Sigma Test Light
Intelligence is the most important characteristic of living beings, and it is thanks to it that humans have dominated our planet. There are many animals that are bigger, stronger, and faster than humans, but they have all been subdued thanks to our intelligence. It was intelligence that took us out of the caves and into space.
All educated people understand the importance of self-knowledge, and among all the characteristics that need to be well known and well understood, intelligence is the most important.
Knowing your own intelligence is much more important than knowing your height, weight or zodiac sign, however a myth has been spread that IQ tests are not appropriate for assessing intelligence. This is not true.
There have been thousands of studies on this subject, in over 190 countries, over almost 120 years, and the results of these studies clearly show that IQ tests measure intelligence very well within a certain range. Furthermore, IQ is the best understood, most deeply studied and most accurately assessed construct of all the constructs in psychology.
Psychometrics – which studies cognitive tests – is by far the most developed branch of psychology.
The study of Psychometrics is so developed and so important that it has even produced statistical and mathematical tools widely used in other fields of knowledge, such as the correlation coefficient, linear regression, factor analysis and item response theory.
The correlation coefficient is possibly the most widely used statistical tool in the world in all scientific fields. It was thanks to the use of the correlation coefficient that it was discovered that the universe is expanding. It is thanks to the correlation coefficient that it is possible to perform quick and cheap tests such as blood tests. It is thanks to the correlation coefficient that an immense variety of social, political, economic, physical, chemical, astronomical, archaeological and many other phenomena can be understood. No invention in psychology that was not created in Psychometrics has a relevant application in other fields of knowledge.
That is why IQ tests are the psychological instruments most solidly supported by the scientific method and most rigorously tested and validated. Despite this, there is a strong prejudice among people who, because they do not know or understand mathematics, science and logic, make frivolous and completely unfounded criticisms of IQ tests. Even among most psychologists, who generally do not know or understand mathematics, this type of prejudice is very common.
When we look at the facts objectively, what we find is very different from the opinions of these psychologists. Since Terman's pioneering studies in 1928, and in the thousands of studies that have followed, it has been very clear that intelligence correlates with financial success, academic success, social success, specific skills and general abilities, lower incidence of mental disorders, less deviant behavior, and lower crime.
Terman's studies included thousands of children who were divided into two groups: 1,526 children with IQs above 135 and nearly 100,000 children with IQs below 135. Terman and his assistants—who continued his work after his death in 1956—followed the lives of these children for decades and found a clear advantage in academic, literary, artistic, and athletic performance compared to the general population. He also found that they had fewer problems with addiction, crime, and mental disorders, higher incomes, more stable and lasting marriages, and longer lives.
The vast majority of psychologists don’t even know what IQ is, and they often confuse IQ with the score on an IQ test. This difference is explained in detail in one of my videos, as well as a more formal explanation in “The Golden Book of Intelligence” and a summarized version in “The Apodictic Guide”.
A misunderstanding of what IQ is and its importance results in numerous losses. For decades, the largest technology companies have realized this and use IQ tests to select their employees, because they understand the enormous advantage of hiring people who produce 1,000 times more than the average person, and pay only 30 times more. This way, the person hired is happy, earning 30 times the salary of an average person, and the company is even happier by paying 30 people and getting paid for the production of 1,000 average people.
Meanwhile, the most narrow-minded companies prefer to hire based on academic qualifications, referrals, nepotism and other ineffective criteria, resulting in a staff of underqualified employees, thinking they are “saving” money with lower salaries, when in fact they are wasting money with much lower production, hiring people who produce for 1 and earn for 1.
Therefore, knowing your own intelligence is of utmost importance to have a better idea of your potential, your limitations, your value, your strengths and weaknesses. In this context, traditional IQ tests such as WAIS, Stanford-Binet, Cattell, Raven, DAT and others are good assessment instruments for the 70 to 130 IQ range, especially for the 90 to 110 range (in which these tests are more accurate).
However, for people with IQs above 110, and especially above 120 and 130, traditional IQ tests do not assess accurately, and the errors become increasingly large as the actual IQ is further from the mean. This leads to many grossly incorrect diagnoses, as well as serious selection and recruitment errors.
There are cases of people with IQs of over 170, 180, and even over 200 who were incorrectly assessed as having IQs of 120 to 130, due to the limitations of the tests used in clinical practice. Some notable examples are the cases of Feynman, Fischer, and Kasparov, who scored 123 on traditional tests, even though their correct IQ was over 170, and in Feynman's case over 200.
