I just saw it retweeted:
“If you’re 130 IQ you're as different from the mean as if you were 70 IQ on the other side. #NAGC ”
This sounds reasonable, right? Except for one problem: IQ scores are not measures of amount of ability (or need). They are only a relative ranking of scores, corresponding to percentiles. A 30 point interval on one part of the IQ scale may mean a much greater difference in abilities than a 30 point interval on another part of the scale, even if we are talking about the same IQ test!
How the norming process works
To understand why, you need a little background on how modern IQ tests are scored. When IQ tests are developed, the test items are first tried by a norming group. This is a group of people who are supposed to be representative of the population in terms of their range of ages, abilities, genders, ethnicities, and other factors. The test items are ranked according to difficulty, and raw scores are calculated for each subtest. Within each age group, those raw scores form a distribution: most people score somewhere near average for that age group and fewer people score very high or very low. This distribution is normed by fitting the scores to a normal distribution curve with an average of 10 and a standard deviation of 3. Thus for each raw score, there is a corresponding scaled score ranging from 1 – 19 for that subtest. This norming process spreads the raw scores out unevenly because the scaled score depends on how many other people scored below a given raw score. In other words, a difference of 4 points in raw score could correspond to a greater difference in scaled scores in one part of the distribution than in another. The scaled scores tell us only how unusual (how many standard deviations from average) someone's performance is on each subtest.
Once the scaled scores are determined for each subtest, the total of the scaled scores for a certain group of the subtests is similarly fitted to a normal distribution. This generates a table that the psychologist uses to look up the Full Scale IQ score, known as a standard score. This is a score ranging from 1 160 with an average of 100 and a standard deviation of 15. Thus the FSIQ is a measurement of how unusual the sum of the scaled scores of the subtests is. A major drawback to the FSIQ is that when one subtest score is unusually low and another is unusually high, these differences are masked in the sum. Major tests like the WISCIV take this into account by not allowing a valid FSIQ to be calculated when the subtest scores are too widely scattered.
Making sense of raw scores
Could we go back to the raw scores and compare abilities that way? Even that is not a straightforward process. For some subtests, like digit span, it might make sense to say that a person who can remember 6 digits has a memory that is as much better than someone who can remember 3 digits as it is worse than someone who can remember 9 digits. But for other subtests, it's not so easy to quantify differences in amount of difficulty between the test items. Is the first block design puzzle as much easier compared to the second as the second is compared to the third? This is not clear. All we can say to compare people is that this person assembled three puzzles successfully while another person assembled only one, and that assembling three puzzles happens much more often in the population of that age group than assembling only one puzzle.
This meme is everywhere in the gifted universe:
“The child of 160 IQ (top 0.01%) is as different from the child of 130 IQ (top 2%) as that child is from the child of average ability.”
~Leta Hollingworth, Children Above 180 IQ (1942) [1]
“There is the numerical answer: a child of IQ 160 is as different from a moderately gifted child of 130, as that child is from an average child of 100. “ [2]
“Now move in the opposite direction from 100. An IQ score up to one standard deviation above 100 is considered normal, or average. Move up one standard deviation is mildly gifted. That means that a child with a score of 130 is as different from a child with an IQ of 100 as is the child with an IQ of 70, a score which definitely qualifies a child for special services. Move up one more standard deviation and we move into the range of moderately gifted (130144). The same range on the other side of 100 is the mildly retarded range.” [3]
“Let’s pretend that you take an average child with an IQ of 100. Take this child and put them into a classroom where everyone else’s IQ is 70 and below. In other words you are taking an average child and putting him or her into a school environment where all the classmates are mentally retarded. Not only are these classmates mentally retarded but the curriculum is also geared for the mentally retarded children. “ [4]
“What's the difference? Gifted children tend to think differently and learn more quickly than their peers. Compare a gifted child (IQ = 130) to an average child (IQ=100) you will see the difference: the gifted child learns quicker, thinks deeper, and draws conclusions more easily. Compare that gifted child (IQ=130) to the highly gifted child (IQ=160). Again, you will see the difference, in many of the same ways. Now compare the highly gifted child to the normal child, and you face a chasm that by the end of elementary school may place these two children as much as 5 years apart in mental age.
“There's another way to look at it. The difference between the exceptionally gifted and the average child is the same as the difference between the average child and the mentally handicapped child of IQ 40. That's a big difference!” [5]
Why does this matter?

As advocates we should strive to be accurate. Our credibility is at stake!

As advocates we should strive to educate—not spread misinformation just because it is a handy analogy to make a point.

Think about how our advocacy is perceived by others: When we make a comparison that implies average people are mentally impaired compared to gifted people, we alienate most of our listeners.
I understand that the goal is to build awareness of the very real needs of gifted children. So instead let's use the real meaning of IQ scores: a high (or low) score is unusual. Unusual kids are likely to need unusual accommodations.
Please, make a small change, gifted advocates! Be accurate, educate, and build awareness without alienating others. Let's start using a new meme:
Unusual kids
are likely to need
unusual accommodations.
In order to help advocates communicate how unusual gifted scores are in the population, I created this graphic.
The orange squares correspond to the distribution of scores 130 and above in the population, and the purple square is for 145 and above. The green and yellow squares represent scores below 130. I used two colors to help people visualize groups of 32 students in "classrooms". I chose 130 because it is two standard deviations above average, and is often used as a cutoff for gifted programs. This chart illustrates the rarity of these scores. On average, a teacher who has 32 students per year could expect to see a highly gifted student with an IQ of 145 or above once in a 32 year career. In practice, this may happen more or less often because the population is not uniform from one school to the next and because different groups of students may score above 145 on different IQ tests, increasing the number of opportunities for scoring high. Still, I believe the chart can help illustrate that as a student's IQ score increases, the likelihood that the school's regular curriculum will be a good fit decreases.
Post updated: 10/13/2013 to include background information on the scoring of IQ tests and the rarity chart illustrating the IQ score distribution for gifted students.
[1] http://www.pegy.org.uk/page2.html
[2] http://www.hoagiesgifted.org/highly_profoundly.htm
[3] http://giftedkids.about.com/od/gifted101/qt/IQ_scores.htm
[4] http://www.alifeofthemind.com/2011/02/13/mensaiqthe30pointgapandtheoutsiders/