Chris asked me to post some IQ calculations, and I had forgotten until now. He wanted to know the score that corresponds to the top 2000, 1000, and 40 scores, assuming 250,000,000 in the country. To say you scored in the top 2000 means that you scored better than 99.9992% of the people. To say you were in the top 1000 means you scored better than 99.9996% of the people. To say you were in the top 40 means you scored better than 99.999984% of the people. Now for one sentence of technical stuff. To find the IQ score one needs to find the inverse of the cumulative normal distribution (with mean 100 and standard deviation 15 - the IQ scale). To cut to the chase...
IQ for being in the top 2000: 165
IQ for being in the top 1000: 167
IQ for being in the top 40: 75000100
No, that is not a typo. Several things to note. First, these estimates are conservative in that they use the usual IQ scale (normal with mean 100, standard deviation 15). If the test you took is on another IQ scale (e.g., normal with mean 100, standard devation 16), the numbers would actually be higher.
Second, and more importantly, these values do not account for measurement error. As I very poorly tried to state in the original post, the reason why no one should tell you that you scored in the top 40 is not that it's impossible, but that the measurement isn't precise enough.
Third, and most importantly, these scores are based on the model that is used. It is possible that a score well under 75000100 is in fact in the top 40 IQ scores ever recorded. In fact, I'm sure of it, because no one (let alone 40 people alive in the country) has ever scored that high. The model of the normal distribution works well for many situations - IQ testing included - but usually not at the extremes. For example, many things that can't be negative (like IQ scores) are modeled with a normal distribution, even though the normal extends to values below 0 (in fact, to negative infinity). The model is not built for the extemes - it's built for the population as a whole. That is why claims like "your score is among the top 40 in the country" cannot be made on the model alone. It may be the case that your score is among the top 40 ever recorded, but just based on probability, I highly doubt it. If you'd like, I'd be happy to share an excel spreadsheet for doing these calculations.
Posted by Roy at July 29, 2004 05:13 PMThanks Roy, that's cool. According to those numbers I'm well within the top 1000...which I find hard to believe. But IQs mean so many different things, they're probably, at their very core, useless - they attempt to solidly quantify something (intelligence) that is widely understood to be varied and individual (for example, your intellectual gears turn rationally, almost opposite my interpretive/creative/abstract stylings). In fact they must be crap, you'd have to argue, if I'm one of the "smartest" people in the world. I wouldn't be surprised - in fact I'd bet on - all of our scores being over 150, and there are people like us everywhere. We just drink more than them, and play less Dungeons and Dragons.
Thanks for the math. Maybe IQs just represent the probablilty one will pull a straight flush. Or four queens. Snoogins.
Posted by: Chris at July 29, 2004 11:57 PMI think this is what Roy's been saying all along, but I don't think IQs are worthless- you just have to be careful in how you interpret them. There are a lot of factors that determine how productive/successful an individual will be, and IQ is not a very precise measurement. But, I'd imagine that it is very good for population studies, or for probabilites. Kind of like smoking. Not everyone that smokes is going to develop cancer, but it's still a good indicator of the likeliness that you will develop cancer. And using Chris's example of all of our scores being over 150- look where we all are. We're either in college or college graduates, most of us with cushy office jobs. I think that's a pretty good indicator right there. Yeah, we've got other factors in common that could have contributed to that (white, suburban, middle class), but there were plenty of people from my high school that never went to college or dropped out after they got there, and there's probablly a pretty good corellation to IQ.
Posted by: fatboy at July 30, 2004 08:58 AMHere's my only interaction with IQ affecting life (for those of you that I don't know, I am a special ed. teacher in H-town): In Pennsylvania, the model for determining if a student is eligible for special education is based solely on IQ ,which I think is ridiculous. It's known as the discrepency model and it basically says if there is a discrepency betweened assesed ability (IQ tests) and actual achievement then the student is learning disabled and qualifies for special education. Which translates to a child must have an "average" or "above avergage" IQ to receive special ed. On the other hand, if a student has a low IQ and is performing at the expected level of achievement, he/she receives NO special ed services and is expected to function normally in the general education classroom. God I love our education system as it stands.
Posted by: Denise at July 30, 2004 01:39 PM