theories and individual tests of intelligence and achievement theories of intelligence and factor...

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.


• 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.


• 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.


• 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.


• 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

• 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 high-speed 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.


• 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, maximum-likelihood method, image factoring, and alpha factoring. Most of the methods yield highly similar results.


• 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.


• 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.


• 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.


• 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.”


• 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


• 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).


• 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 second-order factors.


• 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 second-order 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.


• 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.)


• 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 two-factor 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.


• 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).


• Verbal comprehension

• Word fluency

• Number

• Space

• Associative memory

• Perceptual speed

• Inductive reasoning


• 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


• 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 well-established abilities. The narrow abilities at stratum I include approximately 70 abilities.

Definitions of CHC Broad Ability Factors

• 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

• “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-Of-Intellect (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-Of-Intellect (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 long-term memory), schemes (rule of thinking), control processes (rules and strategies such as self-checking and rehearsal), and metacognition (self-awareness 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.


• 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)


• 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

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