Regression toward the mean

[Chilly]

Coli's ignoring me because I don't eat at Taco Bell.

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mmm.... indesgestion in a tortilla. What could be better?

[Ramius]

Coli isnt ignoring me...at leats not to my knowledge. But then again, i am a middle of the road dem, so he likes me.

[GG]

To be honest, gotta love the Internet revolution - that HA had broadband access from Tehran this week.

[Orton's Arm]

Yeah.  Coli's ignoring you because he's a liberal and you've shamed him.  I'm sure that's it.

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When on earth did I say I'd "shamed" Coli? I wrote that Coli knows that if you have a normally distributed population, and if you administer an imperfect test to said population, those who obtain extreme scores will tend to score somewhat closer to the mean upon being retested. I wrote that Coli would probably love to feed some humble pie to a guy who's advocating eugenics, but that he can't do so in this case because he knows the specific claim I've outlined above is correct. So he's keeping his mouth shut.

[Ramius]

When on earth did I say I'd "shamed" Coli? I wrote that Coli knows that if you have a normally distributed population, and if you administer an imperfect test to said population, those who obtain extreme scores will tend to score somewhat closer to the mean upon being retested. I wrote that Coli would probably love to feed some humble pie to a guy who's advocating eugenics, but that he can't do so in this case because he knows the specific claim I've outlined above is correct. So he's keeping his mouth shut.

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No, Coli just doesnt want to waste time arguing with an idiot who was no clue what they are talking about, hence the reason he'll aruge with me or bungee, but not you.

[Orton's Arm]

The statistical term "regression," from a Latin root meaning "going back," was first used by Francis Galton in his paper "Regression towards Mediocrity in Hereditary Stature."1 Galton related the heights of children to the average height of their parents, which he called the mid- parent height (figure). Children and parents had the same mean height of 68.2 inches. The ranges differed, however, because the mid-parent height was an average of two observations and thus had its range reduced. Now, consider those parents with a mid-height between 70 and 71 inches. The mean height of their children was 69.5 inches, which was closer to the mean height of all children than the mean height of their parents was to the mean height of all parents. Galton called this phenomenon "regression towards mediocrity"; we now call it "regression towards the mean." The same thing happens if we start with the children. For the children with height between 70 and 71 inches, the mean height of their parents was 69.0 inches. This is a statistical, not a genetic phenomenon.

 

If we take each group of mid-parents by height and calculate the mean height of their children, these means will lie close to a straight line. This line came to be called the regression line, and hence the process of fitting such lines became known as "regression."

 

In mathematical terms, if variables X and Y have standard deviations sX and sY, and correlation r, the slope of the familiar least squares regression line can be written rsy/sx. Thus a change of one standard deviation in X is associated with a change of r standard deviations in Y. Unless X and Y are exactly linearly related, so that all the points lie along a straight line, r is less than 1. For a given value of X the predicted value of Y is always fewer standard deviations from its mean than is X from its mean. Regression towards the mean occurs unless r=1, perfect correlation, so it always occurs in practice. We give some examples in a subsequent note.

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This sounds more like something you came across, than something you wrote yourself. Unless you have multiple personality disorder or have started referring to yourself in the royal plural, that is. In any case, I don't disagree with anything in the above post.

 

The phenomenon I've been describing is different from the above, in that measurement error or natural fluctuations in a person's underlying I.Q. are necessary for it to take place. The fact that both phenomena were labeled "regression toward the mean" certainly makes the discussion more confusing. Wraith, at least, felt that the phenomenon I've been describing exists, but should not be labled "regression toward the mean." He could well be right, though there are other sources such as Hyperstats and the Wikipedia article which would indicate a broader definition of regression toward the mean.

 

Whether the phenomenon I've been describing meets the technical definition of regression toward the mean is far less interesting to me than the fact that it exists in the first place. Suppose you have a group of people who scored a 140 on an I.Q. test. This group will have a greater number of lucky 130s than unlucky 150s. When everyone in the group retakes the test, the group's average score is expected to be lower than the original 140. Call this phenomenon whatever you want (except you, Bungee Jumper), but know that it exists.

[Orton's Arm]

No, Coli just doesnt want to waste time arguing with an idiot who was no clue what they are talking about, hence the reason he'll aruge with me or bungee, but not you.

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When the eugenics debate started, Coli joined in. He made it clear he was going to present just one post. In that post, he presented the extreme pro-nurture side of the debate, in such a way as to make it seem it was the only view any reasonable scientist had even considered. But he made it clear that would be his last post on the topic of eugnenics.

 

This particular thread isn't intended to be a debate about eugenics, but about a specific statistical principle. Coli doesn't have to spend endless time debating anyone. He could just create a single post stating whether he agrees or disagrees with the specific phenomenon I've described. His refusal to do so speaks volumes.

