Regression toward the mean

[Bungee Jumper]

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 just don't understand the statistical principle of "luck", is all.

 

[Wraith]

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.

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Ah, I understand now, thanks.

[Orton's Arm]

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.

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The widget example and the I.Q. test example are different. You know the underlying population's I.Q. Based on how individual people score from one test to the next, you have a pretty good idea as to what the standard deviation for the error term is. If someone scores a 160 on an I.Q. test, you can confidently say this person is more likely to be a lucky 150 than an unlucky 170, because of your awareness of the underlying distribution. You also know that it's quite possible for a 150 or a 170 to score a 160 on an I.Q. test, based on observation of how people's scores differ from one test to the next.

[Bungee Jumper]

The widget example and the I.Q. test example are different. You know the underlying population's I.Q. Based on how individual people score from one test to the next, you have a pretty good idea as to what the standard deviation for the error term is. If someone scores a 160 on an I.Q. test, you can confidently say this person is more likely to be a lucky 150 than an unlucky 170, because of your awareness of the underlying distribution. You also know that it's quite possible for a 150 or a 170 to score a 160 on an I.Q. test, based on observation of how people's scores differ from one test to the next.

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What? That makes no sense.

 

 

 

 

 

Why the hell am I even surprised by that? Of course it makes no sense...

[Ramius]

What?  That makes no sense. 

Why the hell am I even surprised by that?  Of course it makes no sense...   

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he's still rambling isnt he?

[Orton's Arm]

he's still rambling isnt he?

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No I'm not rambling. I'm pointing out that there are differences between the widget example Bungee Jumper described, and the I.Q. test example that's relevant to the underlying discussion. Your inability to grasp those differences merely reinforces the point I'm about to make.

 

Think of a football team whose players lack fundamental football instincts. The head coach tries to teach the players these instincts, but ultimately fails/gives up. Eventually, he has to start teaching them more advanced stuff, to get them ready for the regular season. But all those complex offenses and defenses will never be executed properly, because the players failed to grasp the underlying fundamentals.

 

I compare that to your situation. You lack a firm grasp of fundamental statistical concepts. You don't have the patience, the interest, or quite frankly the brains to remedy this defect. Nonetheless, someone came along and attempted to teach you more advanced stuff. This extra knowledge made you more arrogant, but it didn't correct your underlying problem understanding the basics. You're fine as long as you can blindly follow the methodology you've been taught. But whenever you have to think on your feet, you fail, because you lack a firm grasp of the fundamentals of statistics.

[Bungee Jumper]

But whenever you have to think on your feet, you fail, because you lack a firm grasp of the fundamentals of statistics.

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Though I've been avoiding pointing out the irony in your posts, I'd be remiss in not observing that this statement is coming from a guy who defines "variance" as "error".

[Orton's Arm]

Though I've been avoiding pointing out the irony in your posts, I'd be remiss in not observing that this statement is coming from a guy who defines "variance" as "error".   

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I've written that variation in a person's underlying I.Q. and measurement error can both cause the phenomenon I've been describing. I don't remember trying to persuade anyone that variance and error were the same thing.

 

I do, however, remember you insisting that repeatedly rolling a pair of dice would create a binomial distribution. The following definition is from page 376 of Introduction to the Practice of Statistics by David Moore and George McCabe:

The Binominal Setting

1. There are a fixed number n of observations

2. The n observations are all independent.

3. Each observation falls into one of just two categories, which for convenience we call "success" and "failure."

4. The probability of a success, call it p, is the same for each observation. . . .

 

The distribution of the count X of successes in the binomial setting is called the binomial distribution with parameters n and p.

If you don't even know what a binomial distribution is, you're not exactly in the best position to pretend you have a better understanding of words like "variance" and "error" than I have.

[Ramius]

Think of a football team whose players lack fundamental football instincts. The head coach tries to teach the players these instincts, but ultimately fails/gives up. Eventually, he has to start teaching them more advanced stuff, to get them ready for the regular season. But all those complex offenses and defenses will never be executed properly, because the players failed to grasp the underlying fundamentals.

 

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Ok, we'll go with your example. You are the coach, and me, bungee jumper, jzmack, and dave_b are the football players. We'll assume you are trying to coach on on offense.

 

Heres the real problem: You as the football coach are trying to teach us offense by instructing to run the triangle, pass the ball along the perimeter and take open jump shots. You are making us spend time on practicing free throws. The problem is, WE ARE TALKING ABOUT FOOTBALL, AND YOU ARE TRYING TO TEACH BASKETBALL. To top it off, you have the coaching skills and prowess of rick venturi (a career 2-17 NFL record), rich kotite, or hank bullough.

 

You dont understand what you are trying to teach, or where the hell you are, and you are so off base, you are in the completely wrong subject.

