rockpile Posted March 6, 2007 Share Posted March 6, 2007 See kiddies, that's why it's important to eat your oatmeal. Otherwise, the parents won't give you the good genes. I think you are just being mean. Link to comment Share on other sites More sharing options...
DC Tom Posted March 6, 2007 Share Posted March 6, 2007 At least based on this paragraph, we're in agreement about the consequences of a test/retest situation, where the correlation between test and retest is less than one. While I can't see any major flaws with your statements about error, the mean of the error isn't what's referred to in the phrase "regression toward the mean." The only reason that's true is because you don't understand that the distribution of a set of measurements of different things and the distribution of error over different measurements of the same thing are two different distributions. You continually treat them as equivalent. They're not. Not even remotely. Which is why you continually fail to understand that you're describing the behavior of the error in its domain, and not the behavior of the population in its domain. Two completely different things...and as I keep saying, things that are different are not the same. 1. A distribution where an average value is more likely than an extreme value2. An initial test where the results are due in whole or in part to random chance 3. Select a subset of members based on their initial test scores. If your subset's scores are above the mean, it will have more lucky members than unlucky ones. If it's below the population mean, the opposite will be true. 4. Retest the members of the subset. The population variance to which you're referring allows condition #1 to be fulfilled. The presence of measurement error allows condition #2 to be fulfilled. Never in the history of mathematics has someone so persistently misunderstood blisteringly simple concepts in the presence of all incontrovertable contradictory evidence. #1 describes the distribution of IQ scores over a population. #2 describes the distribution of error over IQ scores. These are two different distributions. Regression toward the mean of IQ scores in a population is due to the distribution in #1. Regression toward the mean of error is due to the distribution not described in #2 (we'll just assume it's gaussian, as it's a standard assumption). They are two different distributions. You are describing the behavior of #2. It is not the same as the behavior of #1. To prove this: note that the regression toward the mean of each is described by the correlation coefficient of the measured values, which itself is described by the variance of the distribution and covariance of the measured values...in particular, the covariance of measurements in #1 is, though less than 1, significantly greater than zero, whereas the covariance of measurements in #2 IS ZERO. This means that measurements from the two different distributions - IQ scores in #1 and error in #2 - have completely different correlation coefficients. This means that the regression toward the mean, described as it is by the correlation, is completely different for both. This means that IF YOU ARE DESCRIBING THE BEHAVIOR OF THE ERROR OF TEST SCORES, YOU ARE NOT DESCRIBING THE REGRESSION TO THE MEAN OF TEST SCORES. THE MATHEMATICS DOES NOT ALLOW YOU TO DERIVE THE BEHAVIOR OF IQ SCORES FROM THE VARIANCE OF ERROR, BECAUSE THEY ARE DIFFERENT, HENCE NOT THE SAME. And there's your math. I'm reasonably certain you won't understand any of it...but there it is. Link to comment Share on other sites More sharing options...
Orton's Arm Posted March 6, 2007 Author Share Posted March 6, 2007 The only reason that's true is because you don't understand that the distribution of a set of measurements of different things and the distribution of error over different measurements of the same thing are two different distributions. You continually treat them as equivalent. They're not. Not even remotely. Which is why you continually fail to understand that you're describing the behavior of the error in its domain, and not the behavior of the population in its domain. Two completely different things...and as I keep saying, things that are different are not the same. Never in the history of mathematics has someone so persistently misunderstood blisteringly simple concepts in the presence of all incontrovertable contradictory evidence. #1 describes the distribution of IQ scores over a population. #2 describes the distribution of error over IQ scores. These are two different distributions. The point about two different distributions is obvious. Carry on . . . Regression toward the mean of IQ scores in a population is due to the distribution in #1.Regression toward the mean of error is due to the distribution not described in #2 (we'll just assume it's gaussian, as it's a standard assumption). They are two different distributions. You are describing the behavior of #2. It is not the same as the behavior of #1. Okay, I think you're saying that the change in test scores from test to retest is a result of what's going on in #2. If that's what you're saying, you're correct. To prove this: note that the regression toward the mean of each is described by the correlation coefficient of the measured values, which itself is described by the variance of the distribution and covariance of the measured values...in particular, the covariance of measurements in #1 is, though less than 1, significantly greater than zero, whereas the covariance of measurements in #2 IS ZERO. This means that measurements from the two different distributions - IQ scores in #1 and error in #2 - have completely different correlation coefficients. This means that the regression toward the mean, described as it is by the correlation, is completely different for both. This means that IF YOU ARE DESCRIBING THE BEHAVIOR OF THE ERROR OF TEST SCORES, YOU ARE NOT DESCRIBING THE REGRESSION TO THE MEAN OF TEST SCORES. THE MATHEMATICS DOES NOT ALLOW YOU TO DERIVE THE BEHAVIOR OF IQ SCORES FROM THE VARIANCE OF ERROR, BECAUSE THEY ARE DIFFERENT, HENCE NOT THE SAME. And there's your math. I'm reasonably certain you won't understand any of it...but there it is. Your statements in the above paragraph aren't as difficult to understand as you seem to think. In fact, the underlying logic is rather simple and intuitive. There's a strong--but less than 1:1--relationship between your score on I.Q. tests #1 and 2. There's no relationship between the direction or magnitude of the measurement error on the first test and the error on the second test. But the phrase "regression toward mediocrity" was originally coined by Sir Francis Galton, and refers to the regression toward the population's mean. You're certainly welcome to point out whatever sloppiness you feel may exist in that shorthand phrase. But whether you like it or not, the population mean is what's referred to in the phrase "regression toward the mean." Link to comment Share on other sites More sharing options...
