Regression toward the mean

[Ramius]

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?

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Ok, i think ti went like this.

 

1. Holcombs arm spends 500 posts incorrectly arguing that error causes regression to the mean.

 

2. holcombs arm is proved wrong on an hourly basis

 

3. Holcombs arm claims that he was arguing only that regression toward the mean happens

 

4. We call out out holcombs arm due to his flip-flop in #3

 

5. Holcombs arm then claims that he never flip-flopped and us in step #4 are wrong

 

6. Holcombs arm continues to argue that regression to the mean is due to error.

[Orton's Arm]

Ok, i think ti went like this.

 

1. Holcombs arm spends 500 posts incorrectly arguing that error causes regression to the mean.

 

2. holcombs arm is proved wrong on an hourly basis

 

3. Holcombs arm claims that he was arguing only that regression toward the mean happens

 

4. We call out out holcombs arm due to his flip-flop in #3

 

5. Holcombs arm then claims that he never flip-flopped and us in step #4 are wrong

 

6. Holcombs arm continues to argue that regression to the mean is due to error.

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If you want an example of something that's due to error, read your own posts for a change. That should kill off a few of your brain cells, assuming you have any left.

 

I've been arguing--consistently--that if you have a non-uniform underlying distribution, and if you have measurement error, those who obtain extreme scores the first time around will tend to score somewhat closer to the mean upon retaking the test. Your objections to this have displayed only your own stupidity and ignorance. The idea that any objection you're possibly capable of raising would even tempt me to do a flip-flop is utterly laughable.

[erynthered]

My four year old:

 

 

Eryn says: Its not aggression to be mean, but its regression to be a Bills Fan.

But if not for, indisgression we wouldn't have regression of meanies.

[Bungee Jumper]

If you want an example of something that's due to error, read your own posts for a change. That should kill off a few of your brain cells, assuming you have any left.

 

I've been arguing--consistently--that if you have a non-uniform underlying distribution, and if you have measurement error, those who obtain extreme scores the first time around will tend to score somewhat closer to the mean upon retaking the test. Your objections to this have displayed only your own stupidity and ignorance. The idea that any objection you're possibly capable of raising would even tempt me to do a flip-flop is utterly laughable.

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And once again, that proves nothing more than you don't know what error is. A person taking the test the second time around will tend to score (95% of the time, to be precise) within two standard deviations OF ERROR of their first score, IRRESPECTIVE OF THE POPULATION'S STATISTICAL DISTRIBUTION. In other words, any individual who scores an extreme score the first time stands a 50/50 chance of doing better vs. doing worse, BECAUSE THE VARIANCE IN THE POPULATION AND THE VARIANCE IN THE ERROR ARE TWO COMPLETELY DIFFERENT AND SEPARATE THINGS.

 

Jesus Christ. How can you not possibly understand this by now.

[Bungee Jumper]

Ok, i think ti went like this.

 

1. Holcombs arm spends 500 posts incorrectly arguing that error causes regression to the mean.

 

2. holcombs arm is proved wrong on an hourly basis

 

3. Holcombs arm claims that he was arguing only that regression toward the mean happens

 

4. We call out out holcombs arm due to his flip-flop in #3

 

5. Holcombs arm then claims that he never flip-flopped and us in step #4 are wrong

 

6. Holcombs arm continues to argue that regression to the mean is due to error.

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Maybe his regression to the error is due to us being mean...

[Orton's Arm]

And once again, that proves nothing more than you don't know what error is.  A person taking the test the second time around will tend to score (95% of the time, to be precise) within two standard deviations OF ERROR of their first score, IRRESPECTIVE OF THE POPULATION'S STATISTICAL DISTRIBUTION.  In other words, any individual who scores an extreme score the first time stands a 50/50 chance of doing better vs. doing worse, BECAUSE THE VARIANCE IN THE POPULATION AND THE VARIANCE IN THE ERROR ARE TWO COMPLETELY DIFFERENT AND SEPARATE THINGS.

 

Jesus Christ.  How can you not possibly understand this by now.

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You're wrong.

[Wraith]

In other words, any individual who scores an extreme score the first time stands a 50/50 chance of doing better vs. doing worse.

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Did you really mean to say this? Because that is not true and goes against what you've been saying for weeks.

