Orton's Arm

If you understand the way my simulation was set up, and if you understand the definition of a Monte Carlo simulation, you'll know that what I did was in fact a Monte Carlo simulation. The EPA quote also referred to the phenomenon as "regression toward the mean," as did the statistics texbook quote I found; as did the Hyperstat link. In the absence of measurement error, the phenomenon I've described would disappear. Someone with a true I.Q. of 140 would score a 140 on an I.Q. test the first time, the second time, and the third time. Nobody who scored a 140 would be a lucky 130 or an unlucky 150. The Berkeley article is correct. As for your demand that I "do the math" the answer is no. I've done enough work already. I created a Monte Carlo simulation. I've found quotes from numerous credible sources which support exactly what I've been saying. If those quotes aren't mathematical enough for you, too bad. Find quotes you like then. They're out there, and they say the same thing I've been saying. It's you who keeps devolving into semantic arguments by constantly and incorrectly accusing me of not knowing the definitions of specific terms. My arguments have been strictly conceptual, not semantic. You say you want a math discussion, yet almost nothing you've attempted to contribute to this debate has been even remotely mathematical. As far as explaining what my linked articles mean; I've been doing that for dozens of pages now, long before I even found the articles themselves. But I'll do it once again for your benefit. Suppose you're considering those individuals who scored 2 standard deviations above the population mean. Assume measurement error is normally distributed with a mean of zero. There is a probability of X that someone with a true score of 1.9 SDs will get lucky and score 2.0 SDs on the test. Therefore, a given individual with a true score of 2.1 SDs will also have a probability of X of getting unlucky and scoring 2.0 SDs on the test. With me so far? You know and I know that there are more people at 1.9 SDs above the population mean than there are at 2.1 SDs above the mean. The number of lucky 1.9s who scored 2.0 will be X * (the number of people 1.9 standard deviations above the mean). The number of unlucky 2.1s who scored 2.0 will be X * (the number of people 2.1 standard deviations above the mean). Do the same thing again, using a probability of Y, and comparing the lucky 1.8s to the unlucky 2.2s. Then use a probability of Z, and compare the lucky 1.7s to the unlucky 2.3s. In each case, you find that more lucky people are flowing in from below, than unlucky people are flowing in from above. In selecting the group that scored 2 standard deviations above the population mean, you're selecting a group that, collectively, has more people who got lucky on the first test than unlucky. Give those people a second test, and the group's score will be closer to the population's mean.

I agree we need to start paying down the debt; but that has to start with the creation of at least some spending discipline. Without spending discipline, additional tax revenue will translate directly into more government spending and no debt repayments. Under FDR, the U.S. endured the longest depression in its history. If people were starving on the street, it was largely because FDR was paying farmers to destroy food.

You talk big about math, and I remember several instances of you promising Monte Carlo simulations. At no point did you deliver on those promises. The only one who's contributed any real math to this debate is me--which I did through my Monte Carlo simulation. Your statement that I've changed my tune even once is dead wrong. Consistently, from the very beginning, I've said the following: suppose an I.Q. test involves measurement error. Someone with a true I.Q. of 130 could get lucky and score a 140, or unlucky and score a 120. Given this (reasonable) assumption, someone who scores a 140 on an I.Q. test is more likely to be a lucky 130 than an unlucky 150. Therefore, people who score 140s on I.Q. tests are expected to, on average, obtain somewhat lower scores upon being retested. I said this in the beginning of the debate, I said it in the middle, and I'm saying it now. Oh, and by the way, I've got articles from Stanford, Berkeley, the University of Chicago, and a number of other sources with which to back up what I've been saying. You imply that I'm igorant because I use words like "luck" and "error" to explain the phenomenon. How, then, do you explain the fact that the author of the Stanford article also used the words "luck" and "error" when saying exactly the same things I've been saying?

While you may or may not be right, that's not what we've been arguing about. The phenomenon in question is described here. But it would be really, really pathetic if, 15 weeks into the season, a playoff scenario thread got hijacked by regression toward the mean. So I now return you to your regularly scheduled playoff scenario thread. Go Bills! Go Dolphins! Go Patriots!