Cornerville Posted March 6, 2007 Share Posted March 6, 2007 This should be good news for parents adopting kids from third world countries. Imagine the savings on the college education. Just buy the lawnmower for the little tyke when he's 12, and off he goes. Link to comment Share on other sites More sharing options...
Bungee Jumper Posted March 6, 2007 Share Posted March 6, 2007 But the phrase "regression toward mediocrity" was originally coined by Sir Francis Galton, and refers to the regression toward the population's mean. You're certainly welcome to point out whatever sloppiness you feel may exist in that shorthand phrase. But whether you like it or not, the population mean is what's referred to in the phrase "regression toward the mean." BUT IT'S NOT DUE TO ERROR. Link to comment Share on other sites More sharing options...
Orton's Arm Posted March 7, 2007 Author Share Posted March 7, 2007 BUT IT'S NOT DUE TO ERROR. Regression toward the mean takes place whenever you have a test/retest situation with a correlation between test and retest of less than one. The presence of measurement error will generally cause the correlation between test and retest to be less than one. But hopefully you knew that already. The truth is there are two similar--but somewhat different--phenomena, that for whatever reason both got labeled "regression toward the mean." Phenomenon A is what Sir Francis Galton observed--the children of tall parents are generally closer to the population's mean. Phenomenon B is where those who obtain extreme scores on an imperfect test score closer to the population's mean upon being retested. The reason these two phenomena got lumped together under the same label is because they both refer to the following: 1. An underlying population in which an average value is more likely than an extreme value 2. An initial measurement 3. Taking some subset of the population based on the value of the initial measurement 4. Some form of remeasurement, where results of the remeasurement have a less than 1:1 correlation with the results of the initial measure. Suppose I were to tell you that, say, 80% of a person's gender-adjusted height could be predicted by knowing the height of his or her parents. If I told you that the parents were 1 SD above the mean, then statistically speaking, the most likely value for their children's heights is 0.8 SDs above the mean. Or let's say I told you that 80% of a person's score on an I.Q. retest could be predicted based on this person's score on the initial test. Someone who scored 1 SD above the mean on the first test would be expected to score 0.8 SDs above the mean on the retest. It's this similarity--caused by correlation coefficients less than one--which got the two phenomena lumped together. This, despite the fact that phenomenon A has to do with children being closer to the population's mean than their parents, while phenomenon B is about measurement error's involvement in the misleading appearance of movement toward the population's mean. Link to comment Share on other sites More sharing options...
Lori Posted March 7, 2007 Share Posted March 7, 2007 This looks like the right thread for some Wiki-related news... Wikipedia editor who posed as professor is Ky. dropout Link to comment Share on other sites More sharing options...
erynthered Posted March 7, 2007 Share Posted March 7, 2007 Suppose I were to tell you that, say, 80% of a person's gender-adjusted height could be predicted by knowing the height of his or her parents. If I told you that the parents were 1 SD above the mean, then statistically speaking, the most likely value for their children's heights is 0.8 SDs above the mean. Or let's say I told you that 80% of a person's score on an I.Q. retest could be predicted based on this person's score on the initial test. Someone who scored 1 SD above the mean on the first test would be expected to score 0.8 SDs above the mean on the retest Then if their not, you'd euthanize them, right? Link to comment Share on other sites More sharing options...
