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Is there some (preferably free) online and accurate IQ test?
One which does not give me an genius IQ and then tries to sell me a diploma.
I need one which measures upto 160 sd15 (or higher). Such a test would probably document its norming process somehow.

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There are at least two problems with measuring high intelligence:

(1) Any IQ test has a maximum difficulty. That means that all subjects above a certain intelligence answer all questions correctly and get the same maximum score. This is called the "ceiling effect".

Now you might say, that we simply need to construct a test that is difficult enough for even the most intelligent person to make some mistakes.

(2) The problem with special "high IQ" tests is that you cannot draw a large enough sample to norm this test. An IQ score is not an absolute value, like height, where you measure from a zero point to a certain length and each length has a meaning in itself in relation to that zero point. IQ does not have a zero point (there is no measurable total absence of intelligence), and the values of an IQ test are defined in relation to the average intelligence of the population that person comes from.

To norm a test, it is applied to a large sample of the population, and the mean and the shape of the distribution are calculated. The mean is defined as 100, the distribution is defined by the standard deviation, which for an IQ test is 15. The norming is done for different countries and at different times. This also means, that you cannot compare an IQ score from France to one from Spain, and that you cannot compare an IQ score from 1950 to one from 2007, at least not without some mathematical trickery similar to calculating the temperature in Centigrade from one given in Fahrenheit.

Now, since there are very few very intelligent people, even if all of them took the test your sample would be too small to reliably calculate a mean and the distribution. (And you couldn't test any of them ever again, because they already took the test and know the questions.)

Finally, you wouldn't know how the scores from this test relate to scores from other tests. In an IQ test with which you test the whole population, the average is set to be 100. Since all different IQ tests are normed for the whole population, you can set all their means at 100 and compare their scores. For a test that tests only a non-average subset of the population, like very intelligent people, the average must be somewhere else, because of course highly intelligent people are not of average intelligence. But where do you set it in relation to the 100 of the average population? You would need their scores from a normal IQ test to calculate this, but (now the circle closes) since a normal IQ test cannot measure them due to the ceiling effect, you don't know where they are in relation to the average IQ of 100.

Conclusion:

While you can create an intelligence test to measure the intelligence of highly intelligent people, this test will not give you a result that has any meaning in relation to the IQ, so in fact it is not an IQ test.

IQ is not intelligence (a trait), but a construct. IQ is what is measured by an IQ test, as the saying goes. A high intelligence test measures a different construct.

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I dont see the problem, IQ testing in the normal range upto 140 is very successfull, for higher range, all you need is harder items and a larger sample. IQ testing has existed for over 50 years and norming has been done on millions. There exist many offline administered tests that measures upto 170 or higher. –  z457731 Jun 11 '13 at 7:27
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@z457731 That was covered in the reply by Jensen RCM. I'll try again: In the middle IQ ranges (average IQ around 100) there are many millions of people that you can test. From these results, you calculate the difficulty of your questions. This is important: the difficulty is not a factum that exists independent of the population. You need to test people to know how difficult a question is. To simplify the process, the difficulty is the number of people who cannot answer the question (from your test subjects). [contd.] –  what Jun 11 '13 at 8:56
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[contd.] For extremely difficult questions there might not be anyone among your subjects who can answer this question. So you don't know its difficulty. From your standpoint, all the questions that no-one could answer, are equally difficult (i.e. impossible) to answer. Or you might have one subject who has an IQ of 180, and he can answer all these difficult questions. Since only he can answer these questions, they appear equally difficult. [contd.] –  what Jun 11 '13 at 8:56
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[contd.] You don't know if there would be someone with IQ 160, who can answer only some of these very difficult questions. On top of that is the problem, that you don't know if a right or wrong answer was due to knowledge or guesswork. That person that had all those difficult questions right might just have had a lucky day. While is becomes less and less likely, the more correct answers he give, we don't know which ones he guessed, and even unlikely events do happen. That is what Jensen RCM means with "noise": the more difficult the questions, the less accurate the scaling of the difficulty. –  what Jun 11 '13 at 8:57
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What you are asking for does not really exist, no serious IQ test would ever give a score of 160.

IQ scores get swamped with noise more than ~30 points from the mean.

For example, an IQ of 160 means you are are more intelligent than 99.996% percent of people while an IQ of 150 means you are more intelligent than 99.957% of people. No test could claim to measure that difference with a strait face.

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Why is that? Do you also think it would be hard to figure out if a person is higher then 99.9957% of people on earth? Or that he is richer then 99.9998% of people in his country? –  z457731 Jun 8 '13 at 19:56
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@z457731 A psychological test does not give the "true value" of a psychological trait. Psychological traits cannot be measured directly like lengths, they must be inferred from their effects. The result from an IQ test means that your IQ probably lies somewhere close to that number. The exact probability is reflected in the reliability of the test; the range of where the true value might lie is defined by the standard deviation (which is 15 points). For example, results from 85 to 115 are all interpreted as reflecting "average intelligence". No finer distinction is supported by such a test. –  what Jun 9 '13 at 19:31
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[contd.] For a finer distinction, it would be necessary to repeatedly test the same person with the same test and calculate an average result. This is impossible, because you can only apply an IQ test once, because the next time the test subject will have learned many of the answers. The same is actually true in physics. For acurate measurement, you need to repeat the measuring and calculate the mean. But measuring a length or weight can be repeated indefinitely without falsifying the results, since there is no learning effect on the part of a scale or yardstick. –  what Jun 9 '13 at 19:34
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