Spearman’s Two-factor Theory of Intelligence Explained



Charles Spearman's Theory of Intelligence

What is intelligence? if you ask this question to different people, everyone may give you a different answer, according to their perspectives. For some people, a person may be intelligent if he/she is quick at solving various problems or answering questions, while for others, it may be related to the success and achievements of the person. Defining the term ‘Intelligence’ has always been debatable among the fraternity of psychologists as different psychologists have different views on the term intelligence. Generally, intelligence is defined as the ability to use all the cognitive processes involving planning, attention, learning, and solving day-to-day problems. To define intelligence, a meeting was organized in 1921, consisting of 13 renowned psychologists specialized in the field of human intellectual abilities. The proceeding of this meeting was published in the “Journal of Educational Psychology” that revealed that every psychologist gave a different definition of intelligence. Some of the definitions of intelligence given by the different psychologists are given below,

According to Stern,

Intelligence, that is to say, reasoning, judgment, memory, and the power of abstraction”

According to Binet,

Intelligence is a general capacity of the individual consciously to adjust his thinking to new requirements”

According to Spearman,

Intelligence is the capacity of the organism to adjust itself to an increasingly complex environment”

Various intelligence theories have been proposed by different researchers, and Spearman’s two-factor theory of intelligence is also one of them. We will learn about this theory in this article.

Charles Edward Spearman

Charles Edward Spearman

Charles E. Spearman was a British psychologist, who was born on 10 September 1863 in London, England. He is the pioneer of a popular statistical method ‘factor analysis’ and is also known for his work on ‘Spearman’s rank correlation coefficient’ and his ‘two-factor theory of intelligence.’ He did his schooling at Royal Leamington Spa College, U.K. In 1883, he joined the British Army as an engineer officer, and while serving in the Royal Munster Fusiliers in 1893, he was promoted to the post of captain. He always had a great interest in philosophy, so he decided to pursue his academics in philosophy. Hence, after serving for 15 years, he resigned from the British Army in 1897. He wanted to study philosophy, but later, he realized that the advancement to the concepts of philosophy can only be done through psychology, which eventually motivated him to study psychology. In 1904, he published his paper on ‘factor analysis of intelligence’ and developed his two-factor theory of intelligence. He completed his PhD at Leipzig University, Germany, where he worked with the ‘Experimental Psychology’ founder ‘Wilhelm Wundt.’ Later, he worked as a professor in the University College, London, and he died on 17 September 1945.

Spearman’s Two-factor Theory of Intelligence

Charles Edward Spearman proposed his two-factor theory of intelligence in 1904. He was the first who introduced the concept of general intelligence called the ”g” factor. To develop his theory, he analyzed different mental aptitude and cognitive tests given by the participants. He noticed that the scores of the same participants were almost similar in every test. Those who had a good score in one aptitude test had also scored well in other aptitude tests, and those who performed badly in one test also performed similarly in other tests, which represents that there exists a factor that is common to all the intellectual and cognitive abilities of the person. Using the factor analysis technique, a technique through which various correlated variables are reduced to the lower number of factors, he examined the cognitive tests and concluded that factors related to intelligence can be measured and expressed numerically, its mathematical explanation is discussed further in this article. Spearman stated that various mental traits are not independent of each other, and there exists a common factor in all the cognitive abilities of the person, he called this common factor a general factor or ”g” factor. He proposed that intelligence consists of two factors, i.e., the ”g” factor (general ability) and the ”s” factor (specific ability), where the ”g” factor is involved in every general mental ability task of the person, and the ”s” factor is responsible for only the specific intellectual abilities of the person. It is to be noted that although the name of this theory is two-factor, there are more than just two factors as the s factor has various sub-factors, depending upon the number of specific abilities in each test. It means that there are two different ‘kinds of factors,’ i.e., a general factor and specific factors. The specific abilities of a person may be drawing interference, coding abilities, mathematical abilities, and so on.