Bungee Jumper Posted March 7, 2007 Share Posted March 7, 2007 Regression toward the mean takes place whenever you have a test/retest situation with a correlation between test and retest of less than one. The presence of measurement error will generally cause the correlation between test and retest to be less than one. But hopefully you knew that already. The truth is there are two similar--but somewhat different--phenomena, that for whatever reason both got labeled "regression toward the mean." Phenomenon A is what Sir Francis Galton observed--the children of tall parents are generally closer to the population's mean. Phenomenon B is where those who obtain extreme scores on an imperfect test score closer to the population's mean upon being retested. The reason these two phenomena got lumped together under the same label is because they both refer to the following: 1. An underlying population in which an average value is more likely than an extreme value 2. An initial measurement 3. Taking some subset of the population based on the value of the initial measurement 4. Some form of remeasurement, where results of the remeasurement have a less than 1:1 correlation with the results of the initial measure. Suppose I were to tell you that, say, 80% of a person's gender-adjusted height could be predicted by knowing the height of his or her parents. If I told you that the parents were 1 SD above the mean, then statistically speaking, the most likely value for their children's heights is 0.8 SDs above the mean. Or let's say I told you that 80% of a person's score on an I.Q. retest could be predicted based on this person's score on the initial test. Someone who scored 1 SD above the mean on the first test would be expected to score 0.8 SDs above the mean on the retest. It's this similarity--caused by correlation coefficients less than one--which got the two phenomena lumped together. This, despite the fact that phenomenon A has to do with children being closer to the population's mean than their parents, while phenomenon B is about measurement error's involvement in the misleading appearance of movement toward the population's mean. So now we've gone from I'm wrong and you're right, to I'm right...and even though you're still wrong because you're talking about a "misleading appearance" of what I'm talking about, you're still right because it's the same thing as what I'm talking about... ...which brings us right back to THINGS THAT ARE DIFFERENT ARE NOT THE SAME. Link to comment Share on other sites More sharing options...
Ramius Posted March 7, 2007 Share Posted March 7, 2007 Suppose I were to tell you that, say, 80% of a person's gender-adjusted height could be predicted by knowing the height of his or her parents. If I told you that the parents were 1 SD above the mean, then statistically speaking, the most likely value for their children's heights is 0.8 SDs above the mean. Or let's say I told you that 80% of a person's score on an I.Q. retest could be predicted based on this person's score on the initial test. Someone who scored 1 SD above the mean on the first test would be expected to score 0.8 SDs above the mean on the retest. Nope. 100% completely and entirely wrong. I'm not sure how long its going to take you to realize that heritability applies to a population, NOT TO INDIVIDUALS. 0.8 heritability will tell us that of all the variance in heights within the population are 80% due to genetics, and 20% due to environment. 0.8 HERITABILITY DOES NOT MEAN THAT OFFSPRING WILL BE 80% OF THE HEIGHT OF THE PARENTS! just as aside, what the hell is your background? your online diploma and email correspondences courses dont count either. Neither does your bryant and stratton "degree" Link to comment Share on other sites More sharing options...
DC Tom Posted March 7, 2007 Share Posted March 7, 2007 just as aside, what the hell is your background? your online diploma and email correspondences courses dont count either. Neither does your bryant and stratton "degree" His parents have PhD's, so he has 80% of a graduate education... Link to comment Share on other sites More sharing options...
molson_golden2002 Posted March 7, 2007 Share Posted March 7, 2007 This looks like the right thread for some Wiki-related news... Wikipedia editor who posed as professor is Ky. dropout Link to comment Share on other sites More sharing options...
Ramius Posted March 7, 2007 Share Posted March 7, 2007 This looks like the right thread for some Wiki-related news... Wikipedia editor who posed as professor is Ky. dropout Well, this answers my question of what holcombs arm does for a living. Thanks Lori. Link to comment Share on other sites More sharing options...