The opposite error is also common, that is, the person has a much higher score than the correct one, such as Adragon de Mello, Ainan Cawley , Michael Kearney and others, whose true IQs were between 150 and 170, but whose IQs measured on tests were above 300.
When a person's IQ is above 130, the errors produced in clinical tests are immense, both more than correct and less than correct.
The simplistic and incorrect interpretation of this situation is that if IQ tests produce such large errors, they are useless. This is a serious and fundamental error. In fact, IQ tests work very well if used within their limits of applicability and if interpreted by qualified individuals. The limits of applicability cover the range of 70 to 130, which includes 95% of the population.
This does not mean that all scores between 70 and 130 will be correct and all scores above 130 will be incorrect. Occasionally, tests also fail within this range, but they generally work well. And even in cases where the results are inconsistent, a good psychologist should (theoretically) be prepared to detect the problem and suggest the application of tests with an appropriate level of difficulty. However, the overwhelming majority of psychologists are not qualified to detect these inconsistencies and write completely absurd reports. The error, therefore, is not in the tests, but in the underqualification of the would-be professionals who use these tests in inadequate conditions.
It's like using a high-precision analytical balance in a chemistry lab to try to weigh an automobile. The scale is fine, but it is not appropriate for that weight range. If someone were to use an analytical balance to try to weigh a car, the problem would be the lack of knowledge and judgment on the part of the person who misused the scale. The same goes for any other instrument that is used outside the context for which it was designed or outside the limits of its applicability.
Therefore, IQ tests like WAIS are very good, very effective, very accurate and reliable in correctly assessing the intellectual level of people with an IQ between 90 and 110, and they continue to work reasonably well up to 130. Above that, errors increase and it becomes necessary to use other instruments that are more appropriate for the respective intellectual levels that one wishes to measure.
In this scenario, the Sigma Test Light (STL) and the Sigma Test Extended (STE) emerge as the best cognitive assessment instruments at the highest levels. The STL makes it possible to correctly measure IQs from 80 to 200, with better accuracy in the range of 110 to 180. The STE makes it possible to correctly measure IQs from 100 to 225, with better accuracy in the range of 120 to 210.
So if you were an outstanding student, if you are curious about scientific and philosophical topics, if you critically analyze everything around you, if you are a person with original opinions, this means that you have some characteristics common to people with above-average intelligence, perhaps you are a gifted person, and the Sigma Test Light may be indicated in your case, so that you have a correct assessment of your intellectual level.
If you have already been examined with another test and obtained a score above 110, and especially above 120, you certainly need a more accurate evaluation, because there is a high chance that your current evaluation is wrong.
The STL will not provide an “absolute truth”, that does not exist, but it will provide a much better-founded and more realistic assessment, with better construct validity and with questions whose difficulty is appropriate to correctly assess IQ at the highest levels.
It is important to understand that clinical IQ tests do not stop working after 110, or 120, or 130. What occurs is a progressive degradation in construct validity and item adequacy. This causes uncertainty in scores on traditional IQ tests to start growing after 110, and gradually worsens until it reaches intolerable levels around 130. In these cases, the Sigma Test Light provides adequate means to continue to assess correctly at levels at which other tests stop working.
Some traditional tests, such as Raven Standard Progressive Matrices (RSPM), use quite realistic nominal ceilings, compatible with the true level of difficulty of the questions and with good construct validity, with a ceiling around 135. But other tests, even more traditional than the RSPM, fail seriously on this point, with very high nominal ceilings, completely incompatible with the real level of difficulty of the questions, establishing falsely high nominal ceilings, which do not correctly represent intelligence at the highest levels.
Two examples of this are the Stanford—Binet (SB), the most traditional in the world, and the Wechsler Adult Intelligence Scale (WAIS), the second most traditional.
The SB generates nominal scores up to 225, but these scores are seriously out of touch with reality after 130. The WAIS generates nominal scores up to 155, but is also not valid above 130.
The STL generates realistic and accurate scores up to about 180, and continues to generate realistic scores up to about 190, although accuracy begins to decrease, making scores above 195 less reliable.