[Bungee Jumper]

When on earth did I say I'd "shamed" Coli? I wrote that Coli knows that if you have a normally distributed population, and if you administer an imperfect test to said population, those who obtain extreme scores will tend to score somewhat closer to the mean upon being retested. I wrote that Coli would probably love to feed some humble pie to a guy who's advocating eugenics, but that he can't do so in this case because he knows the specific claim I've outlined above is correct. So he's keeping his mouth shut.

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Yeah. Keep saying that. That'll make it true.

[X. Benedict]

His refusal to do so speaks volumes.

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The thunder from Coli's refusal is deafening.

 

Ow, ooo, eee, ow, my ears!

[Orton's Arm]

Yeah.  Keep saying that.  That'll make it true. 

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I'm sure Coli would love to help you guys. He's known you and Ramius a lot longer than he's known me. In addition, your political views are probably a lot more similar to his than mine are. He'd love to help you. He just can't.

[Bungee Jumper]

I'm sure Coli would love to help you guys. He's known you and Ramius a lot longer than he's known me. In addition, your political views are probably a lot more similar to his than mine are. He'd love to help you. He just can't.

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Up your meds. Jesus...

[GG]

Whether the phenomenon I've been describing meets the technical definition of regression toward the mean is far less interesting to me than the fact that it exists in the first place. Suppose you have a group of people who scored a 140 on an I.Q. test. This group will have a greater number of lucky 130s than unlucky 150s. When everyone in the group retakes the test, the group's average score is expected to be lower than the original 140. Call this phenomenon whatever you want (except you, Bungee Jumper), but know that it exists.

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Well, there you go again. Of course you still haven't really answered the question.

 

Let me see if a stats rube can understand your simulation. In the backup to your scenario, you indicated that in an IQ test with mean of 100, you'll get 1000 people scoring 130, 800 scoring 140 and only 10 scoring 150? That's quite the leap from 140 to 150. Does that indicate that 150 is well beyond 3 standard deviations to cause such a huge drop from 140 to 150? Or could your example be another case of pulling numbers out of your head?

 

Let's stick with your simulation, though. If there is in fact a huge difference between getting a 130, 140 and 150, is it correct to assign he same probability of error to all grade levels? If the test gets progressively harder to get a 150 vs 130, wouldn't you likely not have the same proportion of lucky 130 vs unlucky 150s?

 

I'm sure a genius like you can handle the simplicity of a proper illustrative example.

[Orton's Arm]

Up your meds.  Jesus...   

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That's the best you could come up with?

 

Look. What I'm saying here should be obvious to anyone. Suppose you were to take the population of, say, New Zealand, and gather up everyone who scored a 140 on an I.Q. test. In the group of people you gathered, do you think lucky 130s and unlucky 150s would be equal in number, or do you think lucky 130s would outnumber unlucky 150s? It's a simple, easy question, and the answer leads directly to the phenomeon I've been describing. There's no way Coli's going to be dumb enough to destroy his own credibility by pretending that there will be as many unlucky 150s as lucky 130s.

[Orton's Arm]

Well, there you go again.  Of course you still haven't really answered the question.

 

Let me see if a stats rube can understand your simulation.  In the backup to your scenario, you indicated that in an IQ test with mean of 100, you'll get 1000 people scoring 130, 800 scoring 140 and only 10 scoring 150?  That's quite the leap from 140 to 150.  Does that indicate that 150 is well beyond 3 standard deviations to cause such a huge drop from 140 to 150?  Or could your example be another case of pulling numbers out of your head?

 

Let's stick with your simulation, though.  If there is in fact a huge difference between getting a 130, 140 and 150, is it correct to assign he same probability of error to all grade levels?  If the test gets progressively harder to get a 150 vs 130, wouldn't you likely not have the same proportion of lucky 130 vs unlucky 150s?

 

I'm sure a genius like you can handle the simplicity of a proper illustrative example.

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I'm afraid you need to go back and reread the example. I wrote that of the people who actually scored a 140 on the first I.Q. test, 1000 of them had true I.Q.s of 130 and got lucky, 800 had true I.Q.s of 140 and were scored incorrectly, and 10 had true I.Q.s of 150 and got unlucky.

 

Imagine those 1810 people sitting down to take the retest. If you were omniscient in kind of a weird way, you'd see 1000 people with little bubbles over their heads which read, "I'm a true 130, who got lucky on the first test and scored a 140." You'd see ten people with little bubbles which read, "I'm a true 150, and I got unlucky on the first test and scored a 140." You'd expect the 1000 true 130s to score an average of 130 upon being retested; just as you'd expect the 10 true 150s to score a 150 upon being retested. Whoever is collecting those retests will get 1000 from true 130s, 800 from true 140s, and 10 from true 150s. The average value for these test scores will be less than 140; so the group's I.Q. will appear to have regressed toward the population mean between the first and second tests.

