seeks to simplify the factor loadings so that each test has significant
loadings on as few factors as possible. The goal of both criteria is to produce a rotated factor matrix that is
straightforward and unambiguous as possible.
The Interpretation of Factors
In order to interpret or name a factor, the researcher must make a reasoned judgement about the
common processes and abilities shared by the tests with strong loadings on that factor. A major use of
factor analysis is the identification of a small number of marker tests from a large test battery and instead
of using a cumbersome battery of 24 tests, a researcher could just select several tests with strong loadings
on the five factors (in reference to the example provided in the textbook).
Issues in Factor Analysis
If there is no gold to be found, then none will be found. Factor analysis will yield meaningful
results only when the research was meaningful to begin with. An important point is that a particular kind
of factor can emerge from factor analysis only if the tests and measures contain that factor in the first
place. GIGO “garbage in, garbage out” – the quality of the output depends upon the quality of the input/
Sample size is also crucial to a stable factor analysis – in general you should have at least 5 subjects for
each test or variable.
Finally, it cannot be overemphasized the extent to which factor analysis is guided by subjective
choices and theoretical prejudices. Crucial choice between orthogonal axes and oblique axes. With
orthogonal axes, the factors are at right angles to eachother, which means they are uncorrelated. With
oblique axes, the factors are correlated among themselves. Some researchers prefer oblique axes to
always be used, whereas others take a more experimental approach
Galton and Sensory Keenness
The first theories of intelligence were derived in the Brass Instruments era of psychology at the
turn of the twentieth century. The sensory keenness theory of intelligence proved to be psychometric dead
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end. The speed of processing measures such as RT might be a useful addition to standardized intelligence
test batteries (approach similar to Galton’s sensory theory).
Spearman and the g Factor
Charles Spearman proposed that intelligence consisted of two kinds of factors: a single general
factor g and numerous specific factors s1, s2, s3 and so on.
In Spearman’s view, an examinee’s performance was determined mainly by two influences: g, the
pervasive general factor, and s, a factor specific to that test or subtest. He concentrated mainly on the
factor g which he likened to an “energy” or “power” that serves in common the whole cortex. In contrast,
he considered s to have a physiological substrate localized in the group of neurons serving the particular
kind of mental operation demanded by a test or subtest.
He reasoned that some tests were heavily loaded with the g factor, while others, especially purely
sensory measures, were representative mainly of a specific factor. Two tests each heavily loaded with g
should correlate quite strongly. Psychological tests not saturated with g should show minimal correlation
with one another.
Spearman believed that individual differences in g were most directly reflected in the ability to
use three principles of cognition: apprehension of experience (understand based on past experience),
eduction of relations (figuring things out – the relation between different things), and eductino of
correlations (ability to apply the inferred principle to the new domain).
Although Spearman’s physiological speculations have been dismissed, the idea of a general factor
has been a central topic in research on intelligence.
Thurstone and the Primary Mental Abilities
Seven factors have been designated primary mental abilities and they are: Verbal comprehension,
word fluency, number, space, associative memory, perceptual speed, inductive reasoning. The Primary
Mental Abilities Test measured each of the PMA’s. Spearman and Thurstone both admitted to the
existence of a general factor and group factors – they just emphasized them differently.
Catteell-Horn-Carroll (CHC) Theory
CHC theory is a taxonomic tour de force that synthesizes the findings from almost a century of
factor analytic research on intelligence. Many refer CHC theory to possess the strongest empirical
foundation of any theory of intelligence.
According to CHC theory, intelligence consists of pervasive, broad, and narrow abilities that hare
hierarchically organized. At the highest and most pervasive level known as Stratum III, a single general
factor, g, oversees all cognitive activities. Stratum II which reside beneath general intelligence contains
broad factors that are the basic constitutional and longstanding characteristics of individuals that can
govern or influence a great variety of behaviours in a given domain. The narrow abilities of Stratum I
include approximately 70 abilities – these narrow abilities represent greater specializations of abilities,
often in quite specific ways that reflect the effects of experience and learning, or the adoption of particular
strategies of performance.
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