Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 We are arguing the same side here, but allow me a slight nitpick. I would very much argue against height being a discrete value. Length in any form (such as height of person) is pretty much as continuous a phenomenon as one could find. An incapable measurement system could make continuous data seem discrete, but it certainly would not make it discrete. It's the so-called "chunky data" effect. 831884[/snapback] True enough...but like you said, it's a nitpick. I'm 76 inches tall, Nervous Guy's 76.003124 inches tall. But in the context of this discussion...we're both 76 inches tall, simply because that's how the data's collected and portrayed by anyone trying to determine the distribution of height among the population (if you'll pardon that phrasing, I know it's awkward). That's also why I used the two dice example before...it is a definitively discrete phenomenon that displays no inaccuracy, no error, and the binomial distribution of possibile values is a reasonable approximation of a normal distribution for the purpose of explaining regression toward the mean. Population height can be treated as discrete...but like you said, it isn't...and now you've just introduced the fact that height measurement is in fact only possible to a certain degree of precision, which is going to make Mr. Potato Head say "See, there's error! I was right!" Link to comment Share on other sites More sharing options...
Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 my head hurts...is he related to BF? 831887[/snapback] I honestly think BF would have figured all this out by now. Seriously, have I really been that unclear in explaining regression toward the mean? I thought my two dice example was pretty !@#$ing clear, myself... Link to comment Share on other sites More sharing options...
Taro T Posted November 10, 2006 Share Posted November 10, 2006 The problem is, even though the average value of a multitude of die rolls (or even the faces of a single die) is 3.5...it doesn't really mean anything. It's an average of a discretely valued system that doesn't actually exist in the set of values of the system. So who cares? It's not a meaningful characterization of any property of the system - it is a characterization, mind you, just not a meaningful one. It sure as hell doesn't mean the die has a "true value" of 3.5, like HA is trying to say. 831883[/snapback] You are definitely correct that the 3.5 has no predictive use. Nor can the state of the die ever be 3.5. Link to comment Share on other sites More sharing options...
GG Posted November 10, 2006 Share Posted November 10, 2006 A dozen? Where did you come up with that number? Ramius's contributions to this discussion have shown me only that it would be a mistake for any employer to hire him to do serious statistical work. 831824[/snapback] There are SIX on this page alone. (which in your logic would cause the dozen to digress to as the mean) Link to comment Share on other sites More sharing options...
Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 You are definitely correct that the 3.5 has no predictive use. Nor can the state of the die ever be 3.5. 831898[/snapback] But you can use it to determine the error of a single die roll! Link to comment Share on other sites More sharing options...
Wraith Posted November 10, 2006 Share Posted November 10, 2006 It was a hypothetical example, intended strictly to show what happens in systems without measurement error versus systems with such error. The fractional inch problem you described isn't relevant to that hypothetical example. Mostly, the point I'm illustrating is that the presence of measurement error on the first test means that the results from second test will tend to regress toward the mean. The larger the measurement error, the greater the expected regression toward the mean. For instance, say that your measurement system had the potential to be off by a foot. Someone who measured 7'5" the first time around is likely to regress toward the mean quite considerably upon being retested. This is because there are more people who are 6'5" available for getting lucky than there are people who are 8'5" available for getting unlucky. 831892[/snapback] So what exactly are you arguing for/against in this entire debate? What you've said is true, but not because measurement error is causing regression towards the mean but because both sample population and measurement error are normally distributed. What is the conflict about? Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 I honestly think BF would have figured all this out by now. Seriously, have I really been that unclear in explaining regression toward the mean? I thought my two dice example was pretty !@#$ing clear, myself... 831895[/snapback] no not unclear...4 dice example would be better. and BTW I'm actually 76.004124 inches...close enough though.... Link to comment Share on other sites More sharing options...
Ramius Posted November 10, 2006 Share Posted November 10, 2006 So what exactly are you arguing for/against in this entire debate? What you've said is true, but not because measurement error is causing regression towards the mean but because both sample population and measurement error are normally distributed. What is the conflict about? 831902[/snapback] the whole arguement in this thread is that holcombs arm is claiming that error causes regression toward the mean, not the normal distribution. He claims that he's right, and 3+ published scientists on this board, thousands others elsewhere, and mainstream math is wrong. Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 Population height can be treated as discrete...but like you said, it isn't...and now you've just introduced the fact that height measurement is in fact only possible to a certain degree of precision, which is going to make Mr. Potato Head say "See, there's error! I was right!" 831893[/snapback] discuss: dp x dx > h / (2 x pi) = Planck's constant / (2 x pi)... Link to comment Share on other sites More sharing options...
