#### What is IQ?

IQ is an acronym for “Intelligence Quotient”. In the past, IQ used to be calculated as a person’s Mental Age (MA) divided by that person’s Chronological Age (CA). So a child with advanced mental processing capabilities (i.e. MA) for his/her age (i.e. CA) would be classified as having a high IQ. Although the calculation of IQ scores no longer use ‘quotients’, the term IQ is still widely used today. IQ attempts to summarise an individual’s intellectual abilities into a single score. However, there are many different types of intelligence, which is why IQ tests attempt to measure several important facets of human intelligence including (1) fluid intelligence and (2) crystallized intelligence, both of which can be further decomposed into several aspects including inter alia, verbal processing, visual processing, short term memory, long term memory and processing speed. All of these facets of intelligence are usually distilled into a single global score which is known as ‘G’ or ‘Spearman’s G’. Think of G as a global composite (or a weighted average) of your performance on individual aspects of the IQ test.

#### Normal IQ

It’s all relative. Normal IQ is ascertained relative to the average IQ within a given population. In most modern societies, the average IQ has been set to 100, and depending on the test taken, the standard deviation (or dispersion) or results can either be 15, 16 or 24 points. Statistical rules tell us that about 68% of the population will score within one standard deviation of the test average. So if the standard deviation of the test in question is 16 points, we know that 68% of the population will score between 84 and 116. But based on the distribution of IQs however (and assuming a standard deviation of 16), psychologist normaly agree that an IQ of between 90 and 109 to be average. About 47% of the population will score within this range. So if you have an IQ score which is lower than 90 but higher than 80, you will be considered to have a ‘low average’ IQ. If on the other hand you score between 110-119, you are considered to have a high average IQ. But normal IQ is all about understanding the average IQ within a given population or environment. If you are a member of Mensa, it would be normal for people around you to have a high IQ in the 132+ range (again assuming a 16 point standard deviation). So within the realms of a high IQ society such as Mensa, an IQ of 100 is not possible, let alone normal.

#### How accurate is IQ?

It is not perfect but it is good. There are various components to intelligence. The simplest (and well-supported) g factor analysis is the Cattel-Horn theory of intelligence which breaks down Spearman’s g into: (1) fluid intelligence -gf; and (2) crystallised intelligence -gc. It is important to remember that IQ does not measure things like aptitudes, creativity or general motivation. Rather, IQ (and in particular fluid intelligence) is almost analogous to raw processing power of the brain.

#### How accurate are IQ tests?

Any test or model cannot be 100% accurate in terms of measuring anything at all. For instance, when you go to your GP/Doctor for a general check-up, the doctor has limited time and will carry out a number of tests (e.g. heart rate, blood pressure, temperature and perhaps blood tests) to help establish whether you are healthy. Your doctor cannot afford to spend 48 hours with you to observe your physical condition and vitals across a variety of settings (nor would you want to be followed around by your doctor!).

Similarly, exam finals in school attempt to test your understanding of the key concepts that you will have learned throughout the year, rather than testing every single piece of knowledge that you have on the subject matter (which would not be possible in a 90 minute exam).

IQ tests similarly attempt to measure general intelligence in a short space of time. Some tests are better than others at measuring certain aspects of intelligence (e.g. Culture-fair testing are fairly good at measuring fluid intelligence). You should not know the content of an IQ test before you take it (and hence the concept of solving novel problems). So in theory, all test takers are faced with the same element of surprise and the test should therefore capture differential abilities of the test takers at solving novel problems (therefore measuring fluid intelligence).

#### Are IQ tests biased?

IQ tests as we know them today were born in the late 1890s and the modern-day relatives of those pioneering tests have come a long way in addressing obvious flaws in the testing procedures. The widespread used of several well-adapted IQ tests have yielded millions of test observations, which have been available for the statistical validation of IQ as a robust measure of general intelligence. Culture-fair tests do not require any spoken language (other than understanding simple instructions at the outset of the test) and therefore eliminate many possible cultural and gender biases.

#### High IQ

The mean (average) level of IQ for most developed nations is about 100 (the global mean is about 90 due to the inclusion of poor nations. which drag down the mean IQ – Google search: “IQ and the Wealth of Nations” for more on this topic ). In developed nations (and assuming a 16 point standard deviation), an IQ falling within the band of 90-109 is considered average. An IQ falling between 110-119 is considered a high average, whilst IQs > 120 are considered superior. About 3% of the population have an IQ of 130+, while Mensa accepts testers who are in the top 2% of the population (implying a score of 132 with 16 SD).

Although an IQ in the top 2% appears to be very select at first glance, the group is not that exclusive when you consider that roughly 20 million Chinese have this level of intellect (i.e. 2% of 1 Billion population). This Mensan Chinese would therefore be able to fill all the student seats at Harvard 952 times over.