Orton's Arm Posted March 7, 2007 Author Share Posted March 7, 2007 Nope. 100% completely and entirely wrong. I'm not sure how long its going to take you to realize that heritability applies to a population, NOT TO INDIVIDUALS. 0.8 heritability will tell us that of all the variance in heights within the population are 80% due to genetics, and 20% due to environment. The 80% narrow-sense heritability means that if you were to try to predict the height of tall people's kids before those kids were born, your best prediction for those individuals is to conclude that they'll be 80% as much above-average in height as are their parents. So if the parents are 1 SD above average, the kids will, on average, be 0.8 SDs above average. What you seem to be pointing out is that some of the kids will may be 0.6 or 0.7 SDs above average, while others might be 0.9 or 1.0 SDs above average. It's always amusing whenever you point out something perfectly obvious as though nobody else was aware of it. just as aside, what the hell is your background? your online diploma and email correspondences courses dont count either. Neither does your bryant and stratton "degree" I have a master's degree, and it's from a better school than whatever Cracker-Jack box degree program you conned into taking you on. Link to comment Share on other sites More sharing options...
Orton's Arm Posted March 7, 2007 Author Share Posted March 7, 2007 So now we've gone from I'm wrong and you're right, to I'm right...and even though you're still wrong because you're talking about a "misleading appearance" of what I'm talking about, you're still right because it's the same thing as what I'm talking about......which brings us right back to THINGS THAT ARE DIFFERENT ARE NOT THE SAME. Oddly enough, I'd been expecting an intelligent response from you. I guess you like to be unpredictable. Link to comment Share on other sites More sharing options...
Orton's Arm Posted March 7, 2007 Author Share Posted March 7, 2007 This looks like the right thread for some Wiki-related news... Wikipedia editor who posed as professor is Ky. dropout It's always disappointing when someone uses fake credentials to lie his or her way into a position of influence or power. But at least nobody that the article mentioned was questioning the accuracy of Jordan's work. That's more than can be said about the NY Times' Jayson Blair. Link to comment Share on other sites More sharing options...
DC Tom Posted March 7, 2007 Share Posted March 7, 2007 I have a master's degree, and it's from a better school than whatever Cracker-Jack box degree program you conned into taking you on. Basket weaving? Link to comment Share on other sites More sharing options...
DC Tom Posted March 7, 2007 Share Posted March 7, 2007 Oddly enough, I'd been expecting an intelligent response from you. I guess you like to be unpredictable. Let's review just one small part of this circus. Way back in November, I said You roll a pair of dice [...]The system has an expectation value (a "mean") of 7. Rolls subsequent to very low or very high rolls (2 or 3, or 11 or 12) will tend to regress toward the mean not because dice are error-prone or inaccurate - they're not, they're very accurate and not the least bit subject to error. It's because there's only 3 ways to roll a 2 or 3, and 33 other possibilities the next time you roll. Regression toward the mean happens because your current measure is deterministic, but your future measure is probabilistic. You responded Suppose you have a die, and you roll it to get some idea as to what its average roll might be. You roll it the first time, and get a six. In this case, your attempt to measure the die's true average roll resulted in an error of 2.5. What will the die yield the second time you roll it? Its expected roll is 3.5--in other words, it will, on average, regress fully toward the mean. In the above case, the expected value of the regression toward the mean was 100%, because the trial was entirely luck-based. A day ago, I say Regression toward the mean is a function of the variance in the statistical distribution of a system. The easiest example of this is a pair of dice, where the roll subsequent to a very high or low roll is closer to the system mean because there are more states available to the system near the mean than there are near the very high or low roll. This holds true for any statistical system with any randomness - which means, any statistical system where measurements are correllated by a factor less than 1. Which is the EXACT SAME THING I SAID IN NOVEMBER. But now, you say: You've uncharacteristically written an error-free paragraph about regression toward the mean. Even though you were dead-set against it in November. But you still insist today that you know what you're talking about. And I'm the one not providing intelligent debate? Link to comment Share on other sites More sharing options...
Ramius Posted March 7, 2007 Share Posted March 7, 2007 Let's review just one small part of this circus. Way back in November, I saidYou responded A day ago, I say Which is the EXACT SAME THING I SAID IN NOVEMBER. But now, you say: Even though you were dead-set against it in November. But you still insist today that you know what you're talking about. And I'm the one not providing intelligent debate? Ha just got pwned...again Link to comment Share on other sites More sharing options...
Alaska Darin Posted March 7, 2007 Share Posted March 7, 2007 I have a master's degree, and it's from a better school than whatever Cracker-Jack box degree program you conned into taking you on. You should check and see if they offer a course in "Knowing When to STFU". Link to comment Share on other sites More sharing options...
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