[Orton's Arm]

Ok, we'll go with your example. You are the coach, and me, bungee jumper, jzmack, and dave_b are the football players. We'll assume you are trying to coach on on offense.

 

Heres the real problem: You as the football coach are trying to teach us offense by instructing to run the triangle, pass the ball along the perimeter and take open jump shots. You are making us spend time on practicing free throws. The problem is, WE ARE TALKING ABOUT FOOTBALL, AND YOU ARE TRYING TO TEACH BASKETBALL. To top it off, you have the coaching skills and prowess of rick venturi (a career 2-17 NFL record), rich kotite, or hank bullough.

 

You dont understand what you are trying to teach, or where the hell you are, and you are so off base, you are in the completely wrong subject.

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The bad attitude of the above post is one of the reasons why you're uncoachable. Even if you dropped the attitude, you'd still be uncoachable, because you don't have the brains to be properly coached.

[Ramius]

The bad attitude of the above post is one of the reasons why you're uncoachable. Even if you dropped the attitude, you'd still be uncoachable, because you don't have the brains to be properly coached.

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When i know a supposed "coach" is dead wrong, and further more, has not even the slightest clue of what they are talking about, of course i am not going to listen.

 

plain and simple, you are wrong. I'm right.

[Orton's Arm]

   

 

When i know a supposed "coach" is dead wrong, and further more, has not even the slightest clue of what they are talking about, of course i am not going to listen.

 

plain and simple, you are wrong. I'm right.

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It's appaling that you're so severely unable to understand even the most basic logical concepts. Just about anyone ought to be able to see that a score of 140 on an I.Q. test is more likely to signal a lucky 130 than an unlucky 150. There are simply more 130s available for getting lucky than 150s available for getting unlucky. Therefore, people who get 140s on I.Q. tests will, on average, score somewhat lower upon retaking the test. Your repeated rejection of such an obvious fact merely destroys whatever shred of credibility you had left after defending syhuang.

[justnzane]

It's appaling that you're so severely unable to understand even the most basic logical concepts. Just about anyone ought to be able to see that a score of 140 on an I.Q. test is more likely to signal a lucky 130 than an unlucky 150. There are simply more 130s available for getting lucky than 150s available for getting unlucky. Therefore, people who get 140s on I.Q. tests will, on average, score somewhat lower upon retaking the test. Your repeated rejection of such an obvious fact merely destroys whatever shred of credibility you had left after defending syhuang.

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ok i have to ask this question HA: "What mathematical background do you have, and what statistical backgroudn do you have (please include grades for this one)?"

[EC-Bills]

ok i have to ask this question HA: "What mathematical background do you have, and what statistical backgroudn do you have (please include grades for this one)?"

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Sorry, grades can be misleading. You are assuming that someone who has good grades actually understands the material. I know plenty of folks with book smarts but no real clue on the subject.

Edited December 11, 2006 by EC-Bills

[Bungee Jumper]

Sorry, grades can be misleading.  You are assuming that someone who has good grades actually understands the material.  I know plenty of folks with book smarts but no real clue on the subject.

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And even if he got high grades, they'd be in error, since they'd regress toward the mean the next time he took the test...

[Orton's Arm]

ok i have to ask this question HA: "What mathematical background do you have, and what statistical backgroudn do you have (please include grades for this one)?"

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In answer to the mathematical background question, I've taken classes in calculus and vector analysis. In addition, I've taken stats classes at the undergraduate and graduate levels. In the stats class that was the most vigorous, challenging, and focused on a strong understanding of the fundamentals, I obtained the second-highest final average in the class.

 

Perhaps more importantly, my standardized test scores are good enough not merely for Mensa, but for this organization. When I understand a logical concept clearly--as is the case for the phenomenon I've been describing--Ramius's hooting and hollering does not tempt me to alter my understanding. The only thing which would cause me to reconsider my views is a logical, compelling explanation as to why the phenomenon I've been describing is not something that actually happens. Such an explanation has not and cannot be achieved. I've heard of dice, of widgets of unknown distributions, and other things not relevant to the topic at hand. But in a population where 130s significantly outnumber 150s, a score of 140 is more likely to signal a lucky 130 than an unlucky 150. The implications of this simple fact have been ignored or misunderstood by those who have been arguing against me.

[Ramius]

In answer to the mathematical background question, I've taken classes in calculus and vector analysis. In addition, I've taken stats classes at the undergraduate and graduate levels. In the stats class that was the most vigorous, challenging, and focused on a strong understanding of the fundamentals, I obtained the second-highest final average in the class.