#### Types of IQ tests

There are several types of IQ tests. In simple terms, the two most prevalent types of tests are (1) Crystallized / verbal intelligence tests and (2) fluid intelligence or performance IQ tests. Crystallized intelligence tests measure cognitive abilities that tend to improve with education levels achieved. For instance, verbal intelligence IQ tests will ask questions about the meaning of words, synonyms and antonyms, and general comprehension. The issue with these types of tests is that they will favour individuals with high levels of education.

Fluid intelligence tests, on the other hand, are more akin to measuring the raw processing power of the brain. If well constructed, these tests do not favour individuals with higher education and can thus be classified as being culturally-fair. Culture-fair tests (in particular Cattell IIIa or Raven’s Progressive Matrices) are widely supported in academic and professional circles. They are also widely accepted as cognitive ability tests for admission into several high IQ societies. Mensa accepts, inter alia, both the Cattell IIIa test and RPM, whereas the Tripe Nine Society (a society for the 99.9% percentile) accepts the Cattell Test as one the the allowable tests for admission.

#### Can you raise your IQ?

Is it much more difficult to raise your inteligence than it is to raise your IQ score. You will be able to raise your IQ score by practising the types of questions that may appear on these tests. Our culture fair test aims to replicate the level of difficulty and time pressure that you would face on a Mensa-administered Cattell IIIa test. This may help eliminate some of the surprise element that you would experience on the proctor-administered test. IQ-Brain.com tests are essential practice for the real life test.

## IQ Range

#### IQ Range

The terms IQ stands for ‘Intelligence Quotient’, and is derived through a series of tests to obtain an estimatolde of an individual’s cognitive ability (or as a rough proxy of an individual’s general intelligence – “G”).The IQ score was historically a quotient (i.e. a fraction) that was obtained by dividing an individual’s Mental Age (MA) by that person’s Chronological Age (CA) and multiplying by 100. The MA was derived from a series of mental tests and tasks. This was the predecessor method to calculating modern IQ test scales.

So for example: If a five year old girl (let’s call her Liz) was able to perform the mental tasks and tests as well as an average seven year old, then her Mental Age (MA) was calculated to be 7. Under the historical method, Liz’s IQ would have been (MA / CA) x 100 = (7 / 5) x 100 = 140. In other words, she would have been considered mentally advanced or “intelligent” for her age.

By the start of World War II, some IQ pioneers replaced the old ‘quotient’ method with Standard Scores, which were statistically much more robust and eliminated several problems under the quotient method. New IQ test scales were born.

As hundreds of thousands of tests had already been administered by this time, it emerged that across a population, IQ scores followed a normal distribution, and thus allowed for the natural upgrade to the use of standard scores. A normal distribution can be described using only two variables: the mean and the standard deviation. For simplicity, the mean was set to 100 (which is consistent with the predecessor idea of people’s MA=CA on average), and the standard deviation will depend on the IQ test administered. Note that some of the most influential IQ tests have a Standard Deviation of 15, 16 or 24, which means that an IQ score alone is meaningless unless accompanied by its standard deviation.

#### IQ Score Chart

The observation that IQ followed a normal distribution was revolutionary as it became possible to describe what the population distribution of IQs would looks like with the knowledge of only two variables: Mean (or average) and Standard Deviation (or SD).

IQ scoring charts follow a normal distribution which looks like this:

If the mean and standard deviation of a population are known (e.g. mean is = 100 and SD is = 16), then the following should also hold true:

• 68.3% of all test takers should score within 1 SD of the Mean (i.e. IQ between 84 and 116)
• 95.4% of all test takers should score within 2 SD of the mean (i.e. IQ between 68 and 132)
• 99.7% of all test takers should score between 3 SD of the mean (i.e. IQ between 52 and 148)

#### IQ score chart and classifications

As stated in the previous section, most people (about 68%) will score within 1 SD of the mean of 100. As you move away from the mean in either direction, there are fewer and fewer people who achieve very low or high scores.

The following tables shows what proportion of the population is expected to score within a particular IQ range.

