Regression toward the mean

[Chilly]

Don't tell me you missed the part where he said a rubber band stretches because of measurement error...

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Wait.... WHAT??

[Ramius]

I had been ignoring that other thread since it reached a decent amount of pages for the most part.  I think I'll continue to do so.

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You're not missing much.

 

Bungee throwing monkey proves how holcombs arm is wrong, and explains it fully, and easily understandable. Numerous posters, including published scientists who do stats for a living, agree.

 

Holcombs arm says everyone else is wrong and he's right, and links to only hyperstats, a site that tries to explain stats in laymans terms at a 2nd grade math level.

 

Rinse lather repeat. I think he's just an uuber troll. I refuse to believe a person could be as stupid as he is.

[Ramius]

Wait.... WHAT??

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yes. he said that measurement error causes a rubber band to stretch.

[Bungee Jumper]

Wait.... WHAT??

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Yep...you stretch a rubber band, it's measurement error. You let it go, it regresses toward the mean. I made the mistake of saying he said a rubber band snaps back because of measurement error...he was very adamant that he never said that, but said that it stretches because of measurement error.

 

He was also very adamant that it was a metaphor...not, mind you, an analogy.

[Orton's Arm]

Frankly, i am just waiting to see him post a link to some other site besides wikipedia or hyperstats. Oh wait, any other sources, ie- journals,  will prove he's wrong and an imbecile.

Thanks for that example of bluster, without backing it up in any way whatsoever with actual links to the sources you're describing.

[Bungee Jumper]

Thanks for that example of bluster, without backing it up in any way whatsoever with actual links to the sources you're describing.

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Link, AGAIN.

[Chilly]

Yep...you stretch a rubber band, it's measurement error.  You let it go, it regresses toward the mean.  I made the mistake of saying he said a rubber band snaps back because of measurement error...he was very adamant that he never said that, but said that it stretches because of measurement error.

 

He was also very adamant that it was a metaphor...not, mind you, an analogy.

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This post owes my department a new monitor,

[Bungee Jumper]

This post owes my department a new monitor,

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It just occurred to me, too...what happens if you stretch a rubber band, and it snaps?

[Orton's Arm]

Wait.... WHAT??

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Wraith--who works with statistics for a living--tried to explain regression toward the mean to Bungee Jumper and Ramius. Wraith used a metaphor of a rubber band. If there's measurement error in your I.Q. test, it causes people's I.Q.s to appear to be more spread out than they really are. This is like a rubber band being stretched. Then if you go back and remeasure those who did the best or the worst on the I.Q. test, their scores will generally be a little closer to the population's mean. This is like the rubber band snapping back into place.

 

Consider, for example, a population where the smartest people have a real I.Q. of 190. Some of these people will get lucky when they take the I.Q. test, and score a 200. Measurement error caused the population to appear to be more spread out than it really is. If you ask those who scored a 200 on the test to retake it, their average score the second time around will be 190 or so. The rubber band snaps back into place.

 

The fact that I'm being ridiculed for Wraith's rubber band metaphor demonstrates that Bungee Jumper and Ramius have utterly abandoned even the pretense of using logic, and are acting like badly behaved children.

[Orton's Arm]

Link, AGAIN. 

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Thanks for providing a link to a source which either a) supports what I've been saying, or b) doesn't address the topic at all. Now try finding a link to someone who supports your side.

[Wraith]

Wait.... WHAT??

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He did NOT say that.

 

I pointed out in that thread that the SPECIFIC behavior seen in a scenario laid out by HA in the previous thread DOES happen, and ONLY happens when non-zero error is present.

 

I then said that the debate over whether error was leading to that SPECIFIC behavior is very much a semantic debate. The behavior is CAUSED by the laws of chance, but needs error to be present for it to occur. I likened it to stretching a rubber band and the snap back to original form. The snap back is CAUSED by the elasticity of the rubber, NOT the stretch, but the stretch needs to be present for the snap to happen.

[Bungee Jumper]

Wraith--who works with statistics for a living--tried to explain regression toward the mean to Bungee Jumper and Ramius. Wraith used a metaphor of a rubber band. If there's measurement error in your I.Q. test, it causes people's I.Q.s to appear to be more spread out than they really are. This is like a rubber band being stretched. Then if you go back and remeasure those who did the best or the worst on the I.Q. test, their scores will generally be a little closer to the population's mean. This is like the rubber band snapping back into place.

 

Actually, the act of applying an external force to a system, removing said force, and watching it relax to its equilibrium point is ENTIRELY UNLIKE regression toward the mean. Other than that...it's still a sh------- metaphor, considering it's actually an analogy...

[Bungee Jumper]

I pointed out in that thread that the SPECIFIC behavior seen a scenario laid out by HA in the previous thread DOES happen, and ONLY happens when non-zero error is present.

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Actually, that's untrue. Reference my dice example. The specific behavior only requires a probability distribution. Said distribution can be of perfectly exact measurement, with zero error, and still show regression toward the mean. Error does not only not cause the effect, it is not required for the effect to happen.

