Well, it's not even quantitative metric, it's ordering metric. Making quantitative statements about IQ is quite meaningless. It is not like height or weight.
It seems to be easy to get it wrong. Even the author of the article, who studies giftedness professionally, made such mistake (she tells that IQ 190 to IQ 130 is like IQ 130 to IQ 70).
What's that supposed to mean? The meaning of IQ 190 is that it is 6 standard deviations from the mean (rarity around 1 in billion), while both IQ 130 and 70 are 2 standard deviations from the mean (rarity around 1 in 50).
When talking about children age * IQ / 100 ~= mental if it's under 16 works as a reasonable approximation for younger children across much of the IQ spectrum. So a 10 year old with an IQ of 70 has a mental age of 7, and someone with an IQ of 150 has a mental age of 15 etc. Now we have redefined IQ to have a more mathematical basis but the approximation still holds.
PS: It's not really completely accurate, but you can treat a 6 year old and a 12 year old with the same mental age in about the same way and see similar types of responses.
A very good book about fallacies of treating psychological tests as measurements is Measurement in Psychology: A Critical History of a Methodological Concept
Ah, I see. I usually think about IQ in the way Retric describes, where it is proportional to "mental age." That assumption makes it seem quantitative, so yes, it's easy to get it wrong.
Hmmm, now I realized why child psychologists still use old ratio based definition. It's just more useful for them to think in terms of mental ages.
To respond to your original question, I have a hunch that intelligence variance (as opposed to IQ) is indeed quantitative.
It kind of make sense. Intelligence seems to correlate positively with simple stuff, like reaction speed or short term memory span.
Qualitative differences may arise as consequence of applying different "processing power" throughout your life.
For the first order effects, you can imagine that if you don't have enough "CPU-minutes", for some problems you simply time out.
For the higher order effects, it's like compound interest. For example, as written in the article, smarter kids start to speak and read sooner, thus they acquire more information and they also acquire it at higher rate. And as we know from financial compound interests, even tiny initial amounts can balloon into huge sums given enough time.
Back to my question about the distribution, if IQ is just a rarity ordering metric based on rarity, then IQ testing is somewhat confused. For example, say someone scoring 150 on an IQ test is rarer than someone scoring 160, they should be ranked higher according to your definition of the metric. If the claim in the article that higher IQs occur more frequently than predicted, then something like this scenario is possible and IQ scores may be unreliable as a rarity ordering metric.
At any rate, is there quantitative metric for intelligence?
Simplified view: people solve a test with a number of questions. They are getting ordered by how many questions they get right.
Tests are constructed to produce Gaussian distribution of numbers of correct answers. Some questions are easy, almost everybody can solve them. Some questions are difficult, almost nobody can solve them. There should be progressively less and less people getting more questions right.
But in reality, it's not a perfect Gaussian distribution. There are some numbers of questions that have more people getting them right than would be predicted by normal distribution.
Now, about quantitativeness. We could get somehow quantitative metric, if questions would simple and uniform in structure, for example test composed just of "how fast you can multiply x-digit numbers" task, or test solely composed of "how fast you can arrange pieces into a particular shape" task.
But it's not like this. There are different tests, some of which have several thematically different sections. Even inside one section, questions do differ a lot (for example, some shapes are harder to compose of primitive elements, how would you quantify this difficulty?).
To further complicate matters, usually completely different tests are used for different intelligence ranges.
And we are not even speaking about normalizations. Your rank is computed just for your age group. For the same raw score, you get extra points if you are younger or older than the optimal age.
If I remember well, there is a fast ramp up of raw scores till 18 years, followed by a slow decline afterwards (rate of decline is slower for more intelligent people).
And then there are national/race differences. And Flynn effect. It's much more messy than it looks.
It seems to be easy to get it wrong. Even the author of the article, who studies giftedness professionally, made such mistake (she tells that IQ 190 to IQ 130 is like IQ 130 to IQ 70).
What's that supposed to mean? The meaning of IQ 190 is that it is 6 standard deviations from the mean (rarity around 1 in billion), while both IQ 130 and 70 are 2 standard deviations from the mean (rarity around 1 in 50).