Theories and Individual Tests of
Intelligence and Achievement
Theories of Intelligence and
Factor Analysis
• Intelligence is one of the most highly researched
topics in psychology. Despite this burgeoning
research literature, the definition of intelligence
remains elusive, wrapped in controversy and
mystery.
• In fact, the discussion that follows will illustrate a
major paradox of modern testing:
Psychometricians are better at measuring
intelligence than conceptualizing it!
Definitions of Intelligence
• Operational definitions of intelligence
suffer from two dangerous shortcomings.
First, they are circular. Intelligence tests
were invented to measure intelligence not
to define it. Second, operational definitions
block further progress in understanding
the nature of intelligence, because they
foreclose discussion on the adequacy of
theories of intelligenc.
Definitions of Intelligence
• If established tests serves as the principal
criterion against which new tests are
assessed, then the new tests will be
viewed as valid only to the extent that they
correlate with the old ones. Such a
conservative practice drastically curtails
innovation. The operational definition of
intelligence does not allow for the
possibility that new tests or conceptions of
intelligence may be superior to the existing
ones.
Definitions of Intelligence
• A real definition is one that seeks to tell us
the true nature of the thing being defined.
Perhaps the most common way of
producing real definitions of intelligence is
to ask experts in the field to define it.
Expert Definitions of Intelligence
• Spearman(1904, 1923): a general ability
that involves mainly the eduction of
relations and correlates.
• Binet and Simon (1905): the ability to
judge well, to understand well, to reason
well.
• Thurstone(1921): the capacity to inhibit
instinctive adjustments, flexibly imagine
different responses, and realize modified
instinctive adjustments into overt behavior.
Expert Definitions of Intelligence
• Wehsler(1959): the aggregate or global
capacity of the individual to act purposefully,
to think rationally, and to deal effectively with
the environment.
• Sternberg(1985a, 1986): the mental capacity
to automatize information processing and to
emit contextually appropriate behavior in
response to novelty: intelligence also includes
metacomponents, performance components,
and knowledge-acquisition components.
Expert Definitions of Intelligence
• Gardner(1986): the ability or skill to solve
problems or to fashion products that are
values within one or more cultural settings.
• Broadly speaking, the experts tend to agree
that intelligence is (1) the capacity to learn
form experience, and (2) the capacity to
adapt to one’s environment.
• Very few contemporary intelligence tests
appear to require the examinee to learn
something new or to adapt to new situation
as part an parcel of the examination process.
Layperson and Expert Conceptions of
intelligence
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Table 5.1
Laypersons:
Practical problem-solving ability
Reasons logically and well
Identifies connections among ideas
Sees all aspects of a problem
Experts:
Verbal Intelligence
Display a good vocabulary
Reads with high comprehension
Displays curiously
A Primer of Factor Analysis
• Broadly speaking, there are two forms of
factor analysis: confirmatory and exploratory.
• In confirmatory factor analysis, the purpose
is to confirm that test scores and variables fit
a certain pattern predicted by a 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 Correlation Matrix
• Factor analysis relies on modern highspeed computers to search the correlation
matrix according to objective statistical
rules and determine the smallest number of
factors needed to account for the observed
pattern of intercorrelations.
• The analysis also produces the factor
matrix, a table showing the extent to which
each test loads on (correlates with) each of
the derived factors.
The Factor Matrix and Factor Loadings
• The factor matrix consists of a table of
correlations called factor loadings. The factor
loadings (which can take on values from 1.00 to +1.00) indicate the weighting of each
variable on each factor. Table 5.4.
• The factors may seem quite mysterious, but
in reality they are conceptually quite simple.
A factor is nothing more than a weighted
linear sum of the variables; that is, each
factor is a precise statistical combination of
the tests used in the analysis.
The Factor Matrix and Factor Loadings
• In a sense, a factor is produced by “adding
in” carefully determined portions of some
tests and perhaps “subtracting out” fractions
of other tests.
• Several methods are used to proceed factor
analysis, including: principal components
factor, principal axis factors, method of
unweighted least squares, maximumlikelihood method, image factoring, and
alpha factoring. Most of the methods yield
highly similar results.
The Factor Matrix and Factor Loadings
• The factor loadings depicted in Table 5.4 are
nothing more than correlation coefficients
between variables and factors. These
correlations can be interpreted as showing
the weight or loading of each factor on each
variable.
• For example, variable 9, the test of Word
Meaning, has a very strong loading (0.69) on
factor I, modest negative loadings (-0.45 and
-0.29) on factor II and III, and negligible
loadings (0.08 and 0.00) on factors IV and V.
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.
• Figure 5.1
• The reader will notice that the factor
loadings on the first factor (I) are uniformly
positive, whereas the factor loadings on
the second factor (II) consist of a mixture
of positive and negative.
The Rotated Factor Matrix
• An important point in this context is that
the position of the reference axes is
arbitrary. There is nothing to prevent the
researcher from rotating the axes so that
they produce a more sensible fit with the
factor loadings.
