Introduction

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:

Correlation strength between each cognitive ability and IQ:

Note how Vocabulary is its own component in IQ testing. The vocabulary IQ subtests measure acquired knowledge of word meanings through verbal reasoning, comprehension, and understanding of verbal nuances. All of these skills rely highly on IQ, and although these abilities can be measured by other methods of knowledge acquisition, vocabulary is something most people are exposed to at similar degrees. As such, vocabulary IQ tests only apply to people who spent their life speaking and learning the language and had a conventional schooling career.

Vocabulary is also known as Lexical Knowledge (understanding of words and their uses), and it 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 lucid sentence is a better indication of lexical knowledge than obfuscated and overly-complicated writing. Additionally, using near-synonyms interchangeably or using big words incorrectly only reflects a weak understanding of the word 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.”

It's not self-evident 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 new words 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 a set of symptoms where your face heats up and turns red, your blood pressure noticeably rises, and you feel a strong 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 Mary says or does is probably going to be impulsive and possibly hurtful.

Another example of lexical knowledge is using aggression and violence separately appropriately. Aggression refers to behaviour motivated by the intent to cause harm to another person who wishes to avoid that harm, whereas violence is an extreme subtype of aggression, a physical behaviour with the intent to kill or permanently injure another person. Hence, all violence is aggressive, but not all aggression is violent. Making this distinction would be crucial to, for instance, understand the finding that “Men and women are equally aggressive, but men are more violent.”

Besides the two examples above, another way to look for proper lexical knowledge in one's speech is the proper usage of quantitative words. For instance, words such as “fewer” and “many” only refer to discrete quantities—what can be counted. In contrast, words such as “less” and “much” refer to continuous quantities—what cannot be counted. For example, “less people” is incorrect, but “fewer people” is correct; “there are so much bottles” is incorrect, but “there are so many bottles” is correct.

Hence, 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)”

Here are some examples of questions in vocabulary tests:

However, vocabulary is far from the only thing that should be measured to estimate an IQ score; it's just something that we can easily look for in others.

Here are other examples of IQ test questions so you can get a better understanding of what IQ measures (answers provided at the end of the questions):

1. Which one of the five is least like the other four?

Dog
Mouse
Lion
Snake
Elephant

2. Which number should come next in the series 1 - 1 - 2 - 3 - 5 - 8 - 13 ?

3. John needs 13 bottles of water from the store. John can only carry 3 at a time. What's the minimum number of trips John needs to make to the store?

3
4
4 1/2
5
6

4. If all Bloops are Razzies and all Razzies are Lazzies, all Bloops are definitely Lazzies.

True
False

5. Choose the word most similar to "Trustworthy":

Resolute
Tenacity
Relevant
Insolent
Reliable

6. This sequence of four words, "triangle, glove, clock, bicycle," corresponds to this sequence of numbers "3, 5, 12, 2"

True
False

7. If Richard looks into a mirror and touches his left ear with his right hand, Richard's image seems to touch its right ear with its left hand.

True
False

8. Sixteen hours are to one day as twenty days are to June's length.

True
False

9. In the English alphabet, there are exactly four letters between the letter "M" and the letter "G."

True
False

The issue with the above questions is that they rely on the test-taker to be proficient in the English language and to have a typical Western education. As such, we say it is not culturally fair. A culture fair IQ test is Raven's Progressive Matrices. For example:

10.

11.

12.

Answers

Snake
21
5
True
Reliable
True
True
True
False
Option G
Option A
Option D

Crystallised and Fluid Intelligence

IQ tests for both crystallised and fluid intelligence. In the example questions above, the first set of questions (that aren't culturally fair) rely on some learnt content and hence rely on some crystallised intelligence. However, the second set of questions (the culturally-fair ones), rely entirely on fluid intelligence.

Fluid intelligence is the ability to solve novel problems where crystallised intelligence is regarded as the result, or application, of fluid intelligence. A useful analogy is to think of fluid intelligence as one's adeptness or natural aptitude at writing computer programs (i.e., the capacity to create knowledge) and crystallised intelligence is the computer programs (i.e., the quality of one's knowledge).

So, you may have realised that the vocabulary tests we talked about earlier are tests of crystallised intelligence. However, if we were to give people new words and test how well they master these new words, that would measure fluid intelligence.

Another example of the application of fluid versus crystallised intelligence is often seen in mathematics. Think of that smart person in high school who can 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 studious and conscientious but unintelligent person 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

Additionally, the second person 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.

IQ and Real-World Achievements

Academic Achievement

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

-Some pretentious Wikipedia editor.

In other words, the area that IQ matters the most is in academic performance (unsurprisingly). However, even within the academic world, IQ matters for some subjects more than others. First try to think of the different subjects taught in high school and university and try to rank-order them by how much they rely on IQ, and then see how your guesses compare to the statistics below.

See the summary points from a published 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 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: IQ correlates very strongly with SAT scores)

You might have noticed two things from that last table. First, subjects that rely on understanding complex abstractions are at the top. Second, subjects that rely on a wider range of skills have a stronger correlation with IQ. For instance, performance in physics correlates more strongly with IQ than performance in mathematics because physics relies not only on mathematics but also on understanding the scientific method and scientific writing.

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 confounding 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.

Average IQ Across Levels of Education

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. But first, learn how a box plot works:

And now for the data:

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 Achivement

Try to guess the average IQ for different occupations. Graphs below.

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:

Positive correlation:

Am quick to understand things.
Can handle a lot of information.
Readily solve complex problems.
Have a rich vocabulary.
Think quickly.
Formulate ideas clearly.

Negative correlation:

Have difficulty understanding abstract ideas.
Avoid philosophical discussions.
Avoid difficult reading material.
Learn things slowly.

In fact, studies have shown that one's perceived intelligence correlate about as much with IQ as they do with narcissistic traits such as boastfulness, grandiosity and low modesty.

Better questions to measure personality: Love to reflect on things. Get deeply immersed in music. Need a creative outlet.

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!!

Rationality/logical reasoning vs IQ.

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

Synthesising information is an important and complex skill required in academic

writing. It involves combining ideas from a range of sources in order to group

and present ideas, themes and issues in a logical manner

Unlike summarising and paraphrasing, which use the ideas of one author at a

time, synthesising combines ideas from more than one source and integrates

them into your argument.

Synthesising allows you to:

focus on the issues and ideas rather than authors

combine information from multiple sources to develop and strengthen your

arguments

demonstrate that you’ve read widely on the topic

use and cite multiple sources.

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.