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<blockquote data-quote="Ovinomancer" data-source="post: 6844500" data-attributes="member: 16814"><p>You missed my point. Yes, IQ is forced into a normal distribution. However, the data IQ models isn't normally distributed -- it cannot be because the difference between numbers in the data do not have an equal distance between them. The reason it's forced into a false normal distribution is so that normal statistical processes can be run on the numbers, but these stats are even more likely to be abused than normal stats (which have a high abuse rate, see <a href="https://en.wikipedia.org/wiki/Data_dredging" target="_blank">p-hacking</a>) because the use of stats covers up the ordinal nature of the data.</p><p></p><p>Here, an example that I hope will be illuminating. Take contestants in a foot race. You do not time the runners time, but just mark down the order in which they finish the race. So you have 1st, 2nd, 3rd, ..., nth contestants. You run this race a number of times and record the same types of data while also noting how many times each contestant scores in each position. You review your data, and notice that, over time, only a handful routinely place in the top half, and similarly only a smallish group routinely place in the last places. In the middle, there's a bunch of moving around, with people generally staying withing a few places of where they usually finish. You decide you want to use this data to model the general population in terms of speed, and so force your data into a normal distribution that says that only a small number of people will be 1st placers, a few more 2nd placers, and so on all the way through the bell curve. Viola! You now have your SQ, or speed quotient! It's normally distributed, and you can do math on it.</p><p></p><p>But... you only recorded their place finishes. You have no real data about how much time separates 1st and 2nd place finishers vs m and nth place finishers. The data is ordinal, and so doesn't have a known separation between data points. If you instead used time data in your model, you'd find that your previously normal distribution will now skew heavily into a new shape, because the separation between data points will shift.</p><p></p><p>That was my point. You can stand there and say that IQ has a normal distribution by definition all you'd like, but you're just declaring an arbitrary choice to be okay because it was arbitrarily made. Stats done on ordinal data sets are only roughly useful to compare within the set. It's useless outside the set. "Normal distribution" of an ordinal data set is a fiction that's narrowly useful, and dangerous because people tend to attach meaning to such terms that those terms do not deserve. IQ being a forced normal distribution does not make it okay to compare to other normal distributions -- there's nothing magical about the normal model of data other than it makes people think that there's something useful there. The use is in the data. Stats can help find that use, but never, ever, confuse stats for data or assume that because stats was used the results are useful. In this case, ie comparing IQ to anything other than itself, it's not useful and, in fact, misleading. If you think you can compare IQ distribution to 3d6 distribution because normal distribution, the math has fooled you into believing in a lie.</p></blockquote><p></p>
[QUOTE="Ovinomancer, post: 6844500, member: 16814"] You missed my point. Yes, IQ is forced into a normal distribution. However, the data IQ models isn't normally distributed -- it cannot be because the difference between numbers in the data do not have an equal distance between them. The reason it's forced into a false normal distribution is so that normal statistical processes can be run on the numbers, but these stats are even more likely to be abused than normal stats (which have a high abuse rate, see [URL="https://en.wikipedia.org/wiki/Data_dredging"]p-hacking[/URL]) because the use of stats covers up the ordinal nature of the data. Here, an example that I hope will be illuminating. Take contestants in a foot race. You do not time the runners time, but just mark down the order in which they finish the race. So you have 1st, 2nd, 3rd, ..., nth contestants. You run this race a number of times and record the same types of data while also noting how many times each contestant scores in each position. You review your data, and notice that, over time, only a handful routinely place in the top half, and similarly only a smallish group routinely place in the last places. In the middle, there's a bunch of moving around, with people generally staying withing a few places of where they usually finish. You decide you want to use this data to model the general population in terms of speed, and so force your data into a normal distribution that says that only a small number of people will be 1st placers, a few more 2nd placers, and so on all the way through the bell curve. Viola! You now have your SQ, or speed quotient! It's normally distributed, and you can do math on it. But... you only recorded their place finishes. You have no real data about how much time separates 1st and 2nd place finishers vs m and nth place finishers. The data is ordinal, and so doesn't have a known separation between data points. If you instead used time data in your model, you'd find that your previously normal distribution will now skew heavily into a new shape, because the separation between data points will shift. That was my point. You can stand there and say that IQ has a normal distribution by definition all you'd like, but you're just declaring an arbitrary choice to be okay because it was arbitrarily made. Stats done on ordinal data sets are only roughly useful to compare within the set. It's useless outside the set. "Normal distribution" of an ordinal data set is a fiction that's narrowly useful, and dangerous because people tend to attach meaning to such terms that those terms do not deserve. IQ being a forced normal distribution does not make it okay to compare to other normal distributions -- there's nothing magical about the normal model of data other than it makes people think that there's something useful there. The use is in the data. Stats can help find that use, but never, ever, confuse stats for data or assume that because stats was used the results are useful. In this case, ie comparing IQ to anything other than itself, it's not useful and, in fact, misleading. If you think you can compare IQ distribution to 3d6 distribution because normal distribution, the math has fooled you into believing in a lie. [/QUOTE]
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