The Sigma Test Light offers no advantage over traditional tests for people with IQs below 110, but it is superior to traditional tests for people with IQs above 120 and is much more accurate and reliable for IQs above 130, that is, in the range of 110 to 130, the STL presents similar accuracy to traditional tests, with the STL being slightly more reliable above 120 and much more reliable above 130.
Some of the main advantages of the Sigma Test Light are:
1. There is no time limit. In this way, STL measures your actual ability, rather than measuring your performance at a specific moment, which could be subject to factors such as stress, anxiety, sleep, nervousness, etc.
2. The difficulty levels of the questions are appropriate for the different IQ levels that the test aims to measure, unlike traditional tests, whose questions do not exceed the level of 130 and try to make them artificially difficult due to lack of time. It is known that the speed to solve elementary questions does not measure the same type of ability as the creativity and depth of reasoning to solve more difficult and complex questions, which is why traditional tests fail after 130, while the Sigma Test Light continues to work until just above 190.
3. Construct validity is one of the most important criteria for a good cognitive test, as it indicates that the variable being measured is in fact the one intended to be measured. Most traditional IQ tests perform well on this criterion up to around 120, but start to fail at 125, while the Sigma Test Light has good construct validity up to over 180.
For these and other reasons, the Sigma Test Light (STL) It is a psychometric instrument for intellectual assessment with many important differences compared to other cognitive tests. It follows the same line as the Sigma Test (ST), Sigma Test VI (STVI) and Sigma Test Extended (STE).
The new version of the Sigma Test Extended (2022) has already been published in journals from leading high IQ societies, including In-Sight Journal, Phenomenon and Deus Vult.
In-Sight Journal is the leading publication of high IQ societies, which brings together interviews with the world's leading exponents of high IQ societies and articles on different topics related to IQ, intelligence, psychometrics and cognitive science:
https://in-sightpublishing.com/2022/07/22/ste/ Phenomenon is the magazine of OlympIQ Society (for people with IQ>180): https://winone.iqsociety.org/issues/Phenomenon_25.pdf DEUS VULT is the magazine of the Catholic High IQ Society (IQ>150):
https://drive.google.com/file/d/1bO6CBwgINp7HukCW6wWUo_PboBOWkopw/view
The original version of the Sigma Test (1999) was published in Mensalainen (Mensa Finland ), ComMensal (Mensa Belgium ), Gift Of Fire (Prometheus Society), Papyrus (Glia Society), IQ Magazine (International High IQ Society), Malba Tahan (Interesting Physics).
The Sigma Test has already been accepted as a criterion for admission into some of the major high IQ societies, including Sigma VII, Sigma VI, United Giga Society, Pars Society, OlympIQ Society, and others. High-caliber scientists and mathematicians have been tested using the Sigma test, which is considered the most appropriate for evaluating accurately at the highest levels. This topic is addressed in Hindemburg Melão Jr.'s second interview with In-Sight Journal: https://www.sigmasociety.net/article/interview-scott .
The STE was designed to be the most difficult intelligence test available and with the best construct validity at the highest levels, allowing it to correctly assess people with IQs up to a little above 220, through questions with an appropriate level of difficulty and that require compatible cognitive skills. It is very different from tests such as Stanford—Binet (SB), which allegedly measure up to 225, when in fact the most difficult questions on the SB are at a level of 130. That is, some people with an IQ of 130 would have about a 50% chance of getting the most difficult questions on the SB right, in addition to the cognitive processes involved in solving them being too primary to assess at levels above 125. For more information about the Sigma Test Extended , visit the link at the end of this text.
The Sigma Test Light is a more accessible version of the Sigma Test, aimed at people with IQs between 90 and 190, and can extend a little beyond that range, covering the range from 75 to 200.
The optimal range of precision and accuracy is between 100 and 175, intended for people classified as having above-average intelligence, who obtained scores of 110 or higher in conventional IQ tests and want a more representative assessment of their real intellectual capacity.
Although the meaning of “above average” is arbitrary and vague, it is a widely accepted standard. In academic books on Psychometrics, one can find classifications by IQ range according to the opinions of various authors, including the more traditional ones such as Terman, Wechsler, Levine and Woodcock , as well as others that are less well-known. These classifications are subjective and have no scientific value, in which the cut-off levels are “guessed” by the authors. In the case of Lewis Terman, for example, he decided to “guess” that the classifications should be like this:
Pinter decided they should be like this:
Levine decided they should be like this:
Other authors gave other guesses about what they thought the classifications should be.