Ramius Posted November 10, 2006 Share Posted November 10, 2006 I honestly think BF would have figured all this out by now. Seriously, have I really been that unclear in explaining regression toward the mean? I thought my two dice example was pretty !@#$ing clear, myself... 831895[/snapback] It took holcombs arm 3 hours to cook retatta. But he may have been regressing toward the mean while cooking, so i'm not sure. Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 So what exactly are you arguing for/against in this entire debate? What you've said is true, but not because measurement error is causing regression towards the mean but because both sample population and measurement error are normally distributed. What is the conflict about? 831902[/snapback] To the best of my understanding, the conflict is about this: I feel that someone who scores a 190 on an I.Q. test will, upon being retested, generally obtain a lower score the second time around. I feel that this is because there is an element of luck (or measurement error) in determining someone's true I.Q. Thus, someone with a true I.Q. of 180 might be mislabeled as a 190, or vice versa. The population of people who score a 190 on an I.Q. test consists of those with true I.Q.s of 180 who got lucky, 190s who scored correctly, and 200s who got unlucky. There will be more lucky 180s in this group, than unlucky 200s. When someone who scored a 190 gets retested, that person's expected second score reflects the fact that he might well be a 180 who got lucky the first time around. His expected second score is lower than 190, because the odds that he's a lucky 180 are higher than the odds he's an unlucky 200. Suppose that two people who scored a 190 on the I.Q. test get married and have kids. Suppose further that their kids have I.Q.s in the low 180s. On the surface, it appears as though the children's I.Q.s are closer to the mean than those of their parents. But that's not necessarily the case, because the parents would likely have gotten a score in the low 180s themselves had they retaken the I.Q. test. Link to comment Share on other sites More sharing options...
Wraith Posted November 10, 2006 Share Posted November 10, 2006 the whole arguement in this thread is that holcombs arm is claiming that error causes regression toward the mean, not the normal distribution. 831909[/snapback] If he was ever arguing that, he doesn't appear to be now. Link to comment Share on other sites More sharing options...
GG Posted November 10, 2006 Share Posted November 10, 2006 If he was ever arguing that, he doesn't appear to be now. 831918[/snapback] You have to give him credit for consistently doing that, as well. Link to comment Share on other sites More sharing options...
Wraith Posted November 10, 2006 Share Posted November 10, 2006 You have to give him credit for consistently doing that, as well. 831924[/snapback] I may have missed it when he explicitely stated that measurement error is causing the regression towards the mean, but that doesn't seem to be what the argument is about here at all anymore. I do not think anyone would argue that the phenomenon HA is describing does not happen. It seems to be that you are arguing about what the cause of that phenomenon is. Fair enough: Without measurement error, this phenomenon could not occur. That is because without measurement error, there would be no deviation from the true results. So if HA is saying that measurement error is needed for this phenomenon to occur, he would in fact be correct. However, while measurement error is necessary (because it causes the necessary deviation) the regression towards mean is really happening because the sample population (the range of "true" values) and the error are normally distributed, which is what Bungee Jumper is arguing. This is also true. I have not seen HA say that the normal distribution is NOT causing the regression. His example he just laid out in a response to me shows he understands how the normal distribution is causing the phenomenon. So are we really just arguing over semantics? EDIT: I liken it to someone saying that stretching a rubber band is causing it to snap back to it's original form. Yes, the displacement needs to occur for the snap back to occur, but the snap back is actually occuring because of the elasticity of the rubber band. Both are necessary. It seems to me to be, at least right now, an argument of semantics. Link to comment Share on other sites More sharing options...
daquixers_is_back Posted November 10, 2006 Share Posted November 10, 2006 the whole arguement in this thread is that holcombs arm is claiming that error causes regression toward the mean, not the normal distribution. He claims that he's right, and 3+ published scientists on this board, thousands others elsewhere, and mainstream math is wrong. 831909[/snapback] Who are the 3+ published scientists? Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 I may have missed it when he explicitely stated that measurement error is causing the regression towards the mean, but that doesn't seem to be what the argument is about here at all anymore. I do not think anyone would argue that the phenomenon HA is describing does not happen. It seems to be that you are arguing about what the cause of that phenomenon is. Fair enough: Without measurement error, this phenomenon could not occur. That is because without measurement error, there would be no deviation from the true results. So if HA is saying that measurement error is needed for this phenomenon to occur, he would in fact be correct. However, while measurement error is necessary (because it causes the necessary deviation) the regression towards mean is really happening because the sample population (the range of "true" values) and the error are normally distributed, which is what Bungee Jumper is arguing. This is also true. I have not seen HA say that the normal distribution is NOT causing the regression. His example he just laid out in a response to me shows he understands how the normal distribution is causing the phenomenon. So are we really just arguing over semantics? EDIT: I liken it to someone saying that stretching a rubber band is causing it to snap back to it's original form. Yes, the displacement needs to occur for the snap back to occur, but the snap back is actually occuring because of the elasticity of the rubber band. Both are necessary. It seems to me to be, at least right now, an argument of semantics. 831941[/snapback] An excellent post, and I find the rubber band analogy very apt. I feel you truly understand the phenomenon I've been trying so hard to describe. Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 Who are the 3+ published scientists? 831948[/snapback] BJ, Ramius and myself...there were others...like good old T-Bone (who BTW is confounded by his support of BJ's position in this debate). Link to comment Share on other sites More sharing options...
Ramius Posted November 10, 2006 Share Posted November 10, 2006 BJ, Ramius and myself...there were others...like good old T-Bone (who BTW is confounded by his support of BJ's position in this debate). 831956[/snapback] add in Coli as well. Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 add in Coli as well. 831961[/snapback] my bad...sorry E. Link to comment Share on other sites More sharing options...
Johnny Coli Posted November 10, 2006 Share Posted November 10, 2006 add in Coli as well. 831961[/snapback] The beauty of this thread is that you can leave it for a week and then come back to it and start arguing exactly where you left off ten pages ago. Others will pick up the slack in your absence, and you don't even have to read over what you've missed. Some new and exciting misinterpretation of science and statistics is waiting for you when you return. Link to comment Share on other sites More sharing options...
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