• Thurstone’s (1947) criteria of positive
manifold and simple structure are
commonly applied.
The Rotated Factor Matrix
• In a rotation to positive manifold, the
computer program seeks to eliminate as
many of the negative factor loadings as
possible.
• Negative factor loadings make little sense
in ability testing, because they imply that
high scores on a factor are correlated with
poor test performance.
The Rotated Factor Matrix
• 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 as
straightforward and unambiguous as
possible.
The Rotated Factor Matrix
• It is worth pointing out here that a
researcher encounters many choice points
in the process of conducting a factor
analysis.
• It is not surprising, then, that different
researchers may reach different
conclusions from factor analysis, even
when they are analyzing the same data
set.
The Interpretation of Factors
• In order to interpret or name a factor, the
researcher must make a reasoned
judgment about the common processes
and abilities shared by the tests with
strong loadings on that factor.
Issues in Factor Analysis
• No amount of statistical analysis can
rescue data based on trivial, irrelevant, or
haphazard measures. Factor analysis will
yield meaningful results only when the
research was meaningful to begin with.
• In general, the quality of the output
depends upon the quality of the input. We
can restate this point as the acronym
GIGO, or “garbage in, garbage out.”
Issues in Factor Analysis
• Sample size is crucial to a stable factor
analysis.
• 50 is very poor
• 100 is poor
• 200 is fair
• 300 is good
• 500 is very good
• 1000 is excellent
Issues in Factor Analysis
• We cannot overemphasize the extent to
which factor analysis is guided by
subjective choices and theoretical
prejudices. A crucial question in this regard
is the choice between orthogonal axes and
oblique axes.
• With orthogonal axes, the factors are at
right angles to one another, which means
they are uncorrelated (Figure 5.1 and 5.2
both depict orthogonal axes).
Issues in Factor Analysis
• With oblique axes, the factors are correlated
among themselves. Some researchers
contend that oblique axes should always be
used. Some researchers recommend an
exploratory strategy based on repeated factor
analyses.
• With oblique rotations it is also possible to
factor analyze the factors themselves. Such a
procedure may yield one or more secondorder factors.
Issues in Factor Analysis
• Second-order factors can provide support for
the hierarchical organization of traits and
may offer a rapprochement between ability
theorists who posit a single general factor
(eg., Spearman) and those who promote
several group factors (eg., Thurstone).
• Perhaps both camps are correct, with the
group factors sitting underneath the secondorder general factor.
Galton and sensory Keenness
• The sensory keenness theory of
intelligence promoted by Galton and
Cattell proved to be largely a psychometric
dead end. However, we do see vestiges of
this approach in modern chronometric
analyses of intelligence such as the
Reaction Tim-Movement Time (RT-MT)
apparatus.
Spearman and The g Factor
• 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.
• As a necessary adjunct to his theory,
Spearman helped invent factor analysis to
aid his investigation of the nature of
intelligence.
Spearman and The g Factor
• An examinee’s performance on any
homogenous test or subtest of intellectual
ability was determined mainly by two
influence: g, the pervasive general factor,
and s, a factor specific to that test or
subtest. (An error factor e could also sway
scores, but Spearman sought to minimize
this influence by using highly reliable
instruments.)
Spearman and The g Factor
• Because the specific factor s was different for each
intellectual test or subtest and was usually less
influential than g in determining performance level,
Spearman expressed less interest in studying it.
• The most difficult issue faced by Spearman’s twofactor theory is the existence of group factors. As
early as 1906, Spearman noted that relatively
dissimilar tests could have correlations higher than
the values predicted from their respective g loadings.
This finding raised the possibility that a group of
diverse measures might share in common a unitary
ability other than g.
Spearman and The g Factor
• For example, several tests might share a
common unitary memorization factor that
was halfway between the g factor and the
various s factors unique to each test.
Thurstone and the primary mental
ability
• Thurstone concluded that several broad
group factors—and not a single general
factor—could best explain empirical
results. There are seven group factors
frequently corroborated, which have been
designated primary mental abilities
(PMAs).
Thurstone and the primary mental
ability
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Verbal comprehension
Word fluency
Number
Space
Associative memory
Perceptual speed
Inductive reasoning
Thurstone and the primary mental
ability
• However, Thurstone acknowledged that
his primary mental abilities correlated
moderately with each other, proving the
existence of one or more second-order
factors.
• Vernon (1950) provided a rapprochment
between these two viewpoints (Spearman
vs. Thurstone) by proposing a hierarchical
group factor theory. Figure 5.5
Thurstone and the primary mental
ability
• In his view, g was the single factor at the
top of a hierarchy that included two major
factors labeled verbal-educational (V:ed)
and practical-mechanical-spatial-physical
(k:m). Underneath these two major group
factors were several minor group factors
resembling the PMAs of Thurstone;
specific factors occupied the bottom of the
hierarchy.
Cattell-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. Although
the “big picture” of CHC theory is well
established, researchers continue to refine the
details.
• According CHC theory, intelligence consists of
pervasive, broad, and narrow abilities that are
hierarchically organized (Figure 5.6).
