Regression toward the mean

[Chilly]

Why are you trying to use a beginners Math book which is not based upon explaining Math, but rather explaining how to use it as it pertains to social research?

[Bungee Jumper]

Why are you trying to use a beginners Math book which is not based upon explaining Math, but rather explaining how to use it as it pertains to social research?

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The second part of that is because he's trying to use stats as it pertains to social research.

 

The first part: because he's a !@#$ing idiot. He still hasn't defined "variance"...which is kind of an important point when you're talking about regression.

[Chilly]

The second part of that is because he's trying to use stats as it pertains to social research.

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Yeah, but he's trying to use a book which is not focused on explaining math to explain his math.

 

I mean, wtf.

[Ramius]

Why are you trying to use a beginners Math book which is not based upon explaining Math, but rather explaining how to use it as it pertains to social research?

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Because he doesnt understand the actual math and doesnt understand what his own links are saying. Same as always with him.

 

Since he doesnt unnerstand the actual math, he's attempting to use the layman's terms to understand it. But in doing so, he hasnt properly comprehended what the article is actually saying, and is arguing this with people that understand the math and are trying to point out where he's going wrong.

 

If this arguement was about language, say spanish, then not only does holcomb's arm not understand the language, but he also has no idea how to translate into english. He's trying to say that "Yo quiero futbol" means "I have a green hat". The rest of us here who speak spanish, every spanish textbook, and the entire spanish speaking world, including spain, latin america, and south america are trying to tell him that it means "I like soccer", and he keeps saying that he's right and everyone else is wrong.

[Bungee Jumper]

If this arguement was about language, say spanish, then not only does holcomb's arm not understand the language, but he also has no idea how to translate into english. He's trying to say that "Yo quiero futbol" means "I have a green hat". The rest of us here who speak spanish, every spanish textbook, and the entire spanish speaking world, including spain, latin america, and south america are trying to tell him that it means "I like soccer", and he keeps saying that he's right and everyone else is wrong.

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What's more, he'd tell us he's right and everyone else is wrong because you can't have a hat without soccer, since they're actually the same thing.

[Bungee Jumper]

Yeah, but he's trying to use a book which is less focused on explaining math then using it to explain his math.

 

I mean, wtf.

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He found a source that confirms his idiocy. Therefore, the source is "credible". Any source that doesn't confirm his idiocy is "not credible"...like a textbook.

 

It's typical. Not just of him, either. Look at how the zealous liberals/conservatives here hold so dearly to their liberal/conservative news sources. Don't allow yourself to ever consider a dissenting opinion, and you'll always be right.

[Chilly]

What's more, he'd tell us he's right and everyone else is wrong because you can't have a hat without soccer, since they're actually the same thing. w00t.gif

 

Why else would they have a hat trick in soccer?

[Orton's Arm]

He found a source that confirms his idiocy.  Therefore, the source is "credible".  Any source that doesn't confirm his idiocy is "not credible"...like a textbook. 

 

It's typical.  Not just of him, either.  Look at how the zealous liberals/conservatives here hold so dearly to their liberal/conservative news sources.  Don't allow yourself to ever consider a dissenting opinion, and you'll always be right.

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You've provided zero credible sources to support your view. None. You've provided no verbal logic to support your view either, beyond your raw ability to hurl baseless accusations at people.

 

For example, you make the unsupported claim that I don't understand variance. If you wanted to turn this into something that actually supports your stupid position on regression toward the mean, you'd a) actually define variance yourself, b) demonstrate how this definition supports or undermines the phenomenon described in the Hyperstat article. (It doesn't undermine Hyperstat's description, but don't let that stop you from pretending otherwise.)

 

In contrast to your zero-evidence approach, I've provided a number of links which explain regression toward the mean in the same way I explained it. I've created a model which shows the phenomenon at work. And if this wasn't enough, Wraith (who does statistics for a living) has supported what I've said about regression toward the mean.

 

I've done quite a bit to give credibility and support to what I've been saying about regression toward the mean. You've done precisely nothing to give any support to your mistaken and misguided views. Please don't complain when I don't take your views about regression toward the mean seriously. The problem's not me, it's you.

[Bungee Jumper]

You've provided zero credible sources to support your view. None. You've provided no verbal logic to support your view either, beyond your raw ability to hurl baseless accusations at people.

 

For example, you make the unsupported claim that I don't understand variance. If you wanted to turn this into something that actually supports your stupid position on regression toward the mean, you'd a) actually define variance yourself, b) demonstrate how this definition supports or undermines the phenomenon described in the Hyperstat article. (It doesn't undermine Hyperstat's description, but don't let that stop you from pretending otherwise.)

 

In contrast to your zero-evidence approach, I've provided a number of links which explain regression toward the mean in the same way I explained it. I've created a model which shows the phenomenon at work. And if this wasn't enough, Wraith (who does statistics for a living) has supported what I've said about regression toward the mean.

