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What is the g-factor -- where to look for it and how to estimate it

1. General Overview

The g factor (also known as the general intelligence factor or general mental ability) is a construct developed in psycho-metric investigations of cognitive abilities. The g-factor is the overarching variable that is theorised to explain the positive correlations between a range of cognitive tasks. For instance, individuals' performance on one type of cognitive task (such as word puzzles) correlates with that person's performance on other kinds of cognitive tasks (such as math problems). Although each task involves using different skills, they both rely on a general intelligence factor.

Composite scores ("IQ scores") are based on many tests and are estimates of an individual's standing on the g-factor. Hereafter we will refer to the g-factor by IQ scores.


See the two diagrams below for the sorts of cognitive abilities which are all separate but all dependent on one's IQ:




Strength of correlation between each cognitive ability and IQ:


Note that processing speed has a relatively low but significant correlation with IQ.

It is also crucial to note that "Vocabulary" is its own subtest in IQ testing. Verbal IQ scores measure acquired knowledge, verbal reasoning, comprehension and attention to verbal nuances.

Understanding why vocabulary tests correlate so highly with IQ is integral to understanding what IQ means. Vocabulary, also known as Lexical Knowledge (understanding of words and their uses), is not memorising big, fancy words and using them inefficiently. In fact, being able to put together the right set of words to form a clear, comprehensible sentence is a better indication of lexical knowledge. Using near-synonyms interchangeably or using big words incorrectly only reflects a weak understanding of the word, low self-awareness and a less nuanced understanding of the world. 

For example, jealousy is often used as a substitute for envy. They are clearly related words but they aren't the same. In fact, in a sense, they tend to be experienced by people on opposite sides of a conflicted relationship. Envy is the painful, angry awareness that someone else enjoys some (probably undeserved) advantage that we desire. Jealousy is the angry, often vigilant, suspicion we may lose our beloved to another. Unaware of this distinction, it would be difficult to benefit from or even make sense of the wisdom of Rochefoucauld’s observation that “Jealousy is born with love, but does not die with it.”

Furthermore, it isn't obvious why a simple word like anger has so many synonyms and near-synonyms, some of which are a bit obscure (e.g., iracund, furibund, and zowerswopped!). Would it not be easier to communicate if there were just one word for every concept? It's thus pivotal to consider the question of why words are invented. At some point in the history of a language, people found it important to distinguish one category of experience from others and that this distinction merited a single word. Although most neologisms are outlived by their inventors, a few of them are so useful that they catch on and are used by enough people for enough time that they are considered “official words” and are then taken for granted as if they had always existed. Additionally, people adopt new words not to impress one another but because the word succinctly captures an idea or a distinction that would otherwise be difficult or tiresome to describe indirectly. Rather than saying, “Mary experienced that sensation where your face heats up, turns red, your blood pressure rises, and you feel a strong need desire to be aggressive, whether verbally or physically. You then tend to regret your actions in that state.” It is more efficient to say “Mary was livid with rage.” By convention, the use of the word livid signals that Mary is probably not thinking too clearly at the moment and that the next thing that Shelly says or does is probably going to be impulsive and possibly hurtful. 

Another simple example of lexical knowledge is distinguishing between violent and aggressive. Violence can be defined as the use of physical force with the intent to injure another person or destroy property, while aggression is generally defined as angry or violent feelings or behaviour. As such, one might miss a crucial finding in psychology that "Men women are about equally aggressive, but men are more violent". For example, women often commit far more "character assassinations" via gossip than men do.

A third and last example of good lexical knowledge that reflects IQ is the correct usage of quantitative words. For instance, by distinguishing between fewer and less, or between many and much--the words fewer and many are used for discrete quantities, whereas lesser and much are used for continuous quantities. This is directly related to the concept of continuous and discrete data in statistics.
Fewer and many are used for countable nouns such as chairs or people.
Less and much are used for non-countable nouns such as water and weight.


In The Nature of Vocabulary Acquisition, Robert J. Sternberg of Yale University said:

“… if one wants a quick and not-too-dirty measure of a person’s psychometrically measured intelligence, and thus has time to give just one brief test of it, vocabulary is [probably] the best predictor of overall score on a psychometric IQ test. (p. 90)”


Example of vocabulary test questions:

(Choose the best definition)




Other examples of tests of mental abilities, including tests such as:

  • analogies (e.g., lawyer is to client as doctor is to ___.)
  • classifications (e.g., Which word does not belong with the others? robin, sparrow, chicken, blue jay)
  • and series completions (e.g., What number comes next in the following series? 3, 6, 10, 15, 21,__). 

