Orton's Arm

You're wrong. I was simulating whether the existence of measurement error in an I.Q. test can cause the appearance of regression toward the mean. It can.

I can live with that.

You will have to elaborate more if you want your post to have any meaning.

Bungee Jumper's criticisms of my model are invalid. My model is only designed to say one thing, but to say it very well: error in measurement can cause the appearance of regression toward the mean. The other factors you mentioned are important to a discussion about intelligence in general, but aren't really what we're arguing about right now.

The people in your workplace know only those things about me which you choose to tell them. Given that, their views are unsurprising. As for the rest of your post, I finally understand your thought process a little better. Suppose someone with, ah, a touch of overconfidence were to take a surface view of this situation, without giving it serious thought. You start off with a normally distributed error term, with a mean of zero. You're right in saying that the measured I.Q. for the population as a whole ought to be the same as its true mean. Further, you know that any given individual who sits down to take an I.Q. test is just as likely to get lucky as unlucky. Why, then, did the Monte Carlo simulation demonstrate people with measured I.Q.s above the threshold were, on average, not quite as smart as their test results indicated? Some people with true I.Q. values below the threshold value got lucky the first time they took the test, and were placed in the threshold group. Other people had true I.Q. scores above the threshold value, but got unlucky when they took the test. These people weren't placed in the Threshold group. In other words, some of the people who were eliminated were smarter than some others who were included. Now consider the second test for the Threshold group. Some of the people taking that test don't belong there, because their I.Q.s fall below the threshold value. These people will drag down the Threshold group's average I.Q. when that group gets retested. Meanwhile, you have people with above-threshold I.Q.s sitting there not being retested, because they were excluded from the Threshold group based on their bad luck the first time they took the intelligence test.

Is this your honest attempt to analyze my simulation? Yes, my normally distrubuted variable was error, because I was measuring whether error in measurement can cause the appearance of regression toward the mean! With an error term, people who do exceptionall well on an intelligence test will tend to do worse the second time they take the test. Without an error term, that regression toward the mean disappears. In my simulation, the presence of an error term causes the appearance of regression toward the mean. It causes the regression toward the mean. It's not an effect of anything else, because the simulation was so simple there was nothing else that could possibly be causing the appearance of regression toward the mean. Nothing. You didn't embarrass yourself as much as Ramius did when he came to syhuang's defense. But you certainly did embarrass yourself.

Typically, government bureaucracies want as much funding as possible. They generally respond to funding cuts by eliminating their most necessary services first. Then they throw up their hands and say, "Look at all the things we had to cut because we were underfunded. Give us the money we need, and these things wouldn't happen." This may indeed be an attempt to cut waste. Whether the attempt proves successful remains to be seen.

When I used the phrase "functional equivalence" I had the following thought process in my mind. Suppose that a child's I.Q. is determined solely by that of the parents, without respect to the underlying population group. If this were the case, then giving someone's children an I.Q. test would be just as valid a measure of parental intelligence as giving the parents themselves an I.Q. test. (Yes, there are a lot of factors that I'm ignoring here, and which my opponents will predictably but incorrectly accuse me of being ignorant of. My purpose in ignoring these other factors is to focus exclusively on whether measurement error can cause the appearance of regression toward the mean.) I know reality is far more complex than the world I've described above. But in that world, children appear to regress toward the mean, and they appear to do so strictly because of measurement error. Because measurement error is also a part of real world I.Q. tests, we shouldn't ignore its potential to explain why the children of people with exceptionally high measured I.Q.s tend to have slightly lower measured I.Q.s than their parents.

I'll overlook the tone of your post, and focus on the more substansive portion. First off, I agree with your opening sentence. I indeed measured regression toward the mean as a function of error when the same people take the test multiple times. My Monte Carlo simulation shows that people with high measured I.Q.s are, on average, a little less intelligent than their scores make them appear. Do you agree so far? Now let's turn to the topic of children. Suppose two people with high measured I.Q.s decide to have kids. My simulation demonstrated that, on average, these measured I.Q.s will slightly overstate the true intelligence level of the parents. The children's I.Q.s are a function of the parents' true I.Q.s, not their measured I.Q.s. When you go to measure the children's I.Q.s (the functional equivalent of the second I.Q. test in my simulation) you'll find their measured I.Q.s are closer to the mean than the measured I.Q.s of their parents. This is because the Threshold parents (first test) group had measured I.Q.s scores that mildly overstated their true intelligence, while the Threshold children (second test) had measured I.Q. scores that, on average, stated their intelligence more or less correctly. Assuming you're foolish enough to accurately communicate the details of this discussion to your colleagues, I think you'll find the more insightful will agree with me.

