People used to use an IQ test scale that had 24 instead of the current 15 IQ points as the standard deviation. An 125 IQ in that scale would correspond to 116 IQ in the currently used one.
No, a different standard deviation doesn't change the scores, only the predicted population distribution of the scores.
If you sit down to a standardized IQ test, your score won't change because someone thinks the distribution of scores within the population is wider than someone else does.
It's not about what you guess the distribution in the population to be, it's how you represent distribution you get from the actual test results. Someone who does the IQ test and gets a result 1 standard deviation above the mean of all the test-takers gets an IQ score of 124 from a test-giver using the old scale and an IQ score of 115 from a test-giver using the current scale.
No, it doesn't work that way. The test delivers a specific IQ score for a given performance regardless of the traits of the population of test-takers. One's score doesn't rely on the scores of other test-takers or the statistics of the population as a whole.
If this were not true, people's IQ scores would change depending on the makeup of the tested population, but in fact, it's the other way around -- the statistical makeup of the population, the mean and standard deviation, depends on assessing many individual scores, each of which is immutable and unrelated to the population's overall statistics.
If your position were valid, if one person took one IQ test on a desert island, he would not be able to get a score at all, for lack of a population to give a context to the test result. But this is not how IQ testing works.
Let's simplify this. Let's say it's an arithmetic test of 200 questions of gradually increasing difficulty. An average test-taker can answer 100 of the 200 questions. A very smart person can answer 150 questions. Do you really think an individual's score depends on the average score and distribution of the population of which he is a part?
I must add that, if IQ scores really depended on the population's traits, then IQ testing would really deserve its present terrible reputation. Apropos:
I'm talking about the initial standardization of the test, where they determine which results correspond to which test scores by taking the results of an initial population and fitting it on a mean 100, SD 15 normal distribution: http://www.americanscientist.org/issues/id.881,y.0,no.,conte...
Some scoring systems use an initial standardization where the standard deviation is 15 points, others use 24 points, so the same test performance can get you IQ 115 or IQ 124 depending on whose test you take.
Yes, I know. But that debate has been settled, and AFAIK the result is population mean 100, standard deviation 15.
Unless, of course, different groups of testers are using different assumptions, but without being driven by the analysis of the largest possible collection of standardized test scores. If so, it casts IQ testing into doubt as a reliable tool.
Evidence for this being a settled issue is the fact that workers in this field report a gradual increase in IQ over the decades:
If mean IQ really was adjusted to agree with current test scores, the mean would always be 100, regardless of test score changes over time.
> Some scoring systems use an initial standardization where the standard deviation is 15 points, others use 24 points, so the same test performance can get you IQ 115 or IQ 124 depending on whose test you take. [ephasis added]
The conclusion is still false -- the tests itself doesn't change, only the scoring assumptions. Those who assume σ = 15 could acquire the tests from those who assume σ = 24 and add them to their own dataset, and vice versa. Also, I have to say, either the standard deviation can't change the test scores, or the test scores have no meaning.
One more thing -- the standard deviation shouldn't be an assumption, with one group arbitrary choosing 15 and another choosing 24. The value should be derived from a large set of test scores, not a committee casting a vote.
Your argument seems to be that one's IQ score depends on the population result, along with some arbitrary assumptions like σ = 15 or σ = 24. But that's the reverse of normal statistical practice, in which the mean and standard deviation derive from test scores, not the other way around.
Obviously I'm not doubting that what you say may be so, only that it shouldn't be so -- the standard deviation shouldn't be based on anything but the analysis of a large set of standardized test scores.