 

Perhaps more importantly, my standardized test scores are good enough not merely for Mensa, but for this organization. When I understand a logical concept clearly--as is the case for the phenomenon I've been describing--Ramius's hooting and hollering does not tempt me to alter my understanding. The only thing which would cause me to reconsider my views is a logical, compelling explanation as to why the phenomenon I've been describing is not something that actually happens. Such an explanation has not and cannot be achieved. I've heard of dice, of widgets of unknown distributions, and other things not relevant to the topic at hand. But in a population where 130s significantly outnumber 150s, a score of 140 is more likely to signal a lucky 130 than an unlucky 150. The implications of this simple fact have been ignored or misunderstood by those who have been arguing against me.

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So which class, or was it your mensa meetings, that taught you the true value of a die is 3.5?

[Bungee Jumper]

In answer to the mathematical background question, I've taken classes in calculus and vector analysis. In addition, I've taken stats classes at the undergraduate and graduate levels. In the stats class that was the most vigorous, challenging, and focused on a strong understanding of the fundamentals, I obtained the second-highest final average in the class.

 

Perhaps more importantly, my standardized test scores are good enough not merely for Mensa, but for this organization. When I understand a logical concept clearly--as is the case for the phenomenon I've been describing--Ramius's hooting and hollering does not tempt me to alter my understanding. The only thing which would cause me to reconsider my views is a logical, compelling explanation as to why the phenomenon I've been describing is not something that actually happens. Such an explanation has not and cannot be achieved. I've heard of dice, of widgets of unknown distributions, and other things not relevant to the topic at hand. But in a population where 130s significantly outnumber 150s, a score of 140 is more likely to signal a lucky 130 than an unlucky 150. The implications of this simple fact have been ignored or misunderstood by those who have been arguing against me.

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Of course, by your own logic, if your test scores were that extreme they'd be wrong...

 

As for the rest of this...you are AMAZINGLY clueless. Phenomenally. As evidenced by the very simple fact that you can't apply the other discussions and examples that have gone on to your own misbegotten model. The dice are relevant, because they illustrate regression toward the mean as it's mathematically defined as a function of variance and probability. The widget example's relevant because it illustrates the difference between measuring population variance and measuring error. Neither of which you've shown any capability of understanding, fixated as you are in this "measurement error causes regression toward the mean, which is why smart people aren't as smart as they think they are, even though I'm smarter than I think I am and that's not error, so the government should pay me to have smart kids" stupidity.

[Orton's Arm]

So which class, or was it your mensa meetings, that taught you the true value of a die is 3.5?

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If you repeatedly roll a die, and average the results, you should expect an average score of 3.5. If you were to repeatedly give someone an I.Q. test, and average the results, you'd obtain what I've been referring to as the person's "true I.Q."

 

Suppose you wanted to make these two examples similar enough that the concepts learned in the die example could be usefully applied to the I.Q. test example. The "true value" of someone's I.Q. was defined as how well the person would do over the course of many I.Q. tests. To make the die example similar, you have to define the die's "true value" as its expected average over the course of many die rollings. When a person's actual I.Q. score differed from his underlying true I.Q., you'd treat it the same way you'd treat a die's actual roll differing from the underlying average roll.

 

It's a confusing example that probably set the discussion back several pages--not least because it created the opportunity for my views to be mischaracterized. The logic of the phenomenon I've been describing is more easily understood in reference to I.Q. scores, or 40 yard dash times, than it is with the dice rolling example.

[Bungee Jumper]

If you were to repeatedly give someone an I.Q. test, and average the results, you'd obtain what I've been referring to as the person's "true I.Q."

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Yes, that's right...because it allows you to determine the distribution OF ERROR in the test ("test" hear meaning "the measurement process", including all the variables that can affect the outcome. NOT meaning "The IQ test" itself. "Test" actually has a more specific definition that you've been using - yet another word you can't define, what a !@#$ing surprise.)

 

But what you've been saying is that, because of the error, the person's "true IQ" will regress with repeated testing toward the POPULATION MEAN, and not the mean error of zero. Which is bull sh--. Furthermore, you've been saying that the test results regress toward the population mean BECAUSE OF THE ERROR, which is complete and utter bull sh--.

 

And you're arguing all this to prove that a eugenics program would work...when your argument is that the people you'd favor in the eugenics program are not as exceptional as is required BY the eugenics program. Or, to put it more simply, in deference to your little pea-sized brain: HOW DO YOU CHOOSE YOUR BREEDING POPULATION FOR YOUR EUGENICS PROGRAM WHEN YOU "KNOW" YOUR BREEDING POPULATION IS SCORING "TOO HIGH" ON THE SELECTION CRITERIA BECAUSE OF "ERROR"?

 

The basic reason is that you're a retard who can't string different concepts together to make a coherent argument, even in the rare cases when he DOES understand the concepts.