 

If we continue the assumption that error on the test is normally distributed and centered at zero, the only way someone would have a 50/50 chance of doing better/worse the second time they had the test is if they had zero error (gotten the "true" IQ) the first time they took the test.

 

Unless I've totally misread what you're trying to say.

[Wraith]

And once again, that proves nothing more than you don't know what error is.  A person taking the test the second time around will tend to score (95% of the time, to be precise) within two standard deviations OF ERROR of their first score, IRRESPECTIVE OF THE POPULATION'S STATISTICAL DISTRIBUTION.  In other words, any individual who scores an extreme score the first time stands a 50/50 chance of doing better vs. doing worse, BECAUSE THE VARIANCE IN THE POPULATION AND THE VARIANCE IN THE ERROR ARE TWO COMPLETELY DIFFERENT AND SEPARATE THINGS.

 

Jesus Christ.  How can you not possibly understand this by now.

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You're point in this post, I believe, is that how extreme a person scores in regard to their OWN "mean" or "true IQ" or something determines the probability of scoring higher or lower on a subsequent retest. If I score extremely far below my "real IQ" the first time I take an IQ test, it is very probable I will score higher the second time I take the test, even though my first result was extremely high compared to the overall population mean. This is absolutely reasonable, and more importantly, true.

 

However, you seem to be ignoring the fact that if the overall population being sampled from is normally distributed, and I ask people who scored at some extreme value, I am more likely to get someone who has a "real IQ" closer to average and scored at a more extreme value due to testing variation than I am to get someone who has a "real IQ" further away from average and who scored closer to average due to variation. That will always be the case because there are more people in the center of the distribution of the overall population than there are on the tails. As HA said, if the underlying population were uniformly distributed, this behavior would not happen.

 

So the overall population distribution is an underlying factor and that is the point HA is trying to make here, I believe.

[Taro T]

If you want an example of something that's due to error, read your own posts for a change. That should kill off a few of your brain cells, assuming you have any left.

 

I've been arguing--consistently--that if you have a non-uniform underlying distribution, and if you have measurement error, those who obtain extreme scores the first time around will tend to score somewhat closer to the mean upon retaking the test. Your objections to this have displayed only your own stupidity and ignorance. The idea that any objection you're possibly capable of raising would even tempt me to do a flip-flop is utterly laughable.

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After this post, I'm pretty sure I'm out of the whole discussion. But, 1st, one final question: why do you insist upon stating that IF you have measurement error, extreme scores will tend to move closer to the mean? While measurement error can be a factor, this will occur whether or not there is measurement error (at least as most of the world would define measurement error). (Also, depending upon the magnitude and the form of the measurement error, the effect you are expecting might not be observable.) You have stated that you agree with this, and then you go and continue to repost that you don't agree with it (as in the post I am quoting).

 

Either you are as obtuse as CTM/BJ states, in which case there is no reason to continue this discussion; or you are jerking our chains, in which case there is no reason to continue this discussion. Or quite possibly both, in which case there is definitely no reason to continue the discussion. Wraith seems to suggest a 4th possibility, that you actually understand what you are trying to say but don't have the statistical background to state it properly. I doubt the likelihood of that possibility, but even if that is the case, your continual insistance to continue using your own vernacular makes continuing this discussion too frustrating to bother with.

[Wraith]

After this post, I'm pretty sure I'm out of the whole discussion.  But, 1st, one final question: why do you insist upon stating that IF you have measurement error, extreme scores will tend to move closer to the mean?  While measurement error can be a factor, this will occur whether or not there is measurement error (at least as most of the world would define measurement error).  (Also, depending upon the magnitude and the form of the measurement error, the effect you are expecting might not be observable.)  You have stated that you agree with this, and then you go and continue to repost that you don't agree with it (as in the post I am quoting).

 

Either you are as obtuse as CTM/BJ states, in which case there is no reason to continue this discussion; or you are jerking our chains, in which case there is no reason to continue this discussion.  Or quite possibly both, in which case there is definitely no reason to continue the discussion.  Wraith seems to suggest a 4th possibility, that you actually understand what you are trying to say but don't have the statistical background to state it properly.  I doubt the likelihood of that possibility, but even if that is the case, your continual insistance to continue using your own vernacular makes continuing this discussion too frustrating to bother with.

