SIGMA SOCIETY

Other authors gave other guesses about what they thought the classifications should be like.

 

This way of promoting stratifications and classifications, based on personal hunches, is pseudoscientific, but it is widely used and accepted in psychology, which represents a serious error, from a conceptual point of view.

  

The appropriate way would be to try to identify common characteristics present in people in each IQ range and discriminatory in people in different ranges, and from there establish appropriate cutoff points to delimit these profiles. This should primarily be done using statistical tools such as Wavelets, Cluster Analysis, Factor Analysis or something equivalent.

 

When classifications are carried out properly, the divisions are not positioned 10 out of 10 or 20 out of 20, but rather at variable intervals and with numbers that are rarely round. The Sigma Test, for example, adopts classifications along this line, using Factor Analysis with Ward links and Bhattacharyya's metric for distances between factors, resulting in much more well-founded stratifications with scientific value.

 

Although the classifications listed in the tables above are neither accurate nor conceptually valid, they are widely accepted and used, so when we refer to the “above average” IQ range we are maintaining that standard for now. But in the report we present the correct classification, and we also add, as a curiosity, the other incorrect classifications adopted since 1916.

 

In addition to adopting an incorrect grading system, traditional IQ tests have many other flaws. It would not be possible here to enumerate and comment on all of them; this is done in the “Golden Book of Intelligence”; Here we will mention just some of the most serious problems, among which evaluations with astronomical errors stand out, which can reach more than 100 points.

 

There are many cases of people receiving blatantly incorrect assessments on traditional tests, both up and down, and this can have a number of negative effects. Most of these errors are never discovered, because the person simply “swallows” and believes the assessment, trusting in the psychologist's authority. But there are a few cases that end up being identified and reported, because the error is so scandalous that it is impossible to turn a blind eye. I will cite some examples:

 

There is a competition in the USA that consists of solving difficult Mathematics and Logic problems, similar to the Mathematics Olympics. The questions in this competition cannot be solved simply by applying formulas that students are trained in. It is necessary to understand subtle and complex aspects and invent original methods to solve them. The name of this contest is “Putnam”.

 

Putnam Prize winner and Nobel Prize winner in Physics, Richard Feynman, scored 123 on an IQ test. To get an idea of what this represents, suffice it to say that the US population in Feynman's time was about 200,000,000, and being a Putnam champion put you at least at the 1 in 1,000,000 level and probably above that. However, an IQ of 123 corresponds to the rarity level of 1 in 13, that is, in a classroom with 100 students, around 7 or 8 have an IQ above 123. As if the Putnam Prize were not enough, Feynman also won the Nobel laureate in Physics, he was one of the youngest participants in the Manhattan project and made several important contributions to Physics and Science in general, even deserving more than a Nobel Prize. His intellectual level was safely between 1 in 30,000,000 and 1 in 300,000,000, but his IQ test score said it was at the 1 in 13 level. Feynman's correct IQ is in the range of 210 to 230.

 

Another case of bizarre assessment in an IQ test involves world chess champion Bobby Fischer, who also had a score of 123. Some sources incorrectly quote the value as 187, others quote 184 or 181, but the official documents from the school where Fischer studied in Brooklyn show a score of 123. Ironically, although this 187 value was “invented” by some journalist, it is closer to the true value than the “official” IQ measured by a psychologist.

 

World Chess Champion Garry Kasparov also had 123 on Raven and 135 on Eysenck, although his true Kasparov IQ is between 160 and 180. Some sources also give Kasparov 192, but this is the result of converting his FIDE rating to IQ by Bill McGaugh's formula, which presents several conceptual and quantitative problems, but still generates a score closer to correct than the results he obtained in traditional IQ tests.

 

The most absurd case is probably that of Henry Poincaré, one of the greatest mathematicians of all time, one of the greatest scientists and one of the greatest intellectuals in history, who obtained an IQ of 35, however his correct IQ is between 220 and 240.

 

At the opposite extreme, there are people who achieve scores of 200, 300 and even 400, but whose true IQ is between 150 and 170. Adragon de Mello is an example, who obtained a score of 400 in childhood, but upon reaching adulthood, he did not achieve any of the prophecies about his expected genius, revealing himself to be a very intelligent person, but at a level of 160, far from the astronomical 400.

 

There were several other children in a similar situation, such as Ainan Cawley, Michael Kearney, Edith Stern, Marnen Laibow-Koser, Sho Yano, Michael Grost, Nadia Camukova and many others, who were quick and precocious in performing simple and easy tasks, appropriate to correctly measure up to 130 IQ, but due to errors in the standardization of tests or extrapolation made by examiners, they were evaluated at more than 200, some reaching more than 300, when in fact the correct IQs of these people are close to 150, which is indeed high, but 150 corresponds to a 1 in 1,000 rarity level, while 200 is at a theoretical 1 in 5,000,000,000 level (when correctly adjusting the IQs to a ratio scale and considering the true distribution, which is not Gaussian, so the score 200 corresponds to 1 in 5,000,000).

 

Both these upwardly skewed and downward skewed scores can cause a number of problems. Einstein, as a child, was assessed as retarded, even though he was one of the greatest geniuses in history. Thomas Edison was also under-evaluated, as was the aforementioned Poincaré and many others.

 

In cases like those of Feynman, Einstein, Poincaré and other great scientists, history has taken charge of reviewing the grotesque errors in diagnoses, but how many are the cases of brilliant people who could have changed history, who never even managed to become and become known because some incorrect assessment pushed them down?

 

At the opposite extreme, many problems also occur, that is, when the evaluation is distorted upwards. Justin Chapman was a child prodigy who gained great attention in the media in the late 1990s, for having almost 300 IQ at the age of 4. More precisely, the score given to him by psychologists and the media was 298, but the correct score was around 140 to 150. This led to the creation of a series of problems of excessive demands, exposure, bullying, offenses, etc., to the point that at the age of 6 he even attempted suicide. Imagine a 6-year-old child wanting to kill himself because he cannot bear the hell that his life has become due to the consequences of an incorrect psychological assessment.

 

Another much more famous case is that of William James Sidis, who had his IQ rated between 250 and 300, and almost all tabloids on the subject tend to cite Sidis as the most intelligent person who ever lived, when in fact his true IQ was around from 170 to 190. Sidis also faced excessive charges and several other problems, until he could no longer bear the pressure, when he completed his doctorate at the age of 17 with distinction Cum Laude, but his parents expected him to obtain a Summa Cum Laude, and instead of congratulating him, they reprimanded him harshly. It was the last straw, and from then on Sidis decided to abandon his academic career to live wandering around the world in sub-professional activities and collecting license plates.

 

It is important to highlight that the problem is not the high IQ, but the distortion of the result. Gauss, for example, was correctly evaluated and fulfilled expectations of becoming one of the greatest geniuses in history. The same happened with Pascal, John von Neumann, Évariste Galois and others. There were no IQ tests at the time most of them lived, but they were diagnosed as geniuses since childhood, and confirmed this genius in adulthood, with important discoveries that expanded the horizons of knowledge. This is because they were not diagnosed based on IQ tests that use primary questions, but rather based on their notable achievements, which have already proven impressive from the first years of life, achievements that also involve solving problems in logic, mathematics and science, but with a level of difficulty and complexity much greater than the ceiling of IQ tests, problems similar to those used in Sigma tests.

 

These assessment errors happen because traditional IQ tests are designed to assess the intellectual level of people between -2 and +2 standard deviations from the mean, this includes about 95.5% of the population with an IQ between 68 and 132. When a person is in the 2.3% above 132 or in the 2.3% below 68, the test results do not reflect their real ability as well, and the further away the person's actual IQ is from this range, the higher the potential error between the measured score and the true IQ.

 

Traditional tests used in clinics do not include questions with an appropriate level of difficulty nor do they meet the necessary requirements for construct validity outside this range. This topic is analyzed in a didactic way in my interview with In-Sight Journal.

 

This criticism applies to the most respected tests, such as WAIS, Stanford-Binet, Raven, DAT, Cattell, etc. When it comes to other tests, whose standardization is not as careful and construct validation is not as rigorous, the flaws are much more serious and more numerous, including containing ambiguous questions, incorrect templates, distortions in standards, and the lack of an acceptable answer in some questions etc.

 

In fact, even established tests such as WAIS also present several of these problems, but others present even more serious and more frequent problems. See my analysis of WAIS errors in the “Golden Book of Intelligence.”

 

Despite these flaws, the WAIS is still a very reasonable instrument for measuring intellectual levels between 70 and 130. Although the WAIS produces nominal scores up to 160 or 155, depending on the year of the standard, scores above 130 lack validity. Many psychologists, however, do not have a clear understanding of this limitation and end up issuing reports with unrealistic scores. Many of the children mentioned above were victims of this type of incorrect diagnosis. These psychologists do this not out of malice, but out of ignorance.

 

Lewis Terman, for example, in his study of 1528 gifted children, faced several prediction and interpretation problems due to flaws in IQ tests.

 

Terman examined tens of thousands of children and selected the 1528 who scored above 135, with some reaching more than 200, and followed the evolution of these children throughout their lives for many decades, to see if they would become geniuses in adulthood. .

 

The result confirmed some expectations, and indeed children with an IQ above 135 had an intellectual production well above that of the general population, but none of them, nor those with an IQ above 180 and above 200, turned out to be geniuses nor achieved any achievement. important intellectual award. Furthermore, to Terman's shame, among the children he did not select because they did not have sufficient IQ, that is, with an IQ below 135 in his tests, there were 2 Nobel winners: William Shockley, who scored 125 and won the Nobel Prize in Physics in 1956, and Luis Alvarez, who scored 124 and won the Nobel Prize in Physics in 1968.

 

People who do not know psychometrics attribute this result to flaws in IQ tests, when in fact it is a limitation of the tests used by Terman and a limitation in the judgment capacity of Terman and other psychologists, who do not realize when the score is absurd, incompatible with the observed facts, and they act mechanically, placing the indicated label on the test, without critically evaluating whether that score is plausible.

 

If a person puts a normal-sized whole chicken on a scale, and the weight indicated is 144g, the person needs to have some common sense to know that a whole chicken cannot weigh 144g and something is wrong. If she cannot identify and correct the weighing error, it is better to estimate the weight with common sense than to put a label on the chicken saying it weighs 144 g.

 

It is also important to highlight that in the case of the study carried out by Terman, there was no “problem” in the IQ tests used, but just a limitation. There wasn't a problem because the tests actually measured correctly within a certain range, between 70 and 120 or so, and the tests selected people who were much smarter than average, who were much more successful academically, professionally, financially and socially. . Therefore, in general, the tests were correct in separating the group above 135 and below 135. But they failed precisely in the 2 most notable cases, of people with IQs well above 135, who were immensely underassessed, and the examiner was not able to realize this. IQ tests work well for 95% of the population, but the problem is that precisely in the 2% with the highest IQ, where the test fails, are where the geniuses who can change the world and who would need to be correctly diagnosed.

 

This makes it very clear that yes, IQ tests work very well, but they only work up to a certain point, for IQs below 130 and sometimes below 120. However, there are other tests, more difficult and with more adequate construct validity, to evaluate correctly at the highest levels.

 

In companies like IBM, Microsoft, Google, Facebook, they need people with IQs well above 130, reaching over 150, so they created their own tests to measure correctly at these levels. The tests used by these companies can measure correctly from 130 to around 160, but they also begin to fail at levels above 165.

 

The Sigma Test Extended easily fulfills the function of correctly measuring IQ at a level above 150, reaching more than 220. It also applies to IQs below 150, covering the range from 110 to 220, with the optimal range of accuracy between 130 and 190. The Sigma Test was used to select the team that worked on the development of the Cantor platform (named after Georg Cator), consisting of 6 international Olympic medalists in Mathematics, Physics and Computer Science, and has been accepted as a criterion for admission to some of the world's most exclusive high-IQ societies.

 

This “optimal range of accuracy” is determined by the number of questions whose difficulty falls within the respective level. The more questions appropriate for a given level, the greater the accuracy of the scores at that level.

 

In traditional IQ tests, there are generally less than 10% of questions to discriminate at levels above 125 and 0 questions with an appropriate level of difficulty to correctly measure above 130, however these tests generate scores that can reach 150, 160 and even even above 190, but these scores do not reflect real intellectual capacity, but rather the speed to resolve primary issues. These are numbers without any conceptual value, although they have some statistical meaning, which indicates the rarity of people capable of solving elementary questions with a certain level of speed, and this is not the same as having intelligence at the equivalent level of rarity.

 

The Raven Standard Progressive Matrices has 60 questions. If a person gets 60 right, their IQ is 133. If they get 59 right, their IQ is 129. If they get 58 right, their IQ is 125. In other words, there are only 3 questions in a test with 60 to discriminate between levels above 125. This makes the uncertainty in scores above 125 very large, because it is as if it were a test based on just 3 useful questions to discriminate close to the ceiling (this analysis is actually not that simple. For more details, see our books and articles). As if these flaws were not enough, on top of that they are multiple choice questions, introducing further uncertainty into the measurement, due to the luck factor.

 

Despite all these imperfections, the Raven is still a good instrument for assessing intellectual levels between 70 and 110, reaching 115 or slightly above, but it should not be used to measure IQs above 120. However, in practice, it remains being used for IQs up to the ceiling, 133, or 137 in some older standards. Remembering that the main problem in Raven is not the ceiling, but the small number of questions designed to discriminate at levels close to the ceiling.

 

In the case of Sigma Test Light, around half of the questions are suitable for measuring above 130, which makes the scores reliable and accurate at this level, reaching up to around 160 with good construct validity and good adequacy at the level of difficulty.

 

At levels above 160, Sigma Test Light continues to generate valid scores, but the uncertainties are slightly greater, because the number of questions with adequate difficulty for these levels decreases, and the fewer questions, the greater the uncertainty in the measurement (it is It is recommended to read my books and articles in which I deal with Measurement Theory, to better understand this effect).

 

Sigma Test Light also has a unique characteristic, which is that the same question covers different levels of difficulty. For example: the question about water flow can be answered at different levels. If the person makes a simplified calculation, they receive a proportional score, which depends on how close they got to the “correct” answer. If the person devises a more sophisticated and more effective method to make the calculation, and comes closer to the correct value, he receives more points. In this way, the same question is able to discriminate between different skill levels, according to the quality of the answer.

 

This property of the questions gives Sigma Test Light two very important advantages: the first is that the range of applicability is wider and the second is that each question adapts to the person's skill level. If a person with an IQ of 110 solves the test, they will find about 80% of the questions suitable to correctly measure their IQ range. If another person with an IQ of 160 takes the test, they will also find 80% of the questions to be appropriately difficult to measure in their IQ range, because people with 110 will give a type of answer that will be scored commensurate with 110, while people with 160 will give answers to the same questions, but will be compatible with around 160. In this way, it is as if the test had a greater number of questions in all IQ ranges, being more precise and more accurate across a wide spectrum of skill levels. .

 

In short, these are some of the properties of Sigma Test Light. For more information on this topic, read our books and articles, watch our videos, study Measurement Theory and Statistics.

 

Also discover Sigma Test Extended, with a detailed introductory text in which you will find more information about Psychometrics, critical analysis of the limitations and potential of IQ tests, conceptual information, statistics and much more. Also read our articles, our books and our interviews in text and video, where you will find the most well-founded information about Psychometrics and a wide range of other topics related to Science, Philosophy, Investments, Astronomy, Philosophy of Science and many other topics.

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