EC-Bills Posted November 10, 2006 Share Posted November 10, 2006 Is Holcombs Arm calling you a Fag? Fag! What does that " Mean? " 831807[/snapback] Shut up IH! It's only a matter of time before you regress towards the "mean" Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 No, the fact that I'm "afraid" (sic) to answer the question suggests that I'm aware you need a basic education in statistics before you can comprehend the answer. The answer, by the way, is neither. 831826[/snapback] You're wrong on two fronts: first, you are the one who apparently needs a basic education in statistics. Second, the correct answer (in this case) is 725; though it will vary based on the value of Pearson's correlation. In your pair of dice example, the Pearson's correlation is zero: a pair of dice that both roll sixes are neither more nor less likely to get a high roll the second time around than a pair of dice that both roll ones. With the SAT score (or an I.Q. test score) Pearson's correlation is positive, but less than one. Someone who gets a 750 on the math section of the SAT will, on average, get a 725 upon retaking the test. Link to comment Share on other sites More sharing options...
Nervous Guy 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] look bub, I do stats every friggin' day...taken numerous undergrad and grad level stats courses, as well as experimental design...I can safely say you don't know what your talking about, period, end of story. Link to comment Share on other sites More sharing options...
EC-Bills Posted November 10, 2006 Share Posted November 10, 2006 That marvelous die analysis he posted last night actually caused me physical injury. Literally. I laughed so hard, I fell out of my chair and sprained my wrist when I landed. 831811[/snapback] That sucks. No you have to add that to the shortness of breath from laughing so hard and the sore abs*. *abs = abdominal muscles, not the absolute value of a number nor the Austrailian Bureau of Statistics Link to comment Share on other sites More sharing options...
Ramius Posted November 10, 2006 Share Posted November 10, 2006 AND IT'S NOT BECAUSE OF ERROR, IT'S BECAUSE OF THE PROBABILITY DISTRIUBTION, YOU IDIOT!!!! Jesus Christ... 831834[/snapback] In a few weeks at my prospectus defense, i should explain to my committee that my data from the second trials i ran is correct, because error is eliminated automatically in the second test, and i will tell them that my data isnt bad, its regressing toward the mean due to error and see what they say. I'm guessing i will get laughed out of grad school. Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 AND IT'S NOT BECAUSE OF ERROR, IT'S BECAUSE OF THE PROBABILITY DISTRIUBTION, YOU IDIOT!!!! Jesus Christ... Consider a test with no measurement error--height for example. You stand on the scale at the doctor's office, they take out that height measure thing, and measure you. Someone with a height of 6'2" isn't going to get lucky and have a measurement of 6'4"; nor unlucky with a measurement of 6'0". It's the same every time. If your height is measured at 6'2" the first time, it will be 6'2" the second time, and the third time, etc. No regression toward the mean. Now suppose that you introduce measurement error into this test. Someone who measured out at 6'2" may actually be a 6'0" person who got lucky on the first test. Because there is now measurement error in the system, those who obtained exceptionally high measurements the first time are likely to regress toward the mean upon being remeasured. This is because there are more 6'0"s available for getting lucky, than there are 6'4"s available for getting unlucky. The logic is the same for the math section of the SAT. You want to know what someone's average score would be if they were to take the test 1000 times. You give them the test one time to estimate this score. This system involves measurement error--someone with a true score of 725 could get lucky and score a 750; or unlucky and score a 700. Therefore, someone who scores very well the first time will tend to regress toward the mean a little upon retaking the test. Take away the measurement error on that first test, and you take away the regression toward the mean. Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 look bub, I do stats every friggin' day...taken numerous undergrad and grad level stats courses, as well as experimental design...I can safely say you don't know what your talking about, period, end of story. 831841[/snapback] It doesn't sound to me like you've learned a whole lot in those stats courses. Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 Now suppose that you introduce measurement error into this test. Someone who measured out at 6'2" may actually be a 6'0" person who got lucky on the first test. Because there is now measurement error in the system, those who obtained exceptionally high measurements the first time are likely to regress toward the mean upon being remeasured. This is because there are more 6'0"s available for getting lucky, than there are 6'4"s available for getting unlucky. The logic is the same for the math section of the SAT.... 831853[/snapback] I'm curious as to the manner in which "measurement error" is introduced... I'm not sure this is any form of known logic. Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 It doesn't sound to me like you've learned a whole lot in those stats courses. 831854[/snapback] Link to comment Share on other sites More sharing options...
Wraith Posted November 10, 2006 Share Posted November 10, 2006 Consider a test with no measurement error--height for example. You stand on the scale at the doctor's office, they take out that height measure thing, and measure you. Someone with a height of 6'2" isn't going to get lucky and have a measurement of 6'4"; nor unlucky with a measurement of 6'0". It's the same every time. If your height is measured at 6'2" the first time, it will be 6'2" the second time, and the third time, etc. No regression toward the mean. Now suppose that you introduce measurement error into this test. Someone who measured out at 6'2" may actually be a 6'0" person who got lucky on the first test. Because there is now measurement error in the system, those who obtained exceptionally high measurements the first time are likely to regress toward the mean upon being remeasured. This is because there are more 6'0"s available for getting lucky, than there are 6'4"s available for getting unlucky. The logic is the same for the math section of the SAT. You want to know what someone's average score would be if they were to take the test 1000 times. You give them the test one time to estimate this score. This system involves measurement error--someone with a true score of 725 could get lucky and score a 750; or unlucky and score a 700. Therefore, someone who scores very well the first time will tend to regress toward the mean a little upon retaking the test. Take away the measurement error on that first test, and you take away the regression toward the mean. 831853[/snapback] HA, I'm having a hard time getting past the fact that you claim measuring height has no measurement error. Every measurement system has measurement error, most especially ones that involve human judgement such as measuring height in the manner you describe. Measuring capability takes different forms. You talk about measurement error in this thread in reference to a system reporting the "true" value. However, for a measurement system to be capable, it must also be able to tell the difference between two samples that are known to be different. In your example measurement system, what happens when I am 6' 2 5/8ths" while you are 6' 2 3/8ths". Your measurement system would report us both as 6' 2", which while somewhat "true" (we would both be 6' 2" something) is not valuable because a reasonable measurement system would notice the distincition. This is a long way of saying that in your example, you are hiding the measurement error by using an inappropriate and incapable measurement system. The fact that you've used that in an example makes me wonder about your true understanding of what measurement error is. Link to comment Share on other sites More sharing options...
Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 Consider a test with no measurement error--height for example.831853[/snapback] Or a die...which you've already said exhibits regression toward the mean because of error. This all just proves you can't define "measurement" or "error", either. But to take your height example...there is no regression toward the mean when you measure the height of the same person twice, because it's a discrete, exact value. Not probabilistic. However, when two very tall (or very short) people have kids, it is likely (i.e. "it is probable", "there is a probability greater than 50%") that the kids will be closer to average height than the parents. And it doesn't mean the parents or children are the wrong height. It's strictly because of the frequency distribution of people's height in the population, which is directly related to probability. Got it now? Is your warped little idiot mind starting to twig to the difference between "error" and "probability" yet? Link to comment Share on other sites More sharing options...
Taro T Posted November 10, 2006 Share Posted November 10, 2006 you cannot get a mathematical average, or mean, using discrete values/variables. You cannot assign an average value to a die roll, because it is a probability. There is no !@#$ing error in a die roll! According to you, i can pick my alphabet letters, and i should expect an average letter value of M, but i may have an error value of G or X. If being stupid was a crime, you would have been put to death a long long time ago. 831753[/snapback] Yes, you can get a mean value for discrete variables. If you have a 20 year old person and a 30 year old, their average (mean) age is 25. You are correct however in stating that on any particular roll with a fair die you would expect any value from 1-6 with equal probability. You are also correct in stating that you do not expect to roll a 3.5, although if you rolled 1,000 dice the average of all the rolls would be very close to 3.5. You wouldn't expect to have a mode as none of the values should come up significantly more often than any other value. You are also correct in that the outcomes from rolling a single die are not normally distributed. Link to comment Share on other sites More sharing options...
Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 831859[/snapback] Isn't this a !@#$ing riot? Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 I'm curious as to the manner in which "measurement error" is introduced... I'm not sure this is any form of known logic. 831858[/snapback] You have someone's true height. Then you have measured height, which is a function of their true height plus a measurement error term. For example, error could be normally distributed, with a mean of zero and a SD of 1". Or it could be uniformly distributed, with 20% chance of being underestimated by 2"; a 20% chance of being underestimated by 1", a 20% chance of getting correctly measured, etc. I'm not that fussy, because regression toward the mean will happen regardless. The people with very low measured heights are, on average, less lucky than average. They will tend to regress toward the mean upon being remeasured. Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 The fact that you've used that in an example makes me wonder about your true understanding of what measurement error is. 831871[/snapback] ...indeed. Link to comment Share on other sites More sharing options...
Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 Yes, you can get a mean value for discrete variables. If you have a 20 year old person and a 30 year old, their average (mean) age is 25. You are correct however in stating that on any particular roll with a fair die you would expect any value from 1-6 with equal probability. You are also correct in stating that you do not expect to roll a 3.5, although if you rolled 1,000 dice the average of all the rolls would be very close to 3.5. You wouldn't expect to have a mode as none of the values should come up significantly more often than any other value. You are also correct in that the outcomes from rolling a single die are not normally distributed. 831878[/snapback] 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. Link to comment Share on other sites More sharing options...
Wraith Posted November 10, 2006 Share Posted November 10, 2006 Or a die...which you've already said exhibits regression toward the mean because of error. This all just proves you can't define "measurement" or "error", either. But to take your height example...there is no regression toward the mean when you measure the height of the same person twice, because it's a discrete, exact value. Not probabilistic. However, when two very tall (or very short) people have kids, it is likely (i.e. "it is probable", "there is a probability greater than 50%") that the kids will be closer to average height than the parents. And it doesn't mean the parents or children are the wrong height. It's strictly because of the frequency distribution of people's height in the population, which is directly related to probability. Got it now? Is your warped little idiot mind starting to twig to the difference between "error" and "probability" yet? 831876[/snapback] 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. Link to comment Share on other sites More sharing options...
Bungee Jumper Posted November 10, 2006 Share Posted November 10, 2006 They will tend to regress toward the mean upon being remeasured. 831881[/snapback] THE MEAN OF THE NORMALLY DISTRIBUTED ERROR, YOU !@#$ING MORON!!!! Link to comment Share on other sites More sharing options...
Nervous Guy Posted November 10, 2006 Share Posted November 10, 2006 Isn't this a !@#$ing riot? 831880[/snapback] my head hurts...is he related to BF? Link to comment Share on other sites More sharing options...
Orton's Arm Posted November 10, 2006 Share Posted November 10, 2006 HA, I'm having a hard time getting past the fact that you claim measuring height has no measurement error. Every measurement system has measurement error, most especially ones that involve human judgement such as measuring height in the manner you describe. 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. Link to comment Share on other sites More sharing options...
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