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**Read this article to learn about the theories of intelligence. **

**Theory of Intelligence # 1. Spearman’s Two Factor Theory of Intelligence**:

Spearman gave his two factor theory of intelligence in 1904. **“No single event in the history of mental testing has proved to be such momentous importance as his famous two-factor theory”**—(Guilford-Psycho-metric methods).

According to Spearman the mental traits are not independent; there is a common element in all our cognitive abilities. This is the basis of his famous two-factor theory of intelligence—the theory that every different intellectual activity involves a general factor, which it shares with all other intellectual activities, and a specific factor, which it shares with none.

Spearman declines to designate this general factor as general intelligence, which seems to him to be **“a word with so many meanings that finally it has none.”** He prefers to denote it by a letter “g”, and the specific factor by “s”. It is true that Spearman’s ‘g’ is Often identified with what we commonly term “general intelligence”, but it is well to remember that it is primarily a mathematical quantity derived by mathematical processes from measured data.

Mathematically, Spearman’s theory, in brief, is that every individual measurement of every intellectual ability may be resolved into two factors, one of which is a “general factor” (g) common to all the abilities measured, and the others “specific factor” (s) peculiar to each particular ability. This statement may be translated into mathematical form by representing the score (S) of an individual on a given mental test by the simple equation

S = a_{1}g + a_{2}S,

where the letters “a_{1}” and “a_{2}” represent the “weights” or “loads” of the two factors ‘g’ and ‘s’, respectively.

**Theory of Intelligence # ****2. Mathematical Basis of Spearman’s Theory****: **

The complete mathematical proof of Spearman’s theory is rather intricate and difficult to follow, but the main line of argument may be readily understood from a simple example. Let us begin, as Spearman did, by correlating the results of a number of tests and arranging the co-efficient or correlation systematically in what is known as a ‘correlation-matrix’.

**Let us take 5 tests- a, b, c, d, e, with the titles given below and arrange their “inter-correlations” in a matrix form: **

**We may also express this in an equivalent algebraic form:**

The start of Spearman’s enquiry was “a curious observation” that the cross-products of any square block of four coefficients were approximately equal. For example, from the set of coefficients

we get by cross-multiplication (.48 x .35) = (.40 x .42) or (.48 x .35) – (.40 x.42) =0;

or from another set, (.56 x .30) – (.40 x .42) = 0. A square block of four coefficients Spearman termed a tetrad and the equation expressing the equality of the cross-products the tetrad equation.

**In algebraic terms the first of the above tetrad equations would read: **

t_{ab}._{cd} = r_{ac}.r_{bd }– r_{ad}.r_{bc} = 0; and the second

t_{ab}._{cd} = r_{ab}.r_{cd }– r_{ad}.r_{bc} = 0

The rest of the argument consisted in demonstrating that if intellectual abilities are due to the presence of two factors, one ‘general’ and the other ‘specific’—in other words if the equation S = a_{1}g + a_{2}s holds good, then the tetrad equation r_{ab}.r_{cd }– r_{ad}.r_{bc} = 0 must be satisfied; and, conversely, if the tetrad equation is satisfied for any four abilities a, b, c, d, then the equation S = a_{1}g + a_{2}s must be true, and, consequently, the said abilities are divisible into two factors, one of which is a **“general”** factor common to four abilities.

Spearman and Holzinger later on supplied a method to find out if any departure from the zero requirement of the tetrad equation is due to a “real” difference or to “errors of sampling”. The two-factor theory now rests on a firm mathematical basis. The amount of correlation between any two tests is determined by the extent to which the two tests are loaded with G. Another chart of inter-correlation of 6 tests is given below, arranged in the hierarchical order.

**The chart shows the weightages: **

More clearly, in this table the variables have been arranged in order of the rank of the sums. In every column the coefficients are graded from high to low. This is called by Spearman the hierarchical order. The tests A and B have a relatively higher correlation, that is, they have much in common in G, whereas tests A and C have little correlation, because they have small loadings with G.

Spearman and his followers later admitted the existence of some group factors like **“verbal ability, numerical ability, and possible factor of mental speed, mechanical ability, attention and imagination”. “Tests G and H have a higher correlation than that attributable to G alone. Such an additional common factor as in tests G and H became known as a group factor”. **

Spearman’s two factor theory was criticised vehemently by Thorndike. E. L. Thorndike devised a test—the C A V D (Completion, Arithmetic, Vocabulary, and Understanding of directions and discourse), as a basis of the theory that intelligence is a composite of many different abilities interconnecting in the brain. Thorndike proposed three kinds of intelligence— Social, Concrete and Abstract. This was probably the first multifactor theory of intelligence, though not based on the results of a factor analysis of ability tests.