SEE MORE EXAMPLES IN THESE IQ TESTS: (sent to Kaj on Signal)

Crystallised and Fluid IQ

"Crystallised IQ" tests are often used alongside "fluid IQ" tests to estimate the g-factor.


Fluid intelligence is the ability to solve novel reasoning problems and is correlated with a number of important skills such as comprehension, problem-solving, and learning capacity. 


Crystallized intelligence, on the other hand, is regarded as the result, or application, of fluid intelligence. A useful analogy is to think of fluid intelligence as one's skillfulness/aptitude at writing computer programs (i.e., to create knowledge) and crystallised intelligence is the computer programs (i.e., the quality, depth, breadth and logical consistency of one's knowledge).


Going back to vocabulary, testing one's current understanding of words is a measure of crystallised intelligence. Giving people new words and testing how well they master these new words is a measure of fluid intelligence.


Another example of the application of fluid versus crystallised intelligence is often seen in mathematics. The "smart kid" in high school might easily solve the following problem without having learnt anything prior:

Mary is twice as old as her sister Rita who is eight years old. How old is Rita when Mary is thirty two years old?

Whereas the "studios-but-not-smart" kid can use the algebra they've learnt to solve the problem:

Mary's age = 2 * Rita's Age = 16

[...]

Thus, if M=32: R=32-8 = 24


However, the studious kid would struggle to reason through this problem without the assistance of formulas, pen and paper to keep track of the working. Thus pen-and-paper is used as a necessary cognitive aid for the studious types with lower cognitive capacities.



Real-World Achievements and IQ


Academic Achievement

"The predictive validity of g is most conspicuous in the domain of scholastic performance"

(i.e., IQ matters the most in one's academic performance). This is because g is closely linked to the ability to learn novel material and understand concepts and meanings.


However, even within the academic world, IQ matters for some subjects more than others. See the meta-analysis:

"Concerning the moderating effect of the subject domains, our analyses showed that the mean corrected correlation between scores of intelligence tests and school grades was highest in the Mathematics and Science subgroup (ρ = .50).

[...] 

Nevertheless, the mean corrected correlation between intelligence and school grades in Language (ρ = .42) and Social Sciences (ρ = .43) still is rather high, which indicates that cognitive ability is a substantial prerequisite for scholastic success in these subjects.  

[...]  

[There is also] a corrected mean correlation (ρ = .29) between [music\arts and IQ] which is in line with the literature suggesting a relationship between musicality and intelligence (e.g., Schellenberg, 2005) as well as creativity and intelligence (Batey & Furnham, 2006).  
[...] 
Lastly, there is no correlation found between IQ and performance in sports (physical activity) at school." 

[...] 

This finding appears to be rather straightforward since mathematics and science are subjects that deal with content that relies heavily on logic. As logical thinking is the most dominant competence assessed by intelligence tests, persons with higher tests scores should understand the content of these subject domains better and thus have better grades. A second explanation involves the reliability of school grades in these subjects. As answers in written exams in mathematics and science can easily be evaluated as right or wrong there is no margin of judgment [i.e., error] for the teachers when giving the grades. Thus, the reliability of grades in these school subjects should be higher than in the other school subjects where there is clearly a wider margin of judgment, which in turn influences the height of the correlation which can be achieved maximally.  

[...] 

[The above findings] and the finding that the mean corrected validities are lower [in subjects such as language and art] than in the Mathematics and Science subgroup can be explained by the fact that successful participation in [languages and arts] subjects requires learning content (e.g. historical data) by heart. Thus, motivational aspects play a more important role in these subjects than in the Mathematics and Science subgroup where it is predominantly important to understand the content. 

 

 So it is unsurprising to see results such as these:

(Note that SAT correlates strongly with IQ)


You might notice two things from that last table. Most obviously is that subjects that rely on understanding complex abstraction are at the top. But not self-evident is that subjects that rely on a wider range of skills have a stronger correlation with IQ than subjects that rely only on mathematics or only on writing. Both physics and philosophy necessitate understanding and reasoning through writing as well as mathematically/symbolically.

This makes sense when we think back to IQ being the overarching factor responsible for improved performance across domains. Even though mathematics relies heavily on IQ, mathematics also relies on natural talent for, and interest in, quantitative abstractions. To reduce the latter variable (the noise), IQ tests also measure proficiency in language. Hence, a mix of mathematics, reasoning and complex language in physics makes it a good estimator of IQ.


What is the general IQ of university students?