 

I've done quite a bit to give credibility and support to what I've been saying about regression toward the mean. You've done precisely nothing to give any support to your mistaken and misguided views. Please don't complain when I don't take your views about regression toward the mean seriously. The problem's not me, it's you.

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Sources? Again: READ A TEXTBOOK.

 

Verbal example: a pair of dice, roll an 11, the next roll will more likely be less than 11 than not, because there's 33 possible outcomes of being less than 11, but only three of being greater than or equal to 11...and thus, the value regresses toward the mean, because the difference between 11 and 7 (the mean value of two dice) is relatively high. You'll note two things: 1) this is a verbal example of the mathematically CORRECT definition of regression to the mean, and 2) THERE IS NO ERROR INVOLVED, it is strictly a function of the binomial probability distribution.

 

Those two statements above should be enough to end any conversation on the subject. They WOULD be, if you were even slightly less an idiot. Unfortunately, your extreme idiocy won't regress to the mean idiocy of the population, for yet another reason you don't understand: dependent measurements don't regress toward the population mean. If little Jimmy scores a 750 on his SATs, you would not expect him to score a 450 next time around, even though that's a significant deviation to the mean. You WOULD expect him to score near 750, within the bounds of the error of the test. If he takes it ten times, you might establish the error of the test...and you might find that his second score (of 730, let's say) regresses toward HIS mean score of 725, which is just the error inherent in the test regressing toward the mean error of ZERO. That is what you simulated, that's what you've been describing...you're just too stupid to see that it's an entirely different effect than regression toward the population mean.

[Orton's Arm]

Sources?  Again: READ A TEXTBOOK.

Had you followed your own advice, a very unfruitful debate could have been avoided.

Verbal example: a pair of dice, roll an 11, the next roll will more likely be less than 11 than not, because there's 33 possible outcomes of being less than 11, but only three of being greater than or equal to 11...and thus, the value regresses toward the mean, because the difference between 11 and 7 (the mean value of two dice) is relatively high.  You'll note two things: 1) this is a verbal example of the mathematically CORRECT definition of regression to the mean, and 2) THERE IS NO ERROR INVOLVED, it is strictly a function of the binomial probability distribution.

There's an element of random chance involved in the example you've provided above. As you point out, this random chance produces a quasi-normal distribution with a mean value of 7. You are right in saying that a die roll of 11 is expected to regress toward the mean value of the distribution upon being rerolled. Further, you are right to say that someone who gets lucky or unlucky on an I.Q. test is expected to have neutral luck the second time around--and hence to regress toward his or her true I.Q.

 

However, very high scores on I.Q. tests signal people who are disproportionately lucky on the test. When such people retake the test, some will obtain higher scores, but most will obtain somewhat lower scores. In the aggregate, they mildly regress toward the population mean; because the net positive luck the group experienced the first time around goes away upon being retested. (The reason the group had net positive luck the first time around was because they were selected based on their high scores; which are in part based on good luck.)

 

The average person who gets a 750 on the math section of the SAT got a little lucky in taking it. If such a person retakes it, the expected outcome is 725.

[Bungee Jumper]

There's an element of random chance involved in the example you've provided above. As you point out, this random chance produces a quasi-normal distribution with a mean value of 7. You are right in saying that a die roll of 11 is expected to regress toward the mean value of the distribution upon being rerolled.

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No sh--, I'm right. And it's entirely due to random chance: the chances of rolling less than 11 are much greater than rolling 11 or greater. Period. That's the only reason regression toward the mean happens: because extreme values in a normal distribution (or binomial distribution in this case - which is close enough to a normal distribution for this example) are unlikely to reoccurr.

 

Ditto with normally distributed error in an IQ test: it is highly unlikely that extreme amounts of error will reoccur on further testing. But - and here's the point you consistently refuse to comprehend - that will cause regression toward the mean of the error, not the mean of the sample. That's what you keep confusing; you keep treating the probability distribution of the error and of the sample as the same thing, when they're two COMPLETELY different and unrelated things.

 

That you can't even understand that simple point is absolutely mind-boggling. But then, you didn't even know what a binomial distribution is, apparently ("quasi-normal" distribution. ). But then, why would you? That's something you'd pick up if you READ A GODDAMNED TEXTBOOK, YOU FOOL.

[Orton's Arm]

No sh--, I'm right.  And it's entirely due to random chance: the chances of rolling less than 11 are much greater than rolling 11 or greater.  Period.  That's the only reason regression toward the mean happens: because extreme values in a normal distribution (or binomial distribution in this case - which is close enough to a normal distribution for this example) are unlikely to reoccurr. 

 

Ditto with normally distributed error in an IQ test: it is highly unlikely that extreme amounts of error will reoccur on further testing.  But - and here's the point you consistently refuse to comprehend - that will cause regression toward the mean of the error, not the mean of the sample.  That's what you keep confusing; you keep treating the probability distribution of the error and of the sample as the same thing, when they're two COMPLETELY different and unrelated things.

 

That you can't even understand that simple point is absolutely mind-boggling.  But then, you didn't even know what a binomial distribution is, apparently ("quasi-normal" distribution.  ).  But then, why would you?  That's something you'd pick up if you READ A GODDAMNED TEXTBOOK, YOU FOOL.