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 characteristics in people in different ranges and, from there, establish appropriate cut-off points to delimit these profiles. This should be done primarily using statistical tools such as Wavelets , Cluster Analysis, Factor Analysis or something equivalent.
When classifications are performed properly, the divisions are not positioned in 10 or 20 points, but rather in variable intervals and with numbers that are rarely round. The Sigma Test, for example, adopts classifications along these lines, using Factor Analysis with Ward links and Bhattacharyya metric, resulting in much better-founded stratifications with scientific value. For more details on the classification used in the Sigma Test, see our article on the Sigma Test Light report at https://www.sigmasociety.net/artigoss/significados-stl .
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 this standard for now. However, in the report we present the correct classification, and also add, as a curiosity, the other incorrect classifications adopted since 1916.
In addition to adopting an incorrect classification system, traditional IQ tests have many other flaws. It would not be possible to list and comment on all of them here (this is done in the “Golden Book of Intelligence”); here we will only mention some of the most serious problems, among which we can highlight assessments with astronomical errors, which can reach more than 100 points.
There are many cases of people who have received blatantly incorrect assessments on traditional tests, both upward and downward, and this can have several negative effects. Most of these errors are never discovered, because the person simply “sucks it up” and believes the assessment, trusting the authority of the psychologist. But there are a few cases that end up being identified and reported, because the error is so egregious that there is no way to turn a blind eye. Here are a few examples:
There is a competition in the US that consists of solving difficult Math and Logic problems, similar to the Math Olympiads. The questions in this competition cannot be solved simply by applying formulas that students are trained to repeat mechanically. Instead, it is necessary to understand subtle and complex aspects and invent original methods to solve them. The name of this competition is “Putnam”.
Putnam Prize winner and Nobel Prize winner in Physics Richard Feynman scored 123 on an IQ test. This is an obvious and completely absurd error, but the psychologist who administered the test to Feynman did not realize that he was facing a gross error and signed the report as if Feynman did in fact have an IQ of 123.
This bizarre result by Feynman has been widely cited to discredit IQ tests, when in fact it merely reflects the inexperience of the psychologist who administered the test, without fully understanding the limitations inherent in traditional tests and without having the experience and sensitivity necessary to realize that he was dealing with one of the greatest geniuses of the 20th century, whose true IQ was around 220.
To get an idea of what this represents, suffice it to say that the population of the United States at the time of Feynman was about 200,000,000, and being a champion in the Putnam test placed one at least at the level of 1 in 1,000,000 and probably higher. However, an IQ of 123 corresponds to the rarity level of 1 in 13, that is, in a classroom with 100 students, about 7 or 8 have an IQ above 123. This already makes it very obvious that the score of 123 is grossly incorrect. As if the Putnam prize were not enough, Feynman also won the Nobel Prize in Physics, was one of the youngest participants in the Manhattan Project and made several important contributions to Physics and Science in general, in fact he deserved more than a Nobel Prize.
Feynman's intellectual level was surely in the range between 1 in 30,000,000 and 1 in 300,000,000.
But his IQ test score said he was at the 1 in 13 level.
Feynman's actual IQ is in the range of 210 to 230, but the test indicated 123.
Another case of bizarre IQ testing involves world chess champion Bobby Fischer, who also scored 123. Some sources “incorrectly” cite the value as 187, others cite 184 or 181, but official documents from Fischer’s Brooklyn high school show the score as 123. Ironically, although this 187 value was “made up” by some journalist, it is closer to the true value than the “official” IQ measured by a psychologist.
World Chess Champion Garry Kasparov also scored 123 on the Raven and 135 on the Eysenck , although Kasparov's true IQ is somewhere between 160 and 180. Some sources also give Kasparov a score of 192, but this is the result of converting his highest FIDE rating (2851) into an IQ using Bill McGaugh 's formula , which has several conceptual and quantitative problems but still yields a score closer to the correct one than his results on 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 fulfill 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 similar situations, like Ainan Cawley , Michael Kearney, Edith Stern, Marnen Laibow-Koser , Sho Yano, Michael Grost , Nadia Camukova and many others, who have shown themselves to be fast and precocious in performing simple and easy tasks, suitable for correctly measuring up to 130 IQ, but due to errors in the standardization of the tests or extrapolation made by the examiners, 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 rarity level of 1 in 1,000, while an IQ of 200 is at a theoretical level of 1 in 5,000,000,000. When one correctly adjusts the IQs to a proportion scale and considers the true distribution, which is not Gaussian, then the score 200 corresponds to 1 in 5,000,000.