One dataset with the mean for bachelor's Master's and PhD/LLD/MD:

Bachelor’s degree 113 (81st percentile)

Master’s degree 117 (87th percentile)

PhD, LLD, MD 128 (97th percentile)

A different source of data with a box plot. First, learn how the box plot works:




The jump from Bachelor's to Master's is unsurprising, but the far bigger difference between a Master's and a PhD is surprising to most people. See why that is:

"The focus of master's degrees and doctorate degrees is different. A master's degree is designed to deepen career-oriented knowledge and skills. A doctorate degree is a heavily research-based degree, designed to develop critical research, analytical and writing skills in an effort to fill industry knowledge gaps."

 

"They’re very different. Getting a Master’s is not all that different from getting a Bachelor’s. The work is at a higher level, obviously, but it’s still mostly classwork. The thesis is like an extended term paper. If you do well as an undergrad, take the same study habits you develop there and apply them to your Master’s studies, and you’ll do fine." 

 

"Doing the Ph.D. was about learning to think differently. There’s often additional seminar coursework, but that’s about learning / honing critical thinking. If one is going to do solid research, one needs to know how to read the work in the field and to figure out what’s valuable and what’s not. Additionally, if one knows how to properly evaluate research, one is better prepared to design and evaluate their own work.

Finally, there’s the dissertation, which is about learning how to refine a research problem, how to design a course of action to test the hypothesis / hypotheses, and then evaluating the results.

Elements of all of that should be taught even in primary school, but being able to do that independently and well for large problems is what a PhD is training for. For everyone with whom I’ve discussed their PhD process, that required learning to think differently."


Occupational Achievement

See graphs for the mean IQ for different jobs.





Crucial Distinction Between IQ and Personality


In everyday language, words such as "intelligent" and "smart" are umbrella terms that often include personality. For instance, being honest, reliable, hard-working, sympathetic, industrious, orderly, sociable, etc. are all traits that have no relationship with IQ and are entirely encapsulated by personality measures. 

Though these examples seem obvious, the most common misconception between personality and IQ is that being intellectual, progressive, inquisitive and artistic are all part of intelligence. Although IQ correlates with these traits, and hence these sorts of traits can be used to estimate IQ, the correlation is low and hence they are relatively poor estimates when we compare them to aforementioned measures like vocabulary, reasoning, aptitude in sciences, et cetera. 

 Furthermore, some studies find correlations as high as 0.45 between the personality trait "openness to experience" and IQ. However, these studies have a poor methodology. See this for yourself by examining the questions they use for openness from the big five aspect scale:

Intellect

10-item scale (Alpha = .84)

+ High

Am quick to understand things.

Can handle a lot of information.

Readily solve complex problems.

Have a rich vocabulary.

Think quickly.

Formulate ideas clearly.

– Low

Have difficulty understanding abstract ideas.

Avoid philosophical discussions.

Avoid difficult reading material.

Learn things slowly.


















Low honesty-humility, especially modesty, predicted these L0L

Another flaw with people estimating their own IQ:
graph of low IQ people estimating they're actually average. Interestingly, being rational is more important for a good estimating than IQ alone!!


Clearly, these questions are basically asking respondents to estimate their IQ. Critics of these studies rightfully suggest that rather than using questions to estimate abilities, personality questionnaires should only measure values, interests and behavioural tendencies.

Once studies implement better research strategies, the correlation between IQ and personality drops significantly. In fact, fluid intelligence does not correlate with personality, but only crystallised intelligence. The explanation is that having a personality style for being open minded and inquisitive increases one's knowledge and hence their crystallised intelligence.
Love to reflect on things. Get deeply immersed in music.Need a creative outlet.


SYNTHESISE = IQ


Analytical, critical thinking, logical correlate with but are considered rationality. Can be increased. They are skills similar to how one becomes good at math.




So what are the differences between intelligence and rationality? Intelligence can be defined by IQ, which encompasses visuospatial puzzles, math problems, pattern recognition, vocabulary questions and visual searches. Rationality is the result of critical thinking, which often includes unbiased reflection, goal-oriented skills, flexible insight, and real-world interaction.



The Savanna-IQ Interaction Hypothesis--things to look for in personality!



Size of ideas and sentences to show how much their brain-computing-power can handle--working memory!


How to estimate:


Percentile i.e., smarter than how many in 1,000? Consider that it's a randomly-selected sample that might include very gifted people as well as people who struggled to even graduate high school.

Consider that someone with average/normal intelligence is at the 50th percentile, i.e. scores higher than about 500 in 1,000--half of all people. But also scores lower than about 500 in 1,000.



https://www.smartkidswithld.org/first-steps/evaluating-your-child/understanding-iq-test-scores/

https://en.wikipedia.org/wiki/IQ_classification

https://www.verywellmind.com/what-is-a-genius-iq-score-2795585

https://psychology.fandom.com/wiki/IQ_classification

IQ number (I guess 120 lol)


Normal distribution standing WITHOUT IQ or percentile labelling as not to bias them.