Regression toward the mean

[Orton's Arm]

And again - in another attempt to futilely point out the blisteringly obvious for HA's benefit - that's variation in a single individual's scores, NOT variation in test scores throughout a normally distributed population. 

 

Not that he'll understand it this time, any more than he has the other fifty times I've said it...

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The only point I've been trying to make here is that someone who obtains an exceptionally high score on an I.Q. test will likely obtain a slightly lower score upon retaking the test. That 150 score is more likely to signal someone with an I.Q. of 140 who got lucky, than someone with an I.Q. of 160 who got unlucky.

[justnzane]

The only point I've been trying to make here is that someone who obtains an exceptionally high score on an I.Q. test will likely obtain a slightly lower score upon retaking the test. That 150 score is more likely to signal someone with an I.Q. of 140 who got lucky, than someone with an I.Q. of 160 who got unlucky.

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so if the only point is that simple, hwy have you been arguing for the past two weeks about it? Also, your final sentence is true, not because of regression, but because there less people score a 160 than 140.

 

EDIT: to honor previous requests, please stop referring to statistical variance as luck

[Bungee Jumper]

The only point I've been trying to make here is that someone who obtains an exceptionally high score on an I.Q. test will likely obtain a slightly lower score upon retaking the test. That 150 score is more likely to signal someone with an I.Q. of 140 who got lucky, than someone with an I.Q. of 160 who got unlucky.

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So NOW you're point is "regression toward the mean happens", and not "regression toward the mean happens because of measurement error, just like when you don't roll a 3.5 with a single die..." like it has been for the past month.

 

 

Do you honestly think you can blather on for fifty or so pages, and then suddenly wake up one day and claim you were saying something else?

[Orton's Arm]

So NOW you're point is "regression toward the mean happens", and not "regression toward the mean happens because of measurement error, just like when you don't roll a 3.5 with a single die..." like it has been for the past month. 

 

 

Do you honestly think you can blather on for fifty or so pages, and then suddenly wake up one day and claim you were saying something else? 

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No, I've been saying the same thing all along. But now you're finally starting to understand it.

[Ramius]

No, I've been saying the same thing all along. But now you're finally starting to understand it.

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nice little switch attempt there mr kerry. You spend 50 pages arguing that error causes regression to the mean, and now, since thats been proven wrong, you are arguing that regression to the mean just simply happens. way to change your story after you got spanked like a school girl.

[Bungee Jumper]

No, I've been saying the same thing all along. But now you're finally starting to understand it.

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So what were you last couple hundred posts, then? Measurement error?

[Orton's Arm]

nice little switch attempt there mr kerry. You spend 50 pages arguing that error causes regression to the mean, and now, since thats been proven wrong, you are arguing that regression to the mean just simply happens. way to change your story after you got spanked like a school girl.

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Wrong, again. Suppose you had a population with 10 190s, 100 180s, and 1000 170s. Measure the I.Q.s of these people with a perfect test. The 190s will all get a 190, the 180s will all get a 180, etc.

 

But now suppose it's possible to get lucky or unlucky on the test due to an element of measurement error. Someone who scores a 180 could be either a lucky 170, a luck-neutral 180, or an unlucky 190. Of those three possibilities, the lucky 170 is more likely than the unlucky 190. This is because there are more 170s available for getting lucky, than there are 190s available for getting unlucky. Therefore, someone who scores a 180 on the test the first time around is expected to get a somewhat lower score upon retaking the test.

 

This phenomenon is what I've been describing all along. It requires measurement error to happen, just as it requires a non-uniform distribution to happen. To say that either of these phenomenon alone "cause" the phenomenon would be mistaken; as both are required for it to take place.

[Taro T]

Wrong, again. Suppose you had a population with 10 190s, 100 180s, and 1000 170s. Measure the I.Q.s of these people with a perfect test. The 190s will all get a 190, the 180s will all get a 180, etc.

 

But now suppose it's possible to get lucky or unlucky on the test due to an element of measurement error. Someone who scores a 180 could be either a lucky 170, a luck-neutral 180, or an unlucky 190. Of those three possibilities, the lucky 170 is more likely than the unlucky 190. This is because there are more 170s available for getting lucky, than there are 190s available for getting unlucky. Therefore, someone who scores a 180 on the test the first time around is expected to get a somewhat lower score upon retaking the test.

 

This phenomenon is what I've been describing all along. It requires measurement error to happen, just as it requires a non-uniform distribution to happen. To say that either of these phenomenon alone "cause" the phenomenon would be mistaken; as both are required for it to take place.