I agree that the debt and the dependence on foreign oil are both unacceptable. But the tax cuts need not have added to the debt. It's the combination of tax cuts and the complete absence of spending discipline which has created massive deficits. My own preference is to keep the tax cuts intact, and develop at least some spending discipline. Because if you try to do things the other way--let the government spend what it wants, and tax enough to keep up--you'll never have enough tax revenue. As for the Socialist programs to which you're referring, FDR and LBJ did far more to attack capitalism than they did to save it.

I've remained very consistent throughout this debate. Someone who scored a 140 on an I.Q. test the first time around will, in general, tend to score somewhat closer to the population's mean upon retaking the test. This debate began because you felt the phenomenon described was untrue. The quotes from Stanford, Berkeley, the University of Chicago, the EPA, and the other sources I cited clearly demonstrate that the phenomenon I've been describing for the last 50 pages is real. Your attempts to ridicule me for having described this phenomenon have caused you to look foolish and ignorant.

I think what Bill is getting at is that it doesn't make sense to draft a player in the first round if your plan is to only keep him 4 - 6 years. It's too hard to build something solid if your building blocks slip away from you that quickly. Suppose the Bills were to lose Clements to free agency, while at the same time drafting a CB in the first round. If the Bills' front office lets Clements slip away this year, shouldn't we also expect them to let that new 1st round CB slip away in five or six years? At some point, the Bills have to get off the hamster wheel Bill described. You shouldn't draft CBs in the first round unless there's the willingness and ability to keep them in Buffalo for the vast majority of their careers. The Bills need to display both things with Clements. If they won't or can't get it done with Clements, why expect them to get it done with the next first round CB?

I share your feeling of optimism about this team. If the Bills get into the playoffs, I at very least expect them to put up a good fight. There's so much to like about this team. We had absolutely no right to expect this quality of offensive line play at this point in the season. Jason Peters was moved to left tackle only a few weeks ago. Pennington is a rookie and a 7th round pick. Mike Gandy has never played guard for the Bills. Fowler is new to the team; and Preston is a first-year starter. McNally has surpassed his reputation as an offensive line coach. As for Fairchild, nobody can question his commitment to the run. But the offense also has a Rams-like ability to hurt defenses with the deep pass. I don't see how this group of players could possibly be doing better with some other offensive coordinator than they are with Fairchild. You've got a solid coaching staff that interacts well with the front office. I'm a little unhappy with how our defensive scheme does against the run, but overall I feel this team is on the right track, both for this year and next.

Sick already? Prepare to get even worse! 1) There's a regression toward the mean thread. 2) The thread's 19 pages long. 3) The thread remained on track (more or less) for all 19 pages. 4) That thread is actually a continuation of a larger regression toward the mean debate that consumed at least 50 pages. 5) The debate was about whether people who obtain extreme scores on imperfect tests will tend to score somewhat closer to the population's mean upon being retested. 6) I eventually found quotes from Stanford, Berkeley, the University of Chicago, the EPA, the University of Washington, Ohio State, and other sources which stated that those who obtain extreme scores on imperfect tests tend to score closer to the population mean upon being retested. You'd think those quotes would be enough to close the mouths of those who'd disagreed with me. But two of my opponents have proven especially stubborn.

All real debate ended when I provided the quotes from Stanford, Berkeley, the University of Chicago, et al. Nothing you can possibly say will detract from the truth of those quotes. The quotes say that in test/retest situations, those who obtain extreme scores on the first test will tend to score closer to the population mean upon being retested. I've been so abundantly clear on that issue that nothing you now say will confuse people into believing that I've said otherwise. Unfortunately for yourself, you've been so prolific in mocking my view of this that you can't weasel out now. You've made a complete fool out of yourself. Deal with it.