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Actually, measurement error does need to be present for the behavior Holcomb's Arm has described in his initial premise to occur. Without it, absolutely no "movement" of the scores will be seen on any subsequent retests, no matter how many times you try it.

[Bungee Jumper]

Did you really mean to say this? Because that is not true and goes against what you've been saying for weeks.

 

If we continue the assumption that error on the test is normally distributed and centered at zero, the only way someone would have a 50/50 chance of doing better/worse the second time they had the test is if they had zero error (gotten the "true" IQ) the first time they took the test.

 

Unless I've totally misread what you're trying to say.

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No, I did mean to say that, because after the first test you simply don't know where that score falls with regards to the error. All you really know is that that score has a 95% chance of being within two standard deviations of error of the "zero error point". You don't know how much error is present, or in which direction the error applies.

 

It's as though I was on your aforementioned product line, picking plastic widgets at random, with no foreknowledge of the expected properties of the widgets. I pick the first one, weigh it...and that gives me absolutely no insight as to whether the second one is heavier or lighter. It's a complete toss-up...the key reason being the italicized statement above. For you, it's not a 50/50 proposition, as you know the design specs of the widget. For me...I have a single data point, I can't make any predictions.

 

Same thing with this IQ example. HA is saying that you can make some estimation as to the error and magnitude of the error in a single test based on that test and the population mean and standard deviation. You can't, they're two completely different things.

[Taro T]

Actually, measurement error does need to be present for the behavior Holcomb's Arm has described in his initial premise to occur. Without it, absolutely no "movement" of the scores will be seen on any subsequent retests, no matter how many times you try it.

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In his extremely simplistic original example, you would be correct. However, there are going to be other variables (time of day, alertness, mental state, health, medication, etc.) that will effect the "true IQ". A "perfect test", as he has mentioned in his description at varying times, would detect the subject's "true IQ" at the time the person took the test without any measurement error. As these regressors change for an individual subject upon a retest, even a "perfect test" would/could end up resulting in a different "true IQ" even though the error term in the regression was 0 both times.

 

So, even with an IQ test, you can have variation in an individual's test results without measurement error. I guess I am having a hard time with agreeing that a "perfect test" would have measurement error. If the test IS perfect in design, implementation, and execution; there would not be measurement error.

[Orton's Arm]

In his extremely simplistic original example, you would be correct.  However, there are going to be other variables (time of day, alertness, mental state, health, medication, etc.) that will effect the "true IQ".  A "perfect test", as he has mentioned in his description at varying times, would detect the subject's "true IQ" at the time the person took the test without any measurement error.  As these regressors change for an individual subject upon a retest, even a "perfect test" would/could end up resulting in a different "true IQ" even though the error term in the regression was 0 both times.

 

So, even with an IQ test, you can have variation in an individual's test results without measurement error.  I guess I am having a hard time with agreeing that a "perfect test" would have measurement error.  If the test IS perfect in design,  implementation, and execution; there would not be measurement error.

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A good post. Variation in a person's results from one test to the next can be caused by measurement error, or by the variation in the underlying true I.Q. that you've described. Probably actual variation between one I.Q. test and the next is caused by some combination of measurement error and random fluctuations in underlying I.Q.

 

In terms of the phenomenon I've been describing, it doesn't really matter whether random variation is caused by measurement error or by fluctuation in the underlying true I.Q. Either way, someone who obtained a high score on an I.Q. test will, on average, obtain a somewhat lower score upon retaking the test.

[Orton's Arm]

However, you seem to be ignoring the fact that if the overall population being sampled from is normally distributed, and I ask people who scored at some extreme value, I am more likely to get someone who has a "real IQ" closer to average and scored at a more extreme value due to testing variation than I am to get someone who has a "real IQ" further away from average and who scored closer to average due to variation. That will always be the case because there are more people in the center of the distribution of the overall population than there are on the tails. As HA said, if the underlying population were uniformly distributed, this behavior would not happen.

This is exactly what I've been trying to say for the last 30 pages. Thank you.

[Ramius]

Either way, someone who obtained a high score on an I.Q. test will, on average, obtain a somewhat lower score upon retaking the test.

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This statement is completely and utterly incorrect.