IQ range (16 SD) Classification Population distribution
130+ Very Superior 2.6%
120-129 Superior 7.5%
110-119 High Average 16%
90-109 Average 47.2%
80-89 Low Average 16%
70-79 Well below average 7.5%
69 and below Lower Extreme 2.6%

#### IQ Score range

People very too often state their IQ score without specifying the standard deviation (SD) of the test they have taken. When standard scores were introduced between the end of WWI and the 1960s in the United States, it had been noted across millions of tests observations that the actual calculated standard deviation of test scores was 16. For this reason, localhost/iq-brain has adopted 16 as the standard deviation for its tests and to calculate IQ levels and charts. Now that you know about standard scores, if the mean (or average) of the test is set to 100, and the SD is 16, and combined with the assumption normality, we know that:

• 68.3% of all test takers should score within 1 SD of the Mean (i.e. IQ between 84 and 116)
• 95.4% of all test takers should score within 2 SD of the mean (i.e. IQ between 68 and 132)
• 99.7% of all test takers should score between 3 SD of the mean (i.e. IQ between 52 and 148)

However, many psychologists who were not so good in math began adopting 15 as the standard deviation because of the simplicity of the number. With mean=100 and SD=15, then it follows that:

• 68.3% of all test takers should score within 1 SD of the Mean (i.e. IQ between 85 and 115).
• 95.4% of all test takers should score within 2 SD of the mean (i.e. IQ between 70 and 130).
• 99.7% of all test takers should score between 3 SD of the mean (i.e. IQ between 55 and 145).

#### Nice round IQ numbers!

The following table will also illustrate the importance of SD. Mensa accepts a variety of IQ test for admission into their society. Of all the tests that are accepted (many of which have very different standard deviations), the only requirement for membership is that the applicant’s score be in the top 2% of the population (i.e. the 98th percentile).

Suppose that there are three applicants, each with a reported IQ score of 130 but achieved on different IQ tests. The following table shows the corresponding percentile for this score based on the standard deviation of each test.

Applicant Test Type IQ Score SD of test taken 100 – test score percentile Admit to Mensa?
Liz Weschler (WAIS-IV) 130 15 2.28% Yes (by a hair)
Pierre Culture-fair scale 130 16 3.07% No
Chen Cattell IIIb verbal 130 24 10.56% No

I hope the above table shows you what each of these applicants claiming that they have an IQ of 130 is meaningless without also mentioning the standard deviation!

#### What is the importance of IQ?

Although IQ is not a perfect measure of intelligence, it represents a good proxy of general intelligence. A higher IQ has been shown to positively correlate with several important, real-life variables including:

• Success in relationships including marriage
• Success is the workplace. IQ testing is often used as a recruitment tool in several countries including China, Spain and France. Several researchers have argued that IQ testing remains a better predictor of success at work than other assessment tools (especially unstructured interviews).
• Wealth and lifetime earnings. For instance, the IQ of self-made millionaires is estimated at around 115, while this increases to 120 for self-made billionaires

Similarly, IQ correlates negatively to the following variables:

• Living in poverty
• Having illegitimate children
• Being incarcerated
• Remaining unemployed for long stretches of time

REMEMBER that correlation does not imply causation . But merely represents an association, or how two variables move together.

Importantly, IQ testing does not measure practical intelligence or creativity (Sternberg, 1988), The bottom line is that a high IQ does not guarantee success, but it probably means that such individuals may need to work less hard than people with lower IQ to achieve the same result when intellectual output is required. High IQ individuals should not ‘waste’ this natural ability and should strive to apply it to whatever it is that they seek to do.

Conversely, people with lower IQs are not doomed to failure, but may on average need to work harder to be successful in their intellectual pursuits. It is not to say that having an IQ of 105 (i.e. normal intelligence) would make it impossible to become a professor in Chemistry and to publish in scholarly journals, although on the whole, lower IQ persons will probably face a steeper uphill journey than their higher IQ counterparts striving for the same goal.

#### What is a high IQ Society

A high IQ society is a private association of individuals who are joined in a society by way of having achieved a certain pre-determined IQ score on a recognized IQ test. There are several famous high IQ societies, and a multitude of little known IQ societies. The most famous high IQ society is Mensa, a society formed in Britain in 1946. The sole admission criteria to Mensa is an IQ score in the top 2% of the population. As explained above, the standard deviation of the IQ test in question is critical to making the determination of whether a particular IQ test scores qualifies for Mensa’s membership hurdle. The following high IQ societies have different thresholds for admission.

• Mensa: requires an IQ in the 98th percentile (top 2%) or an IQ score of 132
• EPL high IQ Society: requires an IQ in the 98th percentile (top 2%) or an IQ score of 132.
• The Deep Brain high IQ society: requires an IQ in the 97th percentile – and IQ score of 131 (16 SD), and applicants also require a Masters degree.
• The International High IQ Society: requires an IQ score in the 95th percentile (126 with 16 SD)
• Tensa: requires an IQ score of 121 (16 SD) which represents a score at the 90th percentile

High IQ societies normally accept IQ scores from a raft of recognized IQ tests including Weschler, Binet, Otis, Cattell and other Mensa-developed IQ tests such as the Wonderlic, the Matrix IQ tests, and the Figure Reasoning Test (FRT). Mensa also administers proctored IQ tests which means that the Mensa test can represent a wide variety of tests.