**Theory of Intelligence # ****3. Sampling Theory of Godfrey Thomson**:

In Britain, Spearman’s most active critic has been Godfrey Thomson. He claims that the two factor theory is not the only possible explanation of the facts. According to him these facts may be explained on the hypothesis that there are multiple or group factors in intellectual abilities, each of which is common to a limited number of different intellectual ability, and is, therefore, less restricted in its range than any of Spearman’s specific factors, and yet not of universal range as is his G factor.

G. H. Thomson’s theory is known as the sampling theory. According to the sampling theory, every test samples a certain range of the elementary human abilities; some with a wide range, some with a narrow range. He believes in a “g” factor or general ability, but it is not a basic entity. It is a constant combination of the ability elements.

Similarly, the group factors are combinations, more or less stable, of more limited collections of elements, specific factors are composed of elements that restrict their appearance to single tests— (G. H. Thomson—The Factorial Analysis of Human Ability).

**Theory of Intelligence # ****4. Multifactor Theory**:

The multifactor theory holds that the performance on a certain test depends on one or more common factors, each weighted according to its significance for success in the task.

**The theory is based on various methods of factor analysis: **

“Though Charles Spearman has been credited with being the father of factor analysis, he and his followers did not want to admit importance of group factors. They played up the role of ‘G’ factor. This was especially true of Cyril Burt, Philip Vernon, and R. B. Cattell.”

“It was Thurstone who popularized the multifactor theory and methods in psychology. Geometrically, the multiple factor model is a set of dimensions or vectors extending from the same origin, each vector representing a common factor.”

**“The nearer to a certain factor vector a test vector lies, the greater is the involvement of the test with that factor, the greater is its “loading” on that factor. A factor loading is also the correlation between a test (an empirical variable) and the factor (a purely ideal variable).” **

In short, he applied the centroid method of factorization and oblique rotation of correlations among many different cognitive measures. Thurstone deduced seven primary abilities. His deduction was based on an analysis of Aptitude Research Project experiences. The abilities or factors found are **“Space, perceptual speed, numerical facility, verbal comprehension, rote memory, induction, word fluency, deduction and general reasoning.”**

**Theory of Intelligence # ****5. Hierarchical Theories**:

British psychologists like Cyril Burt (1949) and Vernon (1960) gave an alternative scheme for the organisation of factors. At the top of the hierarchy, Vernon places that ‘G’ factor or the general cognitive factor. At the next level he places two broad group factors, corresponding to verbal-educational (v: ed) and practical-mechanical (k: m.) aptitudes. These major factors may be further sub-divided.

The verbal educational factor may be sub-divided into verbal and numerical sub-factors, and the practical mechanical factor into mechanical information, spatial, and psychomotor ability. At the lowest level of the hierarchy are the special factors. “Such a hierarchical structure thus resembles an inverted genealogical tree, with ‘g’ at the top, ’s’ factors at the bottom, and progressively narrower group factors in between.”

**The graphic representation of Spearman’s two-factor theory (A), of the multifactor theory (B), and of the hierarchical theory (C), showing correlated tests is given below: **

Vernon’s theory is a compromise formula, between Spearman’s two factors and Thurstone’s multifactor theory. It retains G factor, and relegates Thurstone’s and Guilford’s structure of intellect to sub-ordinate level.

**Theory of Intelligence # ****6. R. B. Cattell’s Theory of Fluid and Crystallized Intelligence**:

According to R.B. Cattell, general intelligence is composed of two factors— fluid intelligence (G) and crystallized intelligence (Gc). This is similar to Vernon’s distinction of intelligence A which is product of heredity and intelligence B, which is due to environment. Fluid intelligence, like ‘intelligence A’, depends more on heredity and crystallized ability on environment.

Both types of ability are concerned with the ability to perceive relationships, fluid-ability is general to many fields, and crystallized intelligence is specific to certain fields, like school learning. Fluid intelligence is used more in tasks requiring adaptation to new situations, while crystallized intelligence is used to tasks where habits have become fixed. He applied oblique rotations in his factor analysis. These two factors—fluid and crystallized intelligence—are distinct but correlated.

Jean Piaget has given a theory of intelligence (cognitive development), not based on factor analysis. He believes that cognitive development takes place in a series of four stages – Sensory motor stage (up to 2 years) when the child learns to exercise simple reflexes and coordinate various perceptions, leading to general operational stage (from 11 to 15 years). During adolescence the child can perform more abstract operation. Intelligence increases up to the date of 15 years, it is achievement that increases after 15 years, intelligence, according to him, is the ability to solve new problems.