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Are you really this ignorant about stats? Your two dice example isn't a binomial distribution by any stretch of the imagination. For any given data point on a binomial distribution, there are only two mutually exclusive outcomes--think flipping a coin. Just because you have two dice doesn't make the resulting distribution binomial. It makes it quasi-normal, because those two dice will produce a data curve somewhat similar to a normal distribution.

 

Despite your claims, I'm not confused in the slightest between regression toward the mean of the sample and regression toward the mean error value of zero. The latter phenomenon causes the former. Someone who gets a very high score on a test that's based at least in part on luck is (on average) luckier than normal. Someone who gets a low score on a partially luck-based test will, on average, be less lucky than normal. Upon retaking the relevant test, these people's scores will tend to regress to an error value of zero. This cancels out the good or bad luck they generally experienced the first time around, and causes them to regress somewhat toward the population mean.

[Bungee Jumper]

Are you really this ignorant about stats? Your two dice example isn't a binomial distribution by any stretch of the imagination. For any given data point on a binomial distribution, there are only two mutually exclusive outcomes--think flipping a coin. Just because you have two dice doesn't make the resulting distribution binomial.    It makes it quasi-normal, because those two dice will produce a data curve somewhat similar to a normal distribution.

 

And you're right, if you completely ignore the fact that the probability distribution of a pair of dice is described by THE EQUATION YOU LINKED TO.

 

Despite your claims, I'm not confused in the slightest between regression toward the mean of the sample and regression toward the mean error value of zero. The latter phenomenon causes the former. Someone who gets a very high score on a test that's based at least in part on luck is (on average) luckier than normal. Someone who gets a low score on a partially luck-based test will, on average, be less lucky than normal. Upon retaking the relevant test, these people's scores will tend to regress to an error value of zero. This cancels out the good or bad luck they generally experienced the first time around, and causes them to regress somewhat toward the population mean.

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That makes no sense. It makes NO sense. You just said that one person's "luck" cancels out another person's "unluckiness", and that causes an overall population effect of regression toward the mean...except that as Wraith pointed out to you, the net effect of cancelling out the error is ZERO, which means you should see NO regression toward the mean. That's why researchers use large sample sizes: to reduce the net error. But that only reduces the error! It doesn't cause an otherwise normally distributed sample to magically become single-valued at the mean.

 

Again, you'd see this if you could distinguish between "sample" and "error", and actually had some math skills.

[Chilly]

However, very high scores on I.Q. tests signal people who are disproportionately lucky on the test. When such people retake the test, some will obtain higher scores, but most will obtain somewhat lower scores. In the aggregate, they mildly regress toward the population mean; because the net positive luck the group experienced the first time around goes away upon being retested. (The reason the group had net positive luck the first time around was because they were selected based on their high scores; which are in part based on good luck.)

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Wow. A very high score on an IQ test means that they are "disproportionately lucky"? How the hell does that work?

 

I guess people with High IQs aren't really that smart, they just have more luck than anyone else.

[Ramius]

And you're right, if you completely ignore the fact that the probability distribution of a pair of dice is described by THE EQUATION YOU LINKED TO. 

That makes no sense.  It makes NO sense.  You just said that one person's "luck" cancels out another person's "unluckiness", and that causes an overall population effect of regression toward the mean...except that as Wraith pointed out to you, the net effect of cancelling out the error is ZERO, which means you should see NO regression toward the mean.  That's why researchers use large sample sizes: to reduce the net error.  But that only reduces the error!  It doesn't cause an otherwise normally distributed sample to magically become single-valued at the mean. 

 

Again, you'd see this if you could distinguish between "sample" and "error", and actually had some math skills.

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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.

 

I bet he still thinks dewey defeated truman, and has the newspaper framed on his wall, as the only "credible" source about the outcome of the election.

[Ramius]

Wow.  A very high score on an IQ test means that they are "disproportionately lucky"?  How the hell does that work?

 

I guess people with High IQs aren't really that smart, they just have more luck than anyone else.

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Thats what he been blathering about for 50+ pages. That smart people are lucky, and stupid people are unlucky, and that everyone really has the same IQ.

[Bungee Jumper]

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.

 

Any other sources are also geared to higher than a second-grade level.

 

I bet he still thinks dewey defeated truman, and has the newspaper framed on his wall, as the only "credible" source about the outcome of the election.

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Actually, they were tied. Truman's extra votes were measurement error.

[Chilly]

Thats what he been blathering about for 50+ pages. That smart people are lucky, and stupid people are unlucky, and that everyone really has the same IQ.

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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.

[Bungee Jumper]

Thats what he been blathering about for 50+ pages. That smart people are lucky, and stupid people are unlucky, and that everyone really has the same IQ.

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No, but they regress to the same IQ the more you test them, because the test is wrong. Therefore, we should breed the smart ones, even though they're no smarter than the dumb ones, just luckier.

[Bungee Jumper]

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