ArticlesThe topic of Mensa society came up the other day. Since a good friend of mine joined in the early ’90s, I have been amused by their entrance criterion.
Mensa “welcomes people from every walk of life whose IQ is in the top 2% of the population” [Ref].
The normal way to qualify (in Australia, at least) is to sit two different IQ tests.
One is partly verbal; the other is a so-called culture-fair test. The latter is diagram-based and depends little on knowledge of English or an English-language culture. The tests are separately marked and scored. A qualifying score in either test will get you an invitation to join Mensa. A qualifying score is a result at or above the 98th percentile — that is, a score in the range achieved by the top 2 percent of the population. [Ref]
Some other countries permit two successive tests, rather than two at the same sitting. [Ref]
So, according to Mensa, if you are in the top 2% of Test 1 or you are in the top 2% of Test 2, then you are in the top 2% of the population.
Ermmmm… No, that’s not how it works. I would have thought the Mensa committee would have realised that.
Passers of either of two tests are in the top 2-4% of the population: 2% if the tests are perfectly correlated (in which case there is no need for two tests), 3.96% if the tests are independent, and 4% if they are inversely correlated.
I don’t know what the correlation is between the two tests provided. Wikipedia gives us some idea (with citations!) of the correlations between some IQ tests (these are not necessarily those tests used by Mensa). They range from 0.45 to 0.81, suggesting there could be a sizeable discrepancy between the test scores.
In the meantime, I am thinking Densa might be a better fit for me.
Comment by Sunny Kalsi on February 10, 2008
erm, that’s considering that the tests actually measure your real IQ. If both tests are 100% accurate at measuring your IQ, you’re right. OTOH if you have a chance of a type one or two error (that a test might accidentally accept someone who _isn’t_ in the top two percent, or may reject someone who is), you want to ensure that you maximise the number of people accepted. This is more a policy decision of “when in doubt, accept them into mensa”. This is also in line with common sense. Mensa’s intention is no doubt to enrol only the top 2%. The fact that they accept more is a reality of the quality of the testing that they’ve accepted.
Comment by Sunny Kalsi on February 10, 2008
PS: I realised on the internet you can’t say “I know I was just joking… der”.