There's some truth to this post. But Bungee Jumper and I have arguing about more than just semantics here. I've written that if an I.Q. test involves measurement error, someone who obtains a very high or low score on the first test taking will, on average, score closer to the population's mean upon being retested. Because I voiced this sentiment, Bungee Jumper has questioned my intelligence, my knowledge of statistics, and has indulged in endless "regression toward the mean" jokes at my expense. He's wandered into threads that had nothing to do with me or with the issues we've been debating, and announced his opinion that I belong in a list of the stupidest posters on this board. Fortunately, I've found quotes from sources like Stanford, Berkeley, the University of Chicago, and others, which prove that my description of the phenomenon was correct, and Bungee Jumper's ridicule was absurd. Given the abuse he's shoveled my way, I'm not willing to pretend that Bungee Jumper was aware of this phenomenon all along. He wasn't; and he discouraged others from believing in it. If the debate now seems to be about semantics, it's because Bungee Jumper is no longer (directly) disputing the phenomenon I've worked so hard to describe. But he still feels the need to call me an idiot, and to prove to the world that I must have been wrong about something or another. So now he's turned to vague and unsupported accusations--"you're too stupid to understand the difference between variance and error" would probably be a run of the mill Bungee Jumper post. He eschews the idea of providing information about a) how he thinks I'm defining variance and error, b) how he thinks those terms should be defined, and c) how the difference between a) and b) has supposedly caused a mistaken understanding of the underlying issue. In other words, he's deliberately vague, and avoids getting pinned down. As long as he continues to ridicule something from what I've been saying, he appears to the casual observer to have been consistent. On one level, this is a debate about whether the statistical phenomenon I've been describing exists. But more than that, it's about Bungee Jumper's need to ridicule me about something. So he'll make vague accusations--"you don't understand the articles you're quoting"--not because he thinks these things are true, but because he hopes that others reading this thread will believe the accusations. Most people aren't very confident in their knowledge of stats. Bungee Jumper knows this, and hopes these people will conclude that there's some hidden or mysterious meaning in the quotes I've found, which he was (supposedly) smart enough to see; but which I could not see. He provides no insight into what that alleged hidden meaning might actually be. In general, he's aware that vague accusations--"you're too stupid to understand the article" are harder to refute than specific accusations. Bungee Jumper's communication style doesn't lend itself to the edification of the audience. Very rarely will he attemt to provide actual information about statistics. Consider his statement that I can't distinguish between error and variance. A claim like that cannot possibly be expected to enlighten either myself or any third party reading this thread. He makes no effort to explain this difference; nor to show its relevance to our debate. Those reading this thread are expected to blindly take his word that I don't understand these things, and that this misunderstanding somehow demolishes the points I've been making. Most people don't have the self-confidence in their knowledge of stats to see the absurdity of his claims. They incorrectly assume that if a physicist like him is throwing this type of accusation my way, there must be at least some truth to it. There isn't, but how can people know? I regret that I've sunk to his level as far as name-calling goes. But I've tried to avoid sinking to his level in other ways. Instead of trying to win debates by making vague, Bungee Jumper-style accusations, I try to make the audience a little richer in knowledge than it otherwise would have been. I do not deliberately deceive or mislead people. I tell the truth as I see it. I don't throw insults at people unless they first insult me. These things aren't much, and I'm certainly not claiming to be a saint. But they're at least something.

Right. Because when I wrote that someone who scored a 140 on an I.Q. test could be a lucky 130 or an unlucky 150, it was a sign of sheer idiocy. But when the Stanford author wrote that someone who scored a 140 on an I.Q. test could be a lucky 135 or an unlucky 145, it was a stroke of sheer brilliance. Likewise, when I went on to point out that there are more 130s available for getting lucky than there are 150s available for getting unlucky, it was a sign of a blathering idiot. But when the Stanford author pointed out that there are more 135s available for getting lucky than there are 145s available for getting unlucky, it was a sign of solid scholarship. And when I used the word "error" to describe the difference between someone's measured score and true score, it showed that I didn't know the difference between error and variance. But when the Stanford author used the word "error" to describe the difference between someone's measured score and true score, it was good scholarship.

Dude, stop trying to hijack a perfectly good thread about playoff scenarios by lying about the outcome of our debate over in the regression toward the mean thread.