Taxes are indeed theft if the money is squandered.

Wrong.

You should know.

A troll is someone who makes inflammatory comments while providing little or no evidence with which to back them up. Much like Bungee Jumper has been doing these last 13 pages.

Your post is absurd. The phenomenon I simulated is the same one I described earlier with words. Either a) you didn't understand my words, b) you didn't understand my simulation, c) you didn't understand either the words or the simulation, or d) you realize you're wrong but don't want to admit it.

Both parties have sold out to big business. Neither looks out for the little guy.

What on earth is this a response to? Bungee Jumper wouldn't accept my explanation of regression toward the mean until I did the math. Well guess what? I did the math, and I was right. He and Ramius have so much egg on their faces they'll probably die of cholesterol poisoning, and I'm the one who's supposed to keep his mouth shut? Not likely.

Don't judge him strictly based on his performance in the discussion about regression toward the mean discussion. He (and for that matter Ramius) have, perhaps demonstrated greater levels of competence in their regular professional lives than they have on this issue. If they haven't, they deserve to be fired.

I knew that if I did the math that a) I'd be proven right, and b) you'd choose to ignore this proof, regardless of its strength. I was right on both counts. My Monte Carlo simulation demonstrates that people who have substantially above-average scores on an I.Q. test will tend to have somewhat less impressive performances if they take the test a second time. The reasons for this are explained in the Wikipedia article, as well as in my earlier posts on this issue.

I just finished creating a Monte Carlo simulation. In this simulation, measurement error led to the appearance of regression toward the mean. In other words, I was right. Methodology 1. I created a population of 1000 members. The members were randomly assigned I.Q.s from a normal distribution with a mean of 100 and a standard deviation of 10. I set trueIQ =norminv(rand(),100,10) 2. To obtain a given population member's measured I.Q., I applied an error function to each member's true I.Q. The error function was random and normally distributed, with a mean value of zero and a standard deviation of 2.5. I set measured IQ =trueIQ+norminv(rand(),0,2.5) 3. I arbitrarily defined a threshold of 115. Those members with measured I.Q.s below the threshold were ignored. =if(measuredIQ>threshold,1,0) 4. Members with measured I.Q.s above the threshold were subjected to a second measurement. The second measurement was the original I.Q. plus a random, normally distriubted error function with a mean of zero and a standard deviation of 2.5. =trueIQ+norminv(rand(),0,2.5) 5. I compared the results that threshold members obtained from the second test with those obtained from the first test. I pressed F9 at least ten times. Each time, the average score for threshold members was worse the second time they "took the test" than it was the first time. In other words, those who did well on an I.Q. test appeared to regress toward the mean when tested a second time. The sole source for this regression toward the mean was measurement error.

I'm sorry, but your statements about measurement error and regression toward the mean don't represent mainstream science. In fact, they don't represent anything more than your own inability to understand the Wikipedia article even after I explained it to you.

You think that Weiss identified intelligence in children based on future career aspirations, and I'm the one who can't read? Your other accusations are of course spurious, as perhaps they were meant to be. But without intending to give those accusations a dignity they don't deserve, I wonder why on earth you think I missed the part where Weiss described the flaws and limitations of his study. While no study is perfect, Weiss's was good enough for the relationship between parental and child I.Q. to shine through.

As opposed to being your own.

I completely agree. On the one hand, it's easy for a sportswriter to make a player look good. But in this case--based on Romo's performance on the field as well as on articles like this--he's starting to look like a real quarterback. A player who has the mental edge you described.

If you go back and reread this thread, you'll see that I'm open to the idea that TD's performance in rounds 3 - 7 is par for the course. No, I don't feel you've conclusively proven your case, but neither has your case been disproven.

From what I've heard from Green Bay fans, the Nall you'll get on Sunday is a much better quarterback than the Nall you get during the week. You're probably right in saying the Bills have written Nall off based on what they've seen from his practices. Green Bay probably was equally unimpressed with Nall's practices when they took Aaron Rogers. Given that Nall's season in NFL Europe was comparable to Kurt Warner's, I'm curious to see what would happen were Nall to be placed in a game or two. If he plays poorly, you can always go back to Losman. If he plays well, you keep him in there. Then you wouldn't need to address the QB position in the coming draft.