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There could be a good reason for this. Take a look at the node on Multiple intelligences. Let's assume for a moment that this is correct, and all people are born with unchangable measures of the different intelligences. Everyone has different strengths and weaknesses.

People will polarize towards the jobs they are good at. If you are born with amazing computer skills, you are likely to get a computer-related job. If you have an amazing ability to play football, you may well end up playing a lot of football.

Now, most people aren't going to want to spend the rest of their lives worrying about their inadequacy in certain areas. Thus they will tell themselves that their skills are important. After all, they (the skills) got them (the person) where they are today. They may disregard other skills, rather like PC gamers who don't own consoles will rarely say that yes, a console is overall a superior platform.

Anyway, here's my point: People often judge other people's intelligence in the same category at their own, and vice-versa.

For example, I think my skills (programming) are better than some other guy's (memorising the winners of the last 25 years' Boulton Wanderers games), because I've been just fine up until now without knowing what he knows. But I've used *my* skills a lot.

I am confidently above average in the programming league, because most people can't program. I'm right at the bottom of the Accounting Skills league. I class myself as above-average, because I'm an above-average programmer.

In conclusion: Different people are value different things. By my own standards, I am above average. By yours, I could be really dumb.


Update!

I recently found the Journal of Personality and Social Psychology printed a paper in 1999, brilliantly entitled "Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments".

To summarise: People tend to hold overly favorable views of their abilities in many social and intellectual domains. The authors suggest that this overestimation occurs, in part, because people who are unskilled in these domains suffer a dual burden: Not only do these people reach erroneous conclusions and make unfortunate choices, but their incompetence robs them of the metacognitive ability to realize it.

It's availiable online: http://www.apa.org/journals/psp/psp7761121.html


wick says The paper you cite won a 2000 Ig Nobel prize. You should add that tidbit to your w/u


WonkoTheSane says I agree with your overall point, but I think it is arguable if one is born 'with computer skills', or even with the ability to play football. Football skill(z) can be attributed to a combination of strength, speed, body mass, hand-eye coordination, vision, and, possibly, a little bit of drugs. And practice. Computer programming: logic, practice, patience, practice...I think you get the idea.

Mike1024 says Yeah... When I say 'born with' I kinda mean it as a blanket term covering both nature and nurture... that by a certain age, you tend towards certain skills more than others. If you've had access to a computer from a young age, you will be better with computers, etc. I think.
From a statistical analysis point of view: The IQ score is mapped to the standard distribution curve (see that writeup for a full explanation) like this:
Prob.             |
 .50            ..|..
              ..  |  ..
             .    |    .
 .25        .     |     .
          ..      |      ..
      ....        |        ....
 .00  -------------------------
IQ:         - <- 100 -> +

The mean IQ is 100, so we place that at the center of the curve since the mean is supposed to have the highest probability of occurrence.

According to the normal distribution, we can calculate the following:

  • The 25th percentile (i.e. first quartile) is 89.9 points.
  • The 50th percentile is 100 (obviously).
  • The 75th percentile is is 110.11.
    (See how that's 89.9 but rotated over to the other side of the curve? That's because the curve is equal on both sides.)
  • The 85th percentile is 115.5.
    (This is a curve, not a triangle, so don't expect a linear change!)
  • The 90th percentile is 119.2.
  • The 95th percentile is 124.7.
  • The 99th percentile is 134.9.
  • The probability that a randomly selected person's IQ will be 140 is 0.3%.
    If there are seven billion people in the world, about 21 million can join Mensa. (21 million sounds like a lot, but there are about that many living in Southern California. Compare that to everyone living everywhere else in the world.)
  • The probability that a randomly selected person's IQ is greater than 100 is 47.3%.


Now, if you interview 100 people and 90 say they're above average in intelligence, the probability of them all being right is a little trickier. We must carry out a hypothesis test to determine whether those 90 people are likely to be right. Anyway, in said node (hypothesis test), I have done all the hard work and have arrived at this conclusion:

If you select 100 people at random, the probability that 90 of them will have IQs of 101 or above is 4.02 x 10-14, which is a really, really, really small probability.

Anyway, as the sample size increases, the probability decreases, so the probability that seven billion people have a 101+ IQ score is probably ten zillion to one against.

JerbolaKolinowski says that I should explain the assumption that IQ measures intelligence. If you have ever taken an IQ test, you may remember what the questions were like: Word problems, 3-D spatial analysis, moving numbers around, identifying language syntax, etc. I think it may be fair to say that the IQ test is really a measure of how good you are at being a fancy parsing calculator. It's also fair to assume that most people who know what IQ is probably believe it is directly related to intelligence (subjective reality), and that fits the test of "90% of people think they are of above average intelligence".

An acquaintance of mine, having administered IQ tests to the same people at different ages, has noted that as people age, their IQ tends to drop, but not their problem-solving capability - so they're just as good, but not as fast.

Note that the amount of time you take to finish the test affects your score. You aren't given forever to take it, or an unreasonably long amount of time to take it. The result depends on the time you spend taking the test as well as the accuracy of your answers. I think we can infer that the "just as good, but not as fast" theory is valid. Personally, I think speed and accuracy are as good a measure of computational ability as any.

As far as relevance is concerned, IQ and "intelligence" may not be as relevant in a third-world, agrarian country as they are in a first-world country. Let me put it to you this way. You've grown up in the middle of a farm in a province with an agrarian economy. Which of these would you rather be?

  1. Terrible farmer, with an IQ of 130
  2. Highly skilled farmer, with an IQ of 70

I'll take #2 if I plan to stay in town, and #1 if I have an opportunity to go to university and do something other than farming (and if I'm in a third-world country that probably won't happen). There's no point in being an ultra-smart starving beggar who can't put food on the table.

Let’s ignore the trickiness that is even defining “intelligence” as a monolithic concept. Let’s ignore the many criticisms and problems arising from trying to condensate that nebulous concept into a quantifiable measure. Let’s ignore the problems of self-assessing that nebulous thing called intelligence, and comparing it to others’.

What would it look like if 90% of people really were of above average intelligence?


Let the average intelligence be a constant c. The average intelligence is, obviously, calculated by measuring everyone’s intelligence, adding up all the scores and dividing the resulting number by the number of individuals. Let’s assume we have n individuals in our population.

For simplicity’s sake, we can define then that 90% of the population scores some intelligence x > c. The other 10% have a score1 of y < c. The average is then:


c = x + x + x + x + … + y + y + y

Where there are 0.9n copies of x and 0.1n copies of y, for any population n. Then, the equation can be simplified as this:


c = 0.9nx + 0.1ny

And, with a bit of algebraic manipulation, we come to:


y =  − 9x + 10c/n

Right off the bat we can see that this equation has the form of a straight line, with a slope of  − 9 and a y-intercept of 10c/n. Let’s use the arbitrary values c = 100 and n = 50. The plot will look as follows:2 3 4


+---------------------------------------+
| This graph brought to you by gnuplot! |
+---------------------------------------+

         What if 90% of the population were of above average intelligence?      
                                                                                
   20 +---------------------------------------------------------------------+   
      |  *   +      +      +      +      +      +      +      +      +      |   
      |   A**                                        '90percent.dat' **A*** |   
      |                                                                     |   
      |      A**                                                            |   
    0 |+        *                                                          +|   
      |          A                                                          |   
      |           *                                                         |   
      |            *                                                        |   
      |             A**                                                     |   
  -20 |+               *                                                   +|   
      |                 A**                                                 |   
      |                                                                     |   
      |                    A**                                              |   
  -40 |+                      *                                            +|   
      |                        A**                                          |   
      |                                                                     |   
      |                           A**                                       |   
      |                              *                                      |   
  -60 |+                              A**                                  +|   
      |                                                                     |   
      |                                  A*                                 |   
      |                                    **                               |   
      |                                                                     |   
  -80 |+                                     A**                           +|   
      |                                                                     |   
      |                                         A**                         |   
      |                                            *                        |   
      |                                             A**                     |   
 -100 |+                                                                   +|   
      |                                                A**                  |   
      |                                                   *                 |   
      |                                                    A**              |   
 -120 |+                                                                   +|   
      |                                                       A*            |   
      |                                                         **          |   
      |                                                                     |   
      |                                                           A**       |   
 -140 |+                                                                   +|   
      |                                                              A**    |   
      |                                                                 *   |   
      |                                                                  A  |   
      |      +      +      +      +      +      +      +      +      +      |   
 -160 +---------------------------------------------------------------------+   
      0      2      4      6      8      10     12     14     16     18     20  
                        Intelligence score of the upper 90%                     

But wait! The value of x is not arbitrary! We know, from the premises of this problem, that x > c, which in our arbitrary example means x > 100. Therefore, we must travel a bit through the graphic to see the real deal:

         What if 90% of the population were of above average intelligence?      
                                                                                
  -880 +--------------------------------------------------------------------+   
       |      +      +      +      +      +     +      +      +      +      |   
       |  A**                                        '90percent.dat' **A*** |   
       |     *                                                              |   
       |      A**                                                           |   
  -900 |+                                                                  +|   
       |         A*                                                         |   
       |           **                                                       |   
       |                                                                    |   
       |             A**                                                    |   
  -920 |+                                                                  +|   
       |                A**                                                 |   
       |                   *                                                |   
       |                    A**                                             |   
  -940 |+                                                                  +|   
       |                       A**                                          |   
       |                          *                                         |   
       |                           A**                                      |   
       |                                                                    |   
  -960 |+                             A**                                  +|   
       |                                 *                                  |   
       |                                  A                                 |   
       |                                   *                                |   
       |                                    *                               |   
  -980 |+                                    A**                           +|   
       |                                                                    |   
       |                                        A**                         |   
       |                                           *                        |   
       |                                            A**                     |   
 -1000 |+                                                                  +|   
       |                                               A**                  |   
       |                                                  *                 |   
       |                                                   A**              |   
 -1020 |+                                                                  +|   
       |                                                      A*            |   
       |                                                        **          |   
       |                                                                    |   
       |                                                          A**       |   
 -1040 |+                                                                  +|   
       |                                                             A**    |   
       |                                                                *   |   
       |                                                                 A  |   
       |      +      +      +      +      +     +      +      +      +      |   
 -1060 +--------------------------------------------------------------------+   
      100    102    104    106    108    110   112    114    116    118    120  
                        Intelligence score of the upper 90%                     

There it is! It’s clear from the graphic itself that the only way for 90% of the population to have above average intelligence is for the other 10% to have abysmal scores.

There's another, larger discussion about the perils of using the average (arithmetic mean) alone in statistics, the usage of median, mode and proper context for statistic results, and the mathematical and social education of that «90%»; but is left to the reader as an exercise.


THE IRON NODER CHALLENGE XII: WE'LL RUST WHEN WE'RE DEAD


  1. I’m assuming these population slices have the exact same intelligence score.

  2. Astute readers will realize by now that the main shape of the plot is the same for any realistic values of c and n, since they are both positive.

  3. Even more astute readers will realize that given the fact that, for any values of c and n, the y-intercept is just a different constant value.

  4. It doesn’t take a particularly astute reader to know that the notion of «90% of the population is above average» leads to mathematically interesting but unrealistic results.

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