Orton's Arm

You bring up good points in your first paragraph--Ludendorf was clearly political. Then again, he wasn't one of the generals planning to overthrow Hitler. You're also right in saying that Hitler's minority position within the German government was very powerful. That said, Hindenburg initially wanted to totally exclude Hitler from the government, and let Hitler have that minority position only because he could not maintain a majority government without Hitler's help. Overall, FDR's economic policy was an abysmal failure

Do you think I enjoyed 30 pages of advocating a commonly accepted statistical principle; only to be greeted by ignorant derision? Or take this discussion: Hitler's plans called for Germany to conquer large portions of Europe, but he had no interest in building some global empire. After France fell, Hitler asked Britain for peace; despite the obvious opportunity to conquer British-held places like the Middle East and most of Africa. Hitler's ambitions were confined to Europe, or at most to the Soviet-held portion of Asia. This is not some theory I've concocted; it's an historical fact. Look it up.

Are you really this dense? I wrote that without measurement error, there could be no luck in taking an I.Q. test. Someone with an I.Q. of 130 would always score a 130 on the test--both the lucky 140 possibility and unlucky 120 possibility are precluded. Your Vegas table has precisely zero relevance to this. The purpose of a Vegas table isn't to measure height, or I.Q., or anything else really. It's simply a random number selection device. My point--which apparently sailed right over your head--is that if someone is being measured for the same quality twice, regression toward the mean will tend to occur the second time around, but only if there's measurement error in the underlying test.

I don't have any "theories" about regression toward the mean. I'm simply reiterating statistical facts as discovered by others.

Since you don't know what we're discussing, you can read up on it here

Hindenburg tried to build a non-Hitler coalition, which soon collapsed. Eventually, Hindenburg became convinced that including Hitler in the government might be necessary to avoid a civil war. The Nazis were initially given only a minority of the cabinet positions; which represented Hindenburg's plan to keep Hitler under control. Ultimately, Hindenburg bowed to political pressure created by Hitler, just as the German generals had earlier bowed to political pressure created by the WWI Allies. They would have bowed to political pressure created by FDR; had he cared to impose any. FDR's economic policies were a failure, as demonstrated by the fact he presided over the longest depression in U.S. history. Most of the depression was on his watch, and was a direct result of the climate of uncertainty and unpredictability he created for businesses.

I'm no expert, but I haven't heard any historian suggest that Hitler had plans to invade the U.S. He'd focused his attention on building up his army and air force, not his navy. The navy he had largely consisted of submarines, which would have been unsuitable to any invasion of the United States. On the one hand, Hitler wasn't in a position to conquer the United States. On the other hand, his lebensraum objective would have been achieved by a successful war against the Soviet Union. He lacked both the means and the motive to go to war against the U.S.

The German generals were apolitical men who knew they would lose the war unless they got a peace treaty on either their eastern or western fronts. Their interests were military, not political. They would have accepted a democratic German government, had FDR demanded they do so as a condition of peace. Certainly, this democracy would have been better for Germany and the world than the tearing up and remaking performed by the Soviets in the eastern half of Germany. FDR moved toward a centrally planned economy in that he had more and more spending take place at the federal level, instead of by the people. If goverment spending represents, say, 70% of total national spending, your economy is 70% centrally planned.

This isn't a question of I.Q. changing over time. Suppose someone was to take an I.Q. test, and score a 140. One month later, suppose this person were to retake the I.Q. test. Clearly this person's underlying I.Q. is still the same, unless it was decreased by excessive exposure to these boards. But regression toward the mean indicates that this person's measured I.Q. will probably be lower the second time he or she takes the test. In other words, that initial 140 score was probably based mostly on intelligence, but also on a little luck.

Regression toward the mean is a tricky concept. But after reading through all 30 pages of this thread, you ought to be able to understand it.

There's the start of WWII, which happened in 1939, and U.S. entry into WWII, which didn't happen until 1941. Hitler had initially hoped for a neutral U.S., because he had more than enough other problems to deal with. But when Japan bombed Pearl Harbor, Hitler saw