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No, even with a "perfect test" there will STILL be variation in what individuals within the population will score. It won't be a function of measurement error as most would define measurement error, it will be due to the variance within the test subjects themselves. By definition, a perfect test would exhibit NO measurement error.

 

Actually, you would expect a single someone who scored a 180 (especially on a perfect test) to score a 180 upon retaking the test. You would expect the average score of the entire population that scored 180 on the original test to have an average score that is slightly lower.

 

I guarantee you, if we bet $1,000 on what score each person that took the original test will score on the 2nd test that you will owe me a lot of money betting that those 180's will turn into 170's.

 

At least you realize that measurement error is not required for your observations to occur. Especially, because in your example (a perfect test) there would be NO measurement error.

[Orton's Arm]

No, even with a "perfect test" there will STILL be variation in what individuals within the population will score.  It won't be a function of measurement error as most would define measurement error, it will be due to the variance within the test subjects themselves.  By definition, a perfect test would exhibit NO measurement error.

 

Actually, you would expect a single someone who scored a 180 (especially on a perfect test) to score a 180 upon retaking the test.  You would expect the average score of the entire population that scored 180 on the original test to have an average score that is slightly lower.

 

I guarantee you, if we bet $1,000 on what score each person that took the original test will score on the 2nd test that you will owe me a lot of money betting that those 180's will turn into 170's.

 

At least you realize that measurement error is not required for your observations to occur.  Especially, because in your example (a perfect test) there would be NO measurement error.

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You seem to be saying two different things here: 1) measurement error is not required to produce variation in individual scores, because a given person's ability to think varies based on the amount of rest, time of day, and other factors. 2) someone who scores a 180 on an I.Q. test (even one with measurement error) will, on average, score a 180 upon retaking the test.

 

I agree with point #1, and strongly disagree with point #2.

[Bungee Jumper]

I agree with point #1, and strongly disagree with point #2.

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That's because you're a !@#$ing moron.

[Orton's Arm]

That's because you're a !@#$ing moron.

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Thank you for making your position on point #2 perfectly clear.

[Taro T]

You seem to be saying two different things here: 1) measurement error is not required to produce variation in individual scores, because a given person's ability to think varies based on the amount of rest, time of day, and other factors. 2) someone who scores a 180 on an I.Q. test (even one with measurement error) will, on average, score a 180 upon retaking the test.

 

I agree with point #1, and strongly disagree with point #2.

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I did not state what you think I did on point 2. I said you would expect an INDIVIDUAL that scored a 180 on the test to get it again the 2nd time. Especially, if you assume that you have a "perfect test" and the magnitude of the individual variation is small, then MOST of the people that scored a 180 would have done so because that is what their underlying score should be. There would be a few "true 170's" that scored the 180 on the 1st test and fewer "true 190's" that scored 180 on the 1st test.

 

So, upon retesting, the majority of the people that scored 180 the 1st time would score 180 AGAIN. You would get a few 170's, and fewer 190's. Thus, a SINGLE INDIVIDUAL would be expected to get the 180 again. But the AVERAGE score of the subpopulation as a whole would be expected to be lower than 180.

 

I thought stating

(a)ctually, you would expect a single someone who scored a 180 (especially on a perfect test) to score a 180 upon retaking the test.  You would expect the average score of the entire population that scored 180 on the original test to have an average score that is slightly lower

to be clear and straight forward.

 

Also, and I think you already realize this, but am not positive of that; some of the people that get 160's and 170's on the 2nd test will be people whose "true score" is in fact 180 (there may even be some 190's going there on the 2nd one as well) and conversely for the 2nd test 190's.

 

EDIT: You do realize that the "average" score for an INDIVIDUAL is that individual's score? That is NOT necessarily the "average" score for the subpopulation that you are referring to. Although a particular individual WOULD be expected to get a 180 on the perfect retest, the average score of the individuals taking that perfect retest would be less than 180.

[Orton's Arm]

I did not state what you think I did on point 2.  I said you would expect an INDIVIDUAL that scored a 180 on the test to get it again the 2nd time.  Especially, if you assume that you have a "perfect test" and the magnitude of the individual variation is small, then MOST of the people that scored a 180 would have done so because that is what their underlying score should be.  There would be a few "true 170's" that scored the 180 on the 1st test and fewer "true 190's" that scored 180 on the 1st test. 