The quotes I've provided are correct. The quotes I've provided indicate that generally, those who obtain very high or very low scores on tests tend to regress toward the population mean upon being retested. Your attempts to make fun of this phenomenon have made you look both stupid and ignorant--especially now that I've found numerous sources describing the phenomenon I've been describing. Now, you seem to be trying to distract attention from all the confusion and error you've been sowing by pretending I don't know the difference between error and variance. That's pitiful. In fact, everything about your participation in this discussion has been pitiful. I provided the I.Q. test example, which you ridiculed. Well guess what? Your decision to engage in ridicule sure looks pitiful in light of the fact that the Stanford website provided essentially the same example I provided. They said basically the exact same thing. Oh, oh, let me guess: because it's Stanford, their example of lucky 135s/unlucky 145s takes the difference between error and variance into account, whereas my example of lucky 130s and unlucky 150s shows a complete incomprehension of the issue. Am I really supposed to respect you after seeing you engage in such idiocy or such lack of intellectual honesty? You're being pitiful either way.

In other words, you're on a personal crusade against me, and you're determined to pursue this crusade by making fun of a statistical phenomenon described by Stanford, Berkeley, the University of Chicago, and other credible sources. I understand completely.

I know I'm going against the grain here, but I'll be rooting for Denver in their game against the Bengals. To my way of thinking, the Dolphins almost have to beat the Jets for the Bills to have a real shot. Assuming the Dolphins and Bills both win, then all that's necessary for the Bills to control their own destiny is a New England win over Jacksonville, and the Broncos win over the Bengals.

Most Bills fans are able to enjoy the fact that this team still has a legitimate shot at the playoffs with only two weeks to go. These people are able to enjoy thinking through the various scenarios, and mulling over which team to root for in the Denver/Bengals game. But not you. You saw the word "statistical" in the thread's title, and decided to once again expose the world to your ignorance about a specific statistical phenomenon. I'd appreciate it if in the future you confine your ignorance to the "regression toward the mean" thread over on the PPP boards. Thanks.

I don't see why Ramius and Bungee Jumper expect anyone to be stupid enough to believe I don't understand the quotes I've found. Anyone who's a) been paying at least some attention to this debate, and b) has at least a few working brain cells, will see that those quote communicate exactly the same message I've been trying to get through for the last 50 pages. I just don't see how anyone on these boards could possibly be stupid enough to buy what Ramius and Bungee Jumper are selling.

Right. So now it's "pollution" to dispute a spurious charge leveled against Darin. Gotcha.

I wasn't polluting this thread with talk of regression toward the mean. I was addressing the issue of Darin's Alaskan residency as it related to his so-called hypocrisy. You were the one who chose to hijack this thread by making it about regression toward the mean. Apparently, those quotes I found from Stanford, Berkeley, the University of Chicago, the EPA, and other sources weren't enough to shut you up.

I guess those quotes from Stanford, Berkeley, the University of Chicago, and the other sources I mentioned must have been written by idiots too then. Because they say the same thing I've been saying all along.

Save it for the regression toward the mean thread.

Here's the Berkeley quote again, this time with more explanation: The message in that quote should sound familiar to you. I've been saying it for 50 pages.

Unless Darin has some secret life I don't know about, I don't see how he's guilty of hypocrisy. You seem to be giving him three choices: 1) Sell his Alaska home, and move to a state that gets fewer subsidies. 2) Welcome high levels of government spending, even though he can clearly see this spending is often wasteful or worse. 3) Admit that he's a hypocrite. Quite frankly, I don't see why Darin should have to take any of the three choices you've given him.

I'm not alone: the EPA has been calling it the same thing. I'm not sure why on earth you'd expect anyone to believe that bit about me changing my story. Earlier this page, I gave that I.Q. test example with which the PPP board is now no doubt familiar--someone who scored a 140 on an I.Q. test is more likely to be a lucky 130 than an unlucky 150. Hence, if a group of people who scored a 140 the first time around chose to retake the test, that group's average on the retest would be less than 140. I've been saying this from the beginning of the debate. Why would I feel a need to change this message at the very moment when I've found numerous websites that back me up? Do you honestly think anyone on these boards is stupid enough to believe a line like that?