Cattell-Horn-Carroll (CHC) Theory
• In Figure 5.6.
• At the highest and most pervasive level
known as Stratum III, a single general
factor known as little g oversees all
cognitive activities. Stratum II capacities,
which reside beneath general intelligence,
include several prominent and wellestablished abilities. The narrow abilities
at stratum I include approximately 70
abilities.
Definitions of CHC Broad Ability
Factors
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Fluid intelligence/Reasoning (Gf)
Crystallized Intelligence/Knowledge (Gc)
Domain-Specific Knowledge (Gkn)
Visual-Spatial Abilities (Gv)
Auditory Processing (Ga)
Broad Retriveal [Memory] (Gr)
Cognitive Processing Speed (Gs)
Decision/Reaction Time or Speed (Gt)
Piaget and Adaptation
• Piaget used interviews and informal tests
with children to develop a series of
provocative and revolutionary views about
intellectual development as follows.
• Children’s thought is qualitatively different
from adults’ thought.
• Psychological structures called schemas are
the primary basis for gaining new knowledge
about the world.
• Four stages of cognitive development can be
identified.
Piaget and Adaptation
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“Conservation”,
“Equilibration”,
“Assimilation”,
“Accommodation”
Table 5.6
Sensorimotor: birth to 2 years
Preoperational: 2 to 6 years
Concrete Operational: 7 to 12 years
Formal Operational: 12 years and up
Guilford and the Structure-OfIntellect (SOI) Model
• Guilford’s SOI model classifies intellectual
abilities along three dimensions called
operations, contents, and products.
• Operations: the kind of intellectual
operation required by the test.
• Contents: the nature of the materials or
information presented to the examinee.
• Products: the different kinds of mental
structures that the brain must produce to
derive a correct answer.
Guilford and the Structure-OfIntellect (SOI) Model
• Each combination of an operation (e.g.,
memory), a content (e.g., symbolic), and a
product (e.g., units) represents a different
factor of intellect.
• Prior to Guilford’s contributions, most
tests of intelligence required mainly
convergent production. Guilford raised the
intriguing possibility that divergent
production.
Theory of Simultaneous and
Successive Processing
• This approach focuses upon the mechanics
by which information is processed, it is often
called an information-processing theory.
• Simultaneous processing of information is
characterized by the execution of several
different mental operations simultaneously.
• Successive processing of information is
needed for mental activities in which a
proper sequence of operations must be
followed.
Information-Processing Theories of
Intelligence
• Information-Processing conceptions of intelligence
propose models of how individuals mentally
represent and process information.
• Borkowki(1985) has put forward a comprehensive
theory that bears a loose analogy to the functioning
of a computer. The architectural system (hardware)
refers to biologically based properties necessary for
information processing, such as memory span and
speed of encoding/decoding information. The
architectural system is considered to be relatively
“hardwired” and impervious to change by the
environment.
Information-Processing Theories of
Intelligence
• In addition to the structural component of
intelligence, there are various functional
components (software). The executive system,
which refers to environmentally learned
components that steer problem solving, provides
overall guidance to the functional components.
• Elements of the executive system include the
knowledge base (retrieval of knowledge from longterm memory), schemes (rule of thinking), control
processes (rules and strategies such as selfchecking and rehearsal), and metacognition (selfawareness of one’s own thought process).
Intelligence as a biological
construct
• Figure 5.7
• Intelligence is somehow bound up in the
physiological properties of the brain, even
though we don’t yet understand the
precise biological characteristics that
account for intelligence.
• A PET scan can reveal “hot spots” at the
most active brain sites (where glucose is
being metabolized).
Gardner and the theory of multiple
intelligences
• Howard Gardner (1983, 1993) has proposed
a theory of multiple intelligences based
loosely on the study of brain-behavior
relationships.
• Gardner’s seven intelligences included
linguistic, logical-mathematical, spatial,
musical, bodily-kinesthetic, interpersonal, and
intrapersonal.
• Recently, Garner (1998) has added three
tentative candidates to his list of intelligences.
These are naturalistic, spiritual, and
existential intelligences.
Sternberg and the triarchic theory
of intelligence
• His theory emphasizes what he calls successful
intelligence or “the ability to adapt to, shape, and
select environments to accomplish one’s goals
and those of one’s society and culture.”
• Sternberg’s theory is called triarchic (ruled by
three) because it deals with three aspects of
intelligence: componential intelligence,
experiential intelligence, and contextual
intelligence.
Sternberg and the triarchic theory
of intelligence
• Componential (Analytical) Intelligence:
• Metacomponents or executive processes
(e.g., planning)
• Performance components (e.g., syllogistic
reasoning)
• Knowledge-acquisition components (e.g.,
ability to acquire vocabulary words)
Sternberg and the triarchic theory
of intelligence
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Experiential (Creative) Intelligence:
Ability to deal with novelty
Ability to automatize information processing
Contextual (Practical) Intelligence:
Adaptation to real-world environment
Selection of a suitable environment
Shaping of the environment