Defining IQ

[whswhs]

Originally Posted by johndallman

To make the problem even less tractable, the standard deviation of a 3d6 roll is 3.0.

Though "what percentage of the population has a lower score than this" and "what is the probability of succeeding at a task of average difficulty" aren't necessarily the same question. I expect you know this, but it seems worth mentioning to avoid a possible sidetrack.

[(E)]

Looking at this another way, How would you model an IQ test in Gurps?


Subject A has a GURPS IQ of 14
Subject B has a GURPS IQ of 8 plus lightning calculator, eidetic memory, spacial awareness and a disadvantage that makes their thinking more analytical, throw in a quirk "likes taking tests"

[malloyd]

I'm in the real world IQ scores don't even map to other real world IQ scores camp.

Having spent most of my grade school years in 70s era gifted programs in the DC area, complete with frequent psychological research projects, I suspect I've taken more different kinds of "IQ" and other intelligence tests than most people, and can assure you the correlation is horrible even with each other, never mind anything else. My measured IQ is somewhere between 110 and 220. That's not a measurement, that's a vague suggestion.

I figure IQ testing is about as useful as polygraphs or personality tests - maybe worthwhile as part of some sort of initial screening (if you have a pool that has lots of good candidates in it minimizing time wasted considering the bad ones is often quite a reasonable trade for accidentally screening out some fraction of the good ones after all), but not much more than that.

[Polydamas]

Originally Posted by Icelander

Someone who is very good not only at their specialsation, but also at many other IQ-based tasks, like someone who is a scientist, self-promoter and media personality, is widely popular among peers, good at arranging things and running organisations, etc., that's a candidate for high IQ.

Which is another point. Suppose that you want to create GURPS stats for a historical figure, and you have both an IQ score (how? probably hearsay based on an indirect source which never actually saw the test) and a list of things they were good and bad at (based on multiple, independent sources who saw their work). Given that Intelligence is 'ability at a long list of Skills, plus default Will and Perception' why would anyone use the IQ score, which is a psychometric test trying to estimate another kind of small-i intelligence, and not just rely on the list of skills to decide what balance of Intelligence and Talents to give them?

[JoelSammallahti]

Firstly, my suggestion to the OP, and secondly, my rant on the subject.

1. On the OP's question

I would suggest not treating Gurps IQ as normally distributed. Scores of 5 or less in IQ are, after all, primarily reserved for nonsapient animals and maybe suitable for severely persons with severe mental disabilities, while scores of 15+ are remarkable but not straight-up superhuman. If Gurps IQ is normally distributed, 5- and 15+ should be equally common.

You could treat the square root of IQ as normally distributed. If you do that, you end up with 5- and 17+ being roughly as common, so you get a little more head room in the mid- and upper range where you'll find most PCs. Or instead of a square root (or higher root) transformation, you could take the log of IQ. But I think a simpler and more workable way to go would be to treat each point of IQ below 10 as one standard deviation below average, and each point above 10 as some fraction of a standard deviation above average. At 1/2, you'd get real-world IQ 145 corresponding to Gurps IQ 16, while at 2/3, real-world IQ 160 would be a match for Gurps IQ 16. Something like that.


2. On IQ in general

Caveat: I'm not an expert in psychometrics, but I have studied the field, written my master's thesis in it, administered and scored a couple hundred IQ tests, and participated in designing test protocols. So I'm not a complete outsider either.

TL;DR: Gurps IQ is a reasonably good match for real-life IQ.

The idea that real-life IQ is mostly just a measure of your test taking ability is complete bunk. The central finding in all of psychometrics, by no means obvious, but solidly confirmed by a hundred years of rigorous research, is that all mental abilities are positively correlated, and that a large part of this positive correlation is attributable to one factor, called general intelligence, or g. In psychology, there are few concepts that we can put great confidence in, but general intelligence is definitely in the top 5. We can't measure it perfectly, but the test-retest reliability is higher than or roughly equal to that for many physiological traits we take for granted, like blood pressure or body fat percentage, and the predictive value for real-life outcomes like job performance, academic achievements, and not ending up in prison, is notable if not enormous.

No single task is exactly representative of general intelligence, but in any given mental task in which we can measure performance, some non-negligible part of the variation in performance is explained by g. That includes tasks that would most certainly fall under Per or Will in Gurps, such as visual and auditive detection thresholds, scanning for a particular stimulus, controlling attention under distraction, and delaying gratification. It also includes tasks relating to social cognition, like understanding emotions and predicting the behavior of other people.

In most tasks, the g-loading, or fraction of variance in performance attributable to general intelligence, varies between .2 and .7 or so. That corresponds to correlation coefficients of .45-.83. Those are big numbers! Just like a Gurps character's effective skill on any given mental task is going to have a pretty high, but not perfect, correlation with their IQ score, once you take into account points spent on the skill in question, if any, and bonuses and penalties from Advantages and Disadvantages.

Now, there are any number of anecdotes about people who are supposedly really smart in their own field and dumb in everything else. Now, that's possible in real life, and it's possible in Gurps, but it's not the way to bet in either. In most cases, smart people are smart across the board, with moderate individual strengths and weaknesses relative to overall ability. Some people are more skewed than others, but nobody's a grab-bag of genius here and idiot there. (Or at least, a vanishingly small number of people are like that.)