 

So, upon retesting, the majority of the people that scored 180 the 1st time would score 180 AGAIN.  You would get a few 170's, and fewer 190's.  Thus, a SINGLE INDIVIDUAL would be expected to get the 180 again.  But the AVERAGE score of the subpopulation as a whole would be expected to be lower than 180.

 

I thought stating  to be clear and straight forward.

 

Also, and I think you already realize this, but am not positive of that; some of the people that get 160's and 170's on the 2nd test will be people whose "true score" is in fact 180 (there may even be some 190's going there on the 2nd one as well) and conversely for the 2nd test 190's.

 

EDIT: You do realize that the "average" score for an INDIVIDUAL is that individual's score?  That is NOT necessarily the "average" score for the subpopulation that you are referring to.  Although a particular individual WOULD be expected to get a 180 on the perfect retest, the average score of the individuals taking that perfect retest would be less than 180.

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I think that we're close to being in agreement. What's creating the appearance of difference here is how we're going about describing expected value. I've been taught to think of expected value in probablistic terms. For example, consider a project with two possible outcomes. Outcome 1 produces $0, and outcome 2 produces $100. There's a 20% chance of outcome 1, and an 80% chance of outcome 2. The expected outcome for the project is 20% * $0 + 80% * 100 = $80.

 

What you're calling the "expected outcome" of the retake I would call the "median outcome" of the retake. But other than this difference, we're on the same page.

[Bungee Jumper]

I think that we're close to being in agreement. What's creating the appearance of difference here is how we're going about describing expected value. I've been taught to think of expected value in probablistic terms. For example, consider a project with two possible outcomes. Outcome 1 produces $0, and outcome 2 produces $100. There's a 20% chance of outcome 1, and an 80% chance of outcome 2. The expected outcome for the project is 20% * $0 + 80% * 100 = $80.

 

What you're calling the "expected outcome" of the retake I would call the "median outcome" of the retake. But other than this difference, we're on the same page.

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You're not even reading the same book as everyone else. You're still confusing variance with error.

[Ramius]

Wrong, again. Suppose you had a population with 10 190s, 100 180s, and 1000 170s. Measure the I.Q.s of these people with a perfect test. The 190s will all get a 190, the 180s will all get a 180, etc.

 

But now suppose it's possible to get lucky or unlucky on the test due to an element of measurement error. Someone who scores a 180 could be either a lucky 170, a luck-neutral 180, or an unlucky 190. Of those three possibilities, the lucky 170 is more likely than the unlucky 190. This is because there are more 170s available for getting lucky, than there are 190s available for getting unlucky. Therefore, someone who scores a 180 on the test the first time around is expected to get a somewhat lower score upon retaking the test.

 

This phenomenon is what I've been describing all along. It requires measurement error to happen, just as it requires a non-uniform distribution to happen. To say that either of these phenomenon alone "cause" the phenomenon would be mistaken; as both are required for it to take place.

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Bzzzzzt. Incorrect answer. Please try again.

 

Individual data points do NOT regress towards the population mean.

[justnzane]

today i was in south buffalo for a teaching test, and i saw a question in my booklet that had a bell curve in it. My first thought was "Oh crap where is Holcomb's Arm, i can use his help" MY second thought was "sh-- there is no regression in this question"

[Ramius]

today i was in south buffalo for a teaching test, and i saw a question in my booklet that had a bell curve in it. My first thought was "Oh crap where is Holcomb's Arm, i can use his help"    MY second thought was "sh-- there is no regression in this question"

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I hope that today is the only time you have to take the teaching test. If not, you are in trouble, because according to holcombs arm, your score is going to be worse next time, due to regression to the mean.

[justnzane]

I hope that today is the only time you have to take the teaching test. If not, you are in trouble, because according to holcombs arm, your score is going to be worse next time, due to regression to the mean.

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hahaha, yeah i didn't get a chance to study for this one with huge assignments due this past week and tuesday. (im working on a unit plan as i am typing this) But i think i did well enough, and if i didn't i'll be able to prove HA wrong. In addition, to get certified to teach in NYS, you need to pass 3 different tests and successfully complete student teaching plus another 100 hours in the classroom.

[Bungee Jumper]

Bzzzzzt. Incorrect answer. Please try again.

 

Individual data points do NOT regress towards the population mean.

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Wait...we're back to error causing regression toward the mean again? I thought he just said he didn't say that, after a couple hundred posts of saying it?

[Bungee Jumper]

MY second thought was "sh-- there is no regression in this question"

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You should have looked again. The test would have regressed toward the regression if you remeasured it.