 

Since you have no idea what that person's "real IQ" is, you have no idea whether re-taking the test will cause it to flucuate up or down. IT ISNT GOING TO AUTOMATICALLY REGRESS TO THE MEAN OF THE POPULATION.

 

THE PERSON'S IQ SCORE WILL MOVE TOWARD THAT SPECIFIC PERSON'S INDIVIDUAL IQ SCORE, NOT TOWARDS THE POPULATION MEAN.

[Orton's Arm]

This statement is completely and utterly incorrect.

 

Since you have no idea what that person's "real IQ" is, you have no idea whether re-taking the test will cause it to flucuate up or down. IT ISNT GOING TO AUTOMATICALLY REGRESS TO THE MEAN OF THE POPULATION.

 

THE PERSON'S IQ SCORE WILL MOVE TOWARD THAT SPECIFIC PERSON'S INDIVIDUAL IQ SCORE, NOT TOWARDS THE POPULATION MEAN.

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Yes, it moves towards that person's individual I.Q. score. But if you have a room full of people who scored a 140 on an I.Q. test, there will be more people with I.Q.s of 130 who got lucky on the test, than people with true I.Q.s of 150 who got unlucky. Therefore, the people in the room will, on average, score lower than 140 upon retaking the test. This means that if you have an individual person who scored a 140 on the I.Q. test, the most likely outcome for retaking the test is less than 140.

[Ramius]

Yes, it moves towards that person's individual I.Q. score. But if you have a room full of people who scored a 140 on an I.Q. test, there will be more people with I.Q.s of 130 who got lucky on the test, than people with true I.Q.s of 150 who got unlucky. Therefore, the people in the room will, on average, score lower than 140 upon retaking the test. This means that if you have an individual person who scored a 140 on the I.Q. test, the most likely outcome for retaking the test is less than 140.

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this has nothing at all to do with regression to the mean. When you select a data point that is far from the mean, the next data point has a probability of being closer to the mean due to variance and simple probability, NOT BECAUSE OF ERROR. Just the dice example that Bungee provided. (the one your dumb ass couldnt understand)

 

My God oyu are a dumbass.

[Orton's Arm]

this has nothing at all to do with regression to the mean. When you select a data point that is far from the mean, the next data point has a probability of being closer to the mean due to variance and simple probability, NOT BECAUSE OF ERROR. Just the dice example that Bungee provided. (the one your dumb ass couldnt understand)

 

My God oyu are a dumbass.

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Ramius, you try so hard, yet are so consistent in coming up short. I almost feel bad for you. Almost.

 

If you could make an I.Q. test without measurement error, and if people's I.Q.s didn't vary based on time of day, the amount of rest, etc., then someone who scored a 140 on an I.Q. test would score a 140 upon retaking the test.

 

Introduce measurement error into the above example, and you create the possibility that someone who scored a 140 on an I.Q. test is either a lucky 130 or an unlucky 150. Of these two possibilities, the lucky 130 is more likely than the unlucky 150, because there are more 130s available for getting lucky than 150s available for getting unlucky.

[Ramius]

Ramius, you try so hard, yet are so consistent in coming up short. I almost feel bad for you. Almost.

 

If you could make an I.Q. test without measurement error, and if people's I.Q.s didn't vary based on time of day, the amount of rest, etc., then someone who scored a 140 on an I.Q. test would score a 140 upon retaking the test.

 

Introduce measurement error into the above example, and you create the possibility that someone who scored a 140 on an I.Q. test is either a lucky 130 or an unlucky 150. Of these two possibilities, the lucky 130 is more likely than the unlucky 150, because there are more 130s available for getting lucky than 150s available for getting unlucky.

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I actually feel worse for you, someone who spends 500 posts arguing something you dont even understand. also,something thats completely and utterly wrong.

 

Go back and take a stats class thats above a 2nd grade level, then come back to the adult table for a discussion.

[Orton's Arm]

I actually feel worse for you, someone who spends 500 posts arguing something you dont even understand. also,something thats completely and utterly wrong.

 

Go back and take a stats class thats above a 2nd grade level, then come back to the adult table for a discussion.

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You obviously know a lot more about throwing insults at people than you know about stats. Then again, you know absolutely nothing about stats, so it's not like I'm paying you that huge a compliment about your ability to throw insults at people.