Spearman's Two Factor Theory of Intelligence

According to Spearman, every individual is born with a different level of the ”g” factor, and the greater the ”g” factor, the greater are the chances that the person will succeed in various aspects of life, whereas the ”s” factor is not inborn, people acquire this factor through experiences and from their surrounding environment. The ”g” factor is shared with every other cognitive or intellectual activity of the person, but the ”s” factor is not shared with different intellectual activities, it’s specific to a particular activity. Let us understand it with an example, consider two tests, i.e., ‘numerical’ and ‘verbal,’ which have the specific factor ‘S1’ and ‘S2,’ respectively and common factor ”g,” and consider another two tests, ‘spatial’ and ‘mechanical,’ having specific factors ‘S3’ and ‘S4’ respectively and common factor ”g.” Here, ”g” represents the general ability, and ”s” represents the specific abilities of the person. This can be understood from the figure given below, which shows that the ”g” factor is common in all the specific factors. Spearman stated that the main purpose of the psychological tests is to measure the ”g” factor of the individuals because it is the common factor in all the cognitive abilities, and every individual’s intellectual abilities and performance differ based on their ”g” factor.

g factor and s factors of Spearman's Two Factor Theory of Intelligence

This figure shows that the “g” factor is common in all the specific factors, i.e., S1, S2, S3, and S4.

In 1927, Spearman published his book, “The Abilities of Man,” in which he called the ”g” factor as ‘mental energy,’ and elaborated the concepts of the ”g” and ”s” factors. He stated that the degrees of the ”g” factor or general intelligence vary in every individual, and the ”g” factor of the person can not be increased upon training, but ”s” factors can be improved. Mathematically, The total intelligence score of the person (I) is the sum of the ”g” factor and ”s” factors that an individual possesses, i.e.,

I = g+S1+S2+S3+S4+…

Where S1, S2, and S3 represent the different specific abilities of the person, say mechanical, numerical, vocabulary, or spatial abilities.

Spearman’s Two-factor theory of intelligence has a great contribution in the field of psychology as it introduced the concept of factor analyses, which is now widely used by many other researchers in their studies. An American Psychologist, Joy Paul Guilford, who is popularly known for his psychometric study of human intelligence, has stated that,

No single event in the history of mental testing has proved to be of such momentous importance as Spearman’s proposal of his famous two-factor theory, 1904.”

Mathematical Explanation of Spearman’s Theory

In Spearmans’ two-factor theory of intelligence, we represent the general factor by the letter ”g” and often term it as the “general intelligence,” but it is a mathematical value that is derived from the statistical process from the available quantitative data. It is difficult to arrive at the exact mathematical proof of Spearman’s two-factor theory, but it can be understood by the method of the ”correlation matrix” that he used in his theory. The correlation matrix is a table that consists of systematically arranged correlation coefficients of scores obtained by the person in various mental aptitude tests. The correlation matrix is given below.

Correlation Matrix

Correlation matrix showing different correlation coefficients values of scores obtained by the participant in different tests. Here, a, b, c, d, e represent different tests.

J.P Guilford (1953) showed that the proportionality between different variables can be calculated easily with the help of a correlation matrix, which makes it easy to calculate the tetrad difference between the subtests. Spearman used the ‘tetrad difference’ method to analyze intelligence. This method has been widely used in various psychological investigations; it is represented by the quantity F, and it is the difference between the cross products of two opposites coefficients of any four correlation coefficients in a square block. For example, consider four intellectual activities that are measured in the test, having correlation coefficients R13, R14, R23, R24 in the correlation matrix (nearby four in the correlation matrix), then the mathematical expression of tetrad equation would be,


Spearman observed that the cross multiplication of any two opposite correlation coefficients in the square block (nearby four correlation coefficients) in the correlation matrix was almost equal, i.e., the value of F approximately equals zero. Hence, for the above expression,


This implies, F(R13)(R24)-(R14)(R23)0

Let’s consider the following square block from the above correlation matrix.

Four nearby Correlation Coefficients (square block) from the Correlation Matrix

Four Nearby Correlation Coefficients (square block) from the above Correlation Matrix.