 

 

And Holcomb's Arm DID say that a rubber band stretching is measurement error. That's not your fault though; he's just too damn stupid to understand your analogy.

[Wraith]

Actually, that's untrue.  Reference my dice example.  The specific behavior only requires a probability distribution.  Said distribution can be of perfectly exact measurement, with zero error, and still show regression toward the mean.  Error does not only not cause the effect, it is not required for the effect to happen.

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I'm not referring to the general case of regression towards the mean when I say that non-zero error has to be present in addition to a probability distribution. I am referring to the specific scenario laid out by Holcomb's Arm regarding IQ scores appearing to regress towards the POPULATION mean (as opposed to the individual SAMPLE mean) in the presence of non-zero error.

 

QUOTE(Wraith @ Nov 10 2006, 03:28 PM)

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.

[Bungee Jumper]

I'm not referring to the general case of regression towards the mean when I say that non-zero error has to be present in addition to a probability distribution. I am referring to the specific scenario laid out by Holcomb's Arm regarding IQ scores appearing to regress towards the POPULATION mean (as opposed to the individual SAMPLE mean) in the presence of non-zero error.

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Except that it would follow, then, that the normal distribution of the population - the variance of the scores, basically - is due to the presence of non-zero error in the test. And that IS counter-factual - the variation in IQ among the population is a feature of the population, not the test.

 

Then there's also the fact that his example is sh--: multiple IQ tests of the same person are not independent. If a given person (of unaverage intelligence) takes 100 IQ tests (of the same format - hence same error - but not content), the scores will be normally distributed around a point that is not the population mean (again, assuming the person is of unaverage intelligence). Really, it's not that his example is sh--, it's that his understanding of it is: he measured the regression of the error in a single instance of the population toward the error's mean of zero, and interpreted it as the regression of the population toward the population mean. (Though it should be enough just to say that the mean error over the entire population is zero...that itself should show that there IS no appreciable net effect due to error in anything approaching the bulk limit. Too bad HA is, once again, too dumb to see it).

[Wraith]

Except that it would follow, then, that the normal distribution of the population - the variance of the scores, basically - is due to the presence of non-zero error in the test.  And that IS counter-factual - the variation in IQ among the population is a feature of the population, not the test.

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I had to go back and refresh my memory regarding what exactly the behavior is HA was referring to (regardless of if he called it regression toward the mean or whatever). I haven't been following the on-going debate at all, so imagine my surprise at seeing my name thrown around in multiple threads the last few days.

 

 

 

Anyway, the original premise in HA's scenario, was this (In my own words, as I understand it):

 

- DISCLAIMER: I pay absolutely no attention to IQ scores/tests, so if I use unreasonable IQ test results, error, etc., don't fault me for it, they are hypothetical.

 

- Take a sufficiently large, RANDOM, sample of the population. (I presume human intelligence is normally distributed).

 

- Have them all take a test that measures human intelligence.

 

- The assumed result would be a normal distribution with some mean and standard deviation.

 

- Assume that the test has normally distributed error centered at zero and with some (non-zero) standard deviation.

 

- Take a slice at one segment of the sample that is not located at the mean (offset from the mean). THIS IS IMPORTANT.

 

- Have that segment retake the test.

 

- The mean of that segment's retest scores will tend to be closer to the mean of the population than the original mean of that segment.

 

This actually does happen. Without the normally distributed measurement error, the mean of the segment's retest score would not change after retest.

 

 

 

 

I have defended HA against people who have said that:

 

- This specific behavior does not happen

 

- This specific behavior does not need measurement error (with a probability distribution) for it to occur.

 

I agree with you (Bungee Jumper) when I say:

 

- The underlying cause of the behavior is a probability distribution.

 

- The premise of this scenario is not really proving much.

 

- This is not "regression towards the mean" as statisticians would define it.

 

- The methodology is suspect (In HA's defense, I have forgotten much of the explanation and have not been following the on-going debate, so I am up to date on his methodology).

 

 

 

 

No where do I say that error is causing the distribution of human intelligence to occur instead of a point value at the mean. It is an underlying assumption in HA's scenario that human intelligence has a PDF and in fact, for my explanation to be valid, a distribution of human intelligence has to be present.

[Bungee Jumper]

I had to go back and refresh my memory regarding what exactly the behavior is HA was referring to (regardless of if he called it regression toward the mean or whatever). I haven't been following the on-going debate at all, so imagine my surprise at seeing my name thrown around in multiple threads the last few days.

Anyway, the original premise in HA's scenario, was this (In my own words, as I understand it):

 

- DISCLAIMER: I pay absolutely no attention to IQ scores/tests, so if I use unreasonable IQ test results, error, etc., don't fault me for it, they are hypothetical.

 

- Take a sufficiently large, RANDOM, sample of the population. (I presume human intelligence is normally distributed).

 

- Have them all take a test that measures human intelligence.

 

- The assumed result would be a normal distribution with some mean and standard deviation.