 

The above logic holds true for any population distribution where there is measurement error, and where people tend to be clustered more toward the middle than the extremes. If people with I.Q.s of 150 were as common as people with I.Q.s of 130, the phenomenon I'm describing would not take place. But there are more people with true I.Q.s of 130 available for getting lucky, than there are people with I.Q.s of 150 available for getting unlucky. Any group of people who scored a 140 on an I.Q. test is expected to contain more lucky 130s than unlucky 150s. More generally, any given group of people who scored above the population mean on an imperfect test is expected to contain more people who got lucky on the test, than people who got unlucky.

[GG]

I'm afraid you need to go back and reread the example. I wrote that of the people who actually scored a 140 on the first I.Q. test, 1000 of them had true I.Q.s of 130 and got lucky, 800 had true I.Q.s of 140 and were scored incorrectly, and 10 had true I.Q.s of 150 and got unlucky.

 

[rest] ... blah bla blah. [/rest]

 

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Ok, genius answer the question when there are 10,000 130s, 1,000 140s and 100 150s.

 

Since there is such a huge drop off between 130 and 150, why do you assume that the probability of both groups accidentally scoring 140 is the same?

[Johnny Coli]

Someone PM'd me about this thread, and said I was mentioned in it. I did a quick scan and for some reason HA is calling me out, even though I've not been a part of, nor followed this stupid discussion for weeks.

 

Hey a-hole, I made it pretty freaking clear a long while ago that my position was I would make a single post on the subject of eugenics, much like I've done with respect to Creationist threads, and be done with it. I have found in the past that "debating" with people like you leads to page upon page of wasted effort that doesn't change the other person's mind anyway. What a shocker that this discussion is well over 50 pages.

 

You are using a less-than rudimentary knowledge of statistics to make an argument for eugenics (or at least that is what you were doing a month-or-so ago when this whole thing began). I have no idea what the hell it is you are arguing for now, but based on your track record I'd say there's a pretty good chance that you are dead wrong. How regression to the mean even factors into a eugenics discussion is a question I have no desire to hear your answer for.

 

You may continue to go on thinking my silence proves you right, but in the reality everyone else resides in it's called "ignoring you." Any person arguing a pro-eugenics position is not worth my time.

[Bungee Jumper]

That's the best you could come up with? 

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That's the best you deserve. I'm not arguing with you, genius. I'm mocking you.

[Taro T]

Someone PM'd me about this thread, and said I was mentioned in it.  I did a quick scan and for some reason HA is calling me out, even though I've not been a part of, nor followed this stupid discussion for weeks. 

 

Hey a-hole, I made it pretty freaking clear a long while ago that my position was I would make a single post on the subject of eugenics, much like I've done with respect to Creationist threads, and be done with it.  I have found in the past that "debating" with people like you leads to page upon page of wasted effort that doesn't change the other person's mind anyway. What a shocker that this discussion is well over 50 pages. 

 

You are using a less-than rudimentary knowledge of statistics to make an argument for eugenics (or at least that is what you were doing a month-or-so ago when this whole thing began).  I have no idea what the hell it is you are arguing for now, but based on your track record I'd say there's a pretty good chance that you are dead wrong.  How regression to the mean even factors into a eugenics discussion is a question I have no desire to hear your answer for.

 

You may continue to go on thinking my silence proves you right, but in the reality everyone else resides in it's called "ignoring you."  Any person arguing a pro-eugenics position is not worth my time.

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As near as I can tell, and I could be mistaken as this whole issue becomes rather convoluted (at least in the minds of some people), the apparent regression towards the mean of IQ scores supports eugenics because the people that get scores high enough to warrant inclusion in the eugenics program (or are the smart people out of the program, again it gets confusing) do so due to luck so they and their children don't actually warrant inclusion in the program (or warrant exclusion from the program) so pretty soon we end up where no one is allowed to breed and PETA finally realizes their ultimate goal of animals living free of human encumbrances.

[Chilly]

That's the best you deserve.  I'm not arguing with you, genius.  I'm mocking you.

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Is this why you don't eat at Taco Bell?

[Bungee Jumper]

As near as I can tell, and I could be mistaken as this whole issue becomes rather convoluted (at least in the minds of some people), the apparent regression towards the mean of IQ scores supports eugenics because the people that get scores high enough to warrant inclusion in the eugenics program (or are the smart people out of the program, again it gets confusing) do so due to luck so they and their children don't actually warrant inclusion in the program (or warrant exclusion from the program) so pretty soon we end up where no one is allowed to breed and PETA finally realizes their ultimate goal of animals living free of human encumbrances.

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Don't forget the part where luck and error are both "heritable" (sic)...