Here, the tetrad difference, i.e., F = (.40)(.28)- (.32)(.35) = 0.112 – 0.112 = 0

This explains that the F value (tetrad difference) approximately or equals zero in almost all the intellectual tests, i.e., almost similar performance of the individual in the various mental aptitude tests; this represents the ”g” factor. The variation in the tetrad difference or we can say that the measured intelligence variation in different tests is due to the specific ”s” factor of the individual. An individual shows different specific abilities in different tests. Hence, it proves that the “g” factor, i.e., the general factor is required in all the intellectual tests, and the higher the correlation between the two coefficients, the higher is the saturation of these coefficients with the “g” factor. Let us understand it with graphical representations of “g” and “s” factors done by J.P Guilford (shown in the figure below). Here, the factor “G” is represented by the central large circle, and the different specific factors are represented by the small circles around the central large circle. Each ellipse represents the different mental aptitude tests. It is observed from the below diagram that different ellipses overlap with the central large circle (G factor) to different extents. The large overlapping means that particular tests are largely loaded with the “G” factor than the other tests (tests that measure more “G” factor). The correlation between the two mental aptitude tests can also be analyzed through this graphical representation by looking at the extent of overlapping of the two tests with the central circle (G factor). Here, it is clearly seen that tests a and b are highly correlated with each other than tests a and c because a and b tests have similar loadings with the “G” as compared to the a and c tests, similarly with b and c.

Graphical Representation of Spearman's Two Factor Theory of Intelligence

Graphical representation of G and S factors of Spearman’s Two-Factor Theory of Intelligence

Spearman, along with his students, also explained that apart from the G factor, there also exists something common in some of the tests because it was observed that some tests show more correlation than that of the G factor, and this extra common factor is called group factor regarding which Guildford (1953) stated that,

Among the group factors that spearman and his associates came to recognize are verbal ability, numerical ability, and possible factors of mental speed, mechanical ability, attention, and imagination”

Educational Implications of Spearman’s Intelligence Theory

Spearman’s two-factor theory can be applied in the education sector to analyze the intellectual abilities of children. As we have discussed in this article, every person possesses different levels of “g” and “s” factors. The students need different degrees of “g” and “s” factors to perform well in different academic subjects. For example, the student’s performance in mathematics could be due to his general intelligence and his specific numerical abilities, i.e., g+s1. Similarly, in literature, it may be because of g+s2 factors, and in science, it may be because of g+s3, and so on. Since the “g” factor is common in all specific activities, the performance of the student in academics can be analyzed through their “g” factor. The “g” factor of the students can be checked through a variety of intelligence quotient tests that have a high “g” factor correlation. As we discussed earlier, the “g” factor is inborn and can’t be improved, but the performance of the students can be improved by developing their “s” factors. The schools should organize various academics and sports activities to improve the specific abilities of the students.

Educational Implications of Spearman's Intelligence Theory

Criticisms of Spearman’s Two Factor Intelligence Theory

A British-American psychologist named Raymond Cattell, who was also Spearman’s student, criticized the two-factor theory by arguing that the nature of intelligence could be better understood by the concept of “fluid intelligence” (Gf) and “crystallized intelligence” (Gc). The amount of knowledge, experiences, skills that are accumulated in an individual’s brain throughout his/her life is called fluid intelligence, and the ability to aptly understand and reason the available information or knowledge, and learning new skills, is called fluid intelligence. Cattell referred “g” factor more accurately as “Gc” (crystallized intelligence) and said that tests that incorporate only the “g” factor skip the other intelligence factors that are covered with the fluid intelligence.

Fluid Intelligence vs Crystallized Intelligence

Spearman’s two-factor theory is also criticized because Spearman had only focused on the psychometric approach, i.e., factor analysis technique to measure intelligence, and he did not focus on the cognition processes related to intelligence. The “g” factor of spearman’s theory does not include the various other activities like perception, emotional, and motor abilities.

Cheaters prosper GIF - Find on GIFER

The American Developmental Psychologist Howard Gardner stated that apart from academic intelligence, other domains such as body-kinesthetic, existential intelligence, and musical intelligence should also be considered as an important part of intelligence. There are several examples of people who were bad in academics, but they aced in other domains like music, sports, or dance. He argued that the “g” factor overemphasized academic intelligence, such as verbal and logical intelligence.

Howard Gardner's Theory of Multiple Intelligence

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