 

- Assume that the test has normally distributed error centered at zero and with some (non-zero) standard deviation.

 

- Take a slice at one segment of the sample that is not located at the mean (offset from the mean). THIS IS IMPORTANT.

 

- Have that segment retake the test.

 

- The mean of that segment's retest scores will tend to be closer to the mean of the population than the original mean of that segment.

 

This actually does happen. Without the normally distributed measurement error, the mean of the segment's retest score would not change after retest.

 

Okay, we're agreed, that actually does happen, in that it's an observable effect.

 

HOWEVER...there's several questions with that (some of which you ask below):

1) Is it regression toward the population mean? You yourself, just now, were pretty careful to say the scores will "tend to be closer to the mean of the population". I accept this as true...and contend the effect is observable because - to put it very coarsely - the error is regressing toward the mean error of zero, irrespective of the population distribution. HA seems to contend otherwise.

 

1) Is the methodology appropriate to what HA's trying to demonstrate? I contend: not even remotely. He's chosen a subset of data, demonstrated the subset has a certain behavior, and said "A-ha! The entire population must exhibit the same behavior." And in doing so, he's neglected to realize one thing - that while over the subset there's an observable effect, over the population the effect averages to zero. And he doesn't realize that because he's arbitrarily - and somewhat artificially - chosen a subset of data that excludes data points that would show the net effect is zero. As I keep saying: his simulation is sh--, and he doesn't understand it anyway.

 

I have defended HA against people who have said that:

 

- This specific behavior does not happen

 

Speficially, against me...which was a misunderstanding. I called "the specific behavior" fictitious - by which I meant HA's nonsense description of error causing regression toward the mean in a population. You read it as me calling the behavior of his data subset fictitious. I was obviously not clear about that. And again, this gets down to the basic problem of HA not knowing what he's talking about...you were referring to his actual data, I was referring to his extrapolation to the bulk limit (yeah, I know it's not REALLY a "bulk limit"...the physics training is hard to overcome, so humor me).

 

 

<<chop chop chop...already addressed>>No where do I say that error is causing the distribution of human intelligence to occur instead of a point value at the mean. It is an underlying assumption in HA's scenario that human intelligence has a PDF and in fact, for my explanation to be valid, a distribution of human intelligence has to be present.

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No, you don't. I understand that. HA doesn't, sorry to say. Apologies if you think I'm arguing with you...I'm arguing with HA, and apologize for him throwing "Well, Wraith says so..." in my face every other post and trying to pit me against you...

[Orton's Arm]

Okay, we're agreed, that actually does happen, in that it's an observable effect.

 

HOWEVER...there's several questions with that (some of which you ask below):

1) Is it regression toward the population mean?  You yourself, just now, were pretty careful to say the scores will "tend to be closer to the mean of the population".  I accept this as true...and contend the effect is observable because - to put it very coarsely - the error is regressing toward the mean error of zero, irrespective of the population distribution.  HA seems to contend otherwise.

I've never contended otherwise. I've consistently said that if you select a group of people with very high I.Q. scores, that group will tend to have been luckier than average on the I.Q. test. When you retest that particular group, individual members will once again get lucky or unlucky on the test. But in the aggregate, the positive luck the group experienced the first time around is expected to become neutral luck the second time. This causes the group's average to be somewhat closer to the population mean on the retest.

1) Is the methodology appropriate to what HA's trying to demonstrate?  I contend: not even remotely.  He's chosen a subset of data, demonstrated the subset has a certain behavior, and said "A-ha!  The entire population must exhibit the same behavior."  And in doing so, he's neglected to realize one thing - that while over the subset there's an observable effect, over the population the effect averages to zero.  And he doesn't realize that because he's arbitrarily - and somewhat artificially - chosen a subset of data that excludes data points that would show the net effect is zero.

Of course the net effect is zero. That's not in question here. My point is that if you have a group of people who scored a 150 on an I.Q. test, and if that group sits down to retake the test, the expected average score for that group's retest is less than 150. At the individual level, this means that if someone who scored a 150 on an I.Q. test is sitting down to retake it, his most likely score is less than 150. This is because that 150 score is more likely to signal a lucky 140 than an unlucky 160.

 

I called "the specific behavior" fictitious - by which I meant HA's nonsense description of error causing regression toward the mean in a population.

In the I.Q. test example, measurement error is necessary for the behavior I've described to take place. Those who get very high scores the first time they take the test tend to do a little less well upon being retested. (Obviously this is an aggregate phenomenon, as some of those being retested will do the same or better the second time around.)

[Bungee Jumper]

blah blah blah...

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In other words, you're now saying that error does NOT cause regression toward the mean...but you're still right and everyone else is still wrong.

[Orton's Arm]

In other words, you're now saying that error does NOT cause regression toward the mean...but you're still right and everyone else is still wrong.

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No, I don't feel I'm the only one who's right. The people who wrote the articles to which I linked obviously understand the phenomenon a lot better than you do.