Both these upwardly skewed and downwardly 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-assessed as a child, as was the aforementioned Poincaré and many others.
In cases like Feynman, Einstein and Poincaré, history has taken charge of revising the grotesque errors in diagnosis, but how many cases are there of brilliant people who could have changed history, who never even became known because some incorrect assessment pushed them down?
There are also many problems caused by upward distortions. Justin Chapman was a child prodigy who gained great media attention in the late 1990s for having an IQ of almost 300 at the age of 4. More precisely, the score attributed 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 pressure, exposure, bullying, insults, 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 can't stand the hell that his life has become due to the consequences of an incorrect psychological evaluation.
Another, much more famous case is that of William James Sidis , who had his IQ evaluated between 250 and 300, and almost all the tabloids on the subject usually mention Sidis as the most intelligent person who ever lived, when in fact his true IQ was around 170 to 190. Sidis also faced excessive pressure 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, his parents harshly reprimanded him. It was the last straw and, from then on, Sidis decided to abandon his academic career to live wandering the world in sub-professional activities and collecting car license plates.
It is important to emphasize that the problem is not the high IQ, but the distortion of the result. Gauss, for example, was correctly assessed and lived up to expectations by 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 broadened the horizons of knowledge. This is because they were not diagnosed based on IQ tests that use primary questions, but rather based on their remarkable achievements, which were already 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 higher than the ceiling of IQ tests, problems similar to those used in Sigma tests.
These assessment errors occur because traditional IQ tests are designed to assess the intellectual level of people between -2 and +2 standard deviations from the mean, which 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 the 2.3% below 68, the test results do not reflect their true ability as well, and the further away a person's actual IQ is from this range, the greater the potential error between the measured score and the true IQ.
Traditional tests used in clinical settings do not include questions with an appropriate level of difficulty nor do they meet the requirements necessary to have construct validity outside this range. This topic is analyzed in a didactic way in my first interview for the In-Sight Journal, in 2022, as well as in some of my videos and articles. https://www.sigmasociety.net/interview-jacobsen
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 the construct validation is not as rigorous, the flaws are much more serious and more numerous, including containing ambiguous questions, incorrect answers, distortions in the norms, lack of acceptable answers in some questions, etc. In fact, even well-known tests such as WAIS also have several of these problems, but the others have even more serious and more frequent problems. See my analysis of the 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, and is considered the “gold standard” in the assessment of psychologists, a very questionable gold standard, but in relation to other tests used in the clinic, the WAIS is in fact comparatively one of the best.
Although the WAIS produces nominal scores up to 160 (WAIS-R) or 155 (WAIS-III or IV), 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 not do this out of malice, but out of ignorance.
Lewis Terman, in his study of 1528 gifted children, faced several problems of prediction and interpretation due to the flaws in IQ tests.
Terman and his team examined tens of thousands of children and selected the 1,528 who scored above 135, with some reaching over 200, and followed the evolution of these children throughout their lives for many decades, to see if they would become geniuses in adulthood.
The results confirmed some expectations, and indeed the children with IQs above 135 had an intellectual output well above that of the general population, but none of them, nor those with IQs above 180 or above 200, turned out to be geniuses, nor did they win any important intellectual prize. Furthermore, to Terman's shame, among the children he did not select because they did not have sufficient IQs, that is, with IQs 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 are unfamiliar with 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 act mechanically, labeling the person as indicated by the test result, without critically evaluating whether that score is plausible. The loss of construct validity for scores above 130 is another serious problem, because what the tests used by Terman measured was only a good reflection of intelligence up to about 130, but what they measured above 130 did not represent intelligence well.
If a person places a whole, normal-sized chicken on a scale and it says 144g, that person needs to have common sense to know that a whole chicken cannot weigh 144g and that something is wrong. If they cannot identify and correct the weighing error, it is better to estimate the weight using common sense than to label the chicken with a 144g label. Or if there is a more appropriate scale, it is better to use that to measure it correctly.
It is also important to note that in the case of the study conducted by Terman, there was no “problem” with the IQ tests used, but only a limitation. There was no problem because the tests did in fact measure correctly within a certain range, between 70 and 130. “Proof” of this is that the tests selected people who were much more intelligent than average, people who were much more successful academically, professionally, financially and socially. Therefore, in general, the tests were correct in separating the group above 135 from the group below 135, confirming that the tests work well up to this point. But they failed precisely in the 2 most notable cases, of people with IQs well above 135, who were immensely under-evaluated, and the examiner was unable to perceive this. IQ tests work well for 95% of the population, but the problem is that precisely in the 2% with the highest IQs, where the test fails, is where the geniuses who can change the world and who need to be correctly diagnosed are.
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 correctly assess at higher levels.
At companies like IBM, Microsoft, Google, Facebook, they need people with IQs well above 130 and even above 150, so they have created their own tests to correctly measure at these levels. The tests used by these companies can measure correctly from 130 up to about 160, but they also start to fail at levels above 165.
The Sigma Test Extended easily fulfills the function of correctly measuring IQ at a level above 150, reaching over 220. It also applies to IQs below 150, covering the range from 100 to 225, with the optimal accuracy range between 120 and 210.
The Sigma Test was used to select the team that worked on developing the Cantor platform (named after Georg Cantor), consisting of 6 international Olympic medalists in Mathematics, Physics and Computer Science, and has been accepted as a criterion for admission into some of the most exclusive high IQ societies in the world.
This “optimal accuracy range” 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 the case of the SAT, for example, it has a difficulty ceiling of around 135 to 140, but produces IQ-convertible scores up to 164 by the old norm (pre-1974) and around 160 by the more recent norm (post-1995). However, even if the difficulty ceiling were compatible with the level of 160 and even if the construct validity also reached that level, it would still need to meet another important requirement, which is to contain a sufficient number of questions at the respective level. If there were only 1 or 2 questions that met this requirement, the uncertainty around the ceiling would be low, that is, the test would in fact measure up to 160, but the error in this measurement could be large.
In traditional IQ tests, there are usually less than 10% of questions to discriminate at levels above 125 and 0 questions with a level of difficulty appropriate to correctly measure above 130. However, these tests generate scores that can reach 150, 160 and even above 190. However, these scores do not reflect real intellectual capacity, but rather the speed to solve primary questions. They 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 the person gets all 60 questions 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 2 questions in a test with 60 questions to discriminate at levels above 125. This makes the uncertainty in scores above 125 very large, because it is as if it were a test based on only 2 questions useful for discriminating near the ceiling (in fact, this analysis is 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 yet another 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, and can reach 115 or slightly above, but it should not be used to measure IQs above 120. However, in practice, it continues to be used for IQs up to the ceiling, 133 in the current standard, or 137 in some old standards. Remember that the main problem with the Raven is not the ceiling, but rather the small number of questions designed to discriminate at levels close to the ceiling.
In the case of the Sigma Test Light, about half of the questions are suitable for measuring above 120, which makes the scores reliable and accurate at this level, reaching around 170 with good construct validity and good suitability for the level of difficulty.
At levels above 170, the 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 recommended to read my books and articles in which I deal with Measurement Theory, to better understand this effect).
The Sigma Test Light also has a unique feature, which is that the same question can cover 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 efficient method for making the calculation, and gets closer to the correct value, they receive more points. In this way, the same question is able to discriminate at different levels of ability, according to the quality of the answer. This allows the same question to be optimal for a wide range of scores, which implies personalizing the level of difficulty for each person. This substantially increases the accuracy and precision of the scores, with more than 10 questions appropriate for measuring above 180 and more than 20 appropriate for measuring above 170, in addition to also including more than 30 questions between 90 and 110, maintaining good accuracy both at the highest levels near the average and at all intermediate levels.
This property of the questions gives the 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 takes the test, he will find about 80% of the questions suitable for correctly measuring his IQ range. If another person with an IQ of 170 takes the test, he will also find 80% of the questions with adequate difficulty to measure his IQ range, because people with 110 will give a type of answer that will receive a score compatible with 110, while people with 170 will give answers to the same questions, but that will be compatible with about 170. 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 the Sigma Test Light. For more information on this topic, read our books and articles, watch our videos, and study Measurement Theory, Statistics, and Psychometrics.
Also check out Sigma Test Extended (link) , with a detailed introductory text in which you can find more important information about Psychometrics, a 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 about a wide range of other topics related to Science, Philosophy, Investments, Astronomy, Philosophy of Science and other fields of knowledge.
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