Let's take the Feynman example people are fond of. Undoubtedly a genius, but only got 125 on an IQ test in high school. Now, starting with the fact that 125 is still in the top 5% of the population, we're not talking about a genius physicist who gets a lousy IQ score; we're talking about an overall smart person who's really smart in physics. Second, we don't know what that test he took in high school was like. If it was strongly focused on verbal relative to nonverbal performance, we shouldn't be surprised if his score isn't all that representative of his performance in his strong field. Third, general intelligence has its highest predictive value in the middle region of the distribution, partly owing to the fact (somewhat obvious) that measuring outliers is hard, and partly to the apparent fact (considerably less obvious or certain) that outliers tend to be less uniform. In GURPS, I would have no problem with Feynman as IQ 12 with 3-4 levels of Talent. The system supports that and treats it as exceptional, which Feynman most certainly was.

[AlexanderHowl]

And Feynman could have had a natural talent for Physics that was represented by having a natural level of Physics at IQ+4. When combined with a Physics Talent 4 (which would include Astronomy, Mathematics, Physics, and Research) and IQ 12, he would started with a Physics-20 and just gotten better.

[Sam Baughn]

Originally Posted by Polydamas

Given that Intelligence is 'ability at a long list of Skills, plus default Will and Perception' why would anyone use the IQ score, which is a psychometric test trying to estimate another kind of small-i intelligence, and not just rely on the list of skills to decide what balance of Intelligence and Talents to give them?

Because if IQ tests are too inaccurate for you, an entirely subjective assessment of skill level should be considered even worse and even if you could quantify skill better than general intelligence, skill tells you little about the underlying attribute.

GURPS PCs tend to have skill levels which cluster around their skill levels because that's an efficient way of spending your points. Real world people don't have the option to trade points in a skill for points in attribute, so their ability at a task is likely to be a really bad way to estimate their underlying abilities. A competent doctor might have Physician skill around 14-15 in GURPS, but that doesn't tell you if they are an IQ 16 genius with their skill at IQ-1 or a dull but dedicated type with IQ 10 and skill at IQ+4.

[Rupert]

Originally Posted by malloyd

Having spent most of my grade school years in 70s era gifted programs in the DC area, complete with frequent psychological research projects, I suspect I've taken more different kinds of "IQ" and other intelligence tests than most people, and can assure you the correlation is horrible even with each other, never mind anything else. My measured IQ is somewhere between 110 and 220. That's not a measurement, that's a vague suggestion.

An acquaintance of mine some years ago who was a research psychologist said that giving IQ tests to other psychologists was a waste of time, because even if they didn't know all the answers to that specific test, they'd seen and done so many that they could guess the correct answers often enough to make them worthless (or thought they could, which still makes the results worthless). So-called personality tests were even worse.

[whswhs]

Originally Posted by JoelSammallahti

The idea that real-life IQ is mostly just a measure of your test taking ability is complete bunk. The central finding in all of psychometrics, by no means obvious, but solidly confirmed by a hundred years of rigorous research, is that all mental abilities are positively correlated, and that a large part of this positive correlation is attributable to one factor, called general intelligence, or g. In psychology, there are few concepts that we can put great confidence in, but general intelligence is definitely in the top 5. We can't measure it perfectly, but the test-retest reliability is higher than or roughly equal to that for many physiological traits we take for granted, like blood pressure or body fat percentage, and the predictive value for real-life outcomes like job performance, academic achievements, and not ending up in prison, is notable if not enormous.

However, psychometrics has also identified the "Big 5" traits in personality: Openness to Experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism—or its opposite pole, Emotional Stability. These also seem to have high stability and to keep turning up in a variety of psychological studies. And from looking at Emotional Stability as a trait, it seems to cover a lot of things subsumes under Will fairly closely.

[JoelSammallahti]

Originally Posted by whswhs

However, psychometrics has also identified the "Big 5" traits in personality: Openness to Experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism—or its opposite pole, Emotional Stability. These also seem to have high stability and to keep turning up in a variety of psychological studies. And from looking at Emotional Stability as a trait, it seems to cover a lot of things subsumes under Will fairly closely.

Absolutely. Both Conscientiousness and Neuroticism/Stability would tell you as much or more about a Gurps character's Will score as their intelligence. And the g-loadings for many tasks that are IQ-based in Gurps are low! For example rhythm sense is almost independent of general intelligence, so you could argue that Musical Instrument (Drums) shouldn't be based on IQ. Likewise with emotional recognition, the loadings are really modest. There are other cases like that. And conversely things that Gurps separates completely from IQ do have notable g-loadings, like manual dexterity and even strength. But Gurps makes the reasonable and necessary choice of just basing every task on the Attribute that's the most convenient match overall.

You could do it differently, of course! One of my personal areas of interest is cognitive epidemiology: the relationship between IQ and all-cause mortality is surprisingly strong: smart people not only don't die in accidents as much, they also don't get sick as much! There are somewhat conflicting results regarding how much of that effect is due to smarter people taking better care of their health, how much is due to general fitness-reducing mutational load, how much is assortative mating... It gets complicated, and even big datasets leave a lot of questions on the table. So by no means does Gurps model reality perfectly in this respect, but then again, we have no perfect model to start with.

(Re: Personality, I personally think the developers of the five-factor model made bad choices when selecting the orientations of their factors, and past the first 2-3, the orthogonality and validity of the factors is a little bit iffy. You can have an equally valid factor structure from the same data that corresponds better to some interesting outcome variables and related concepts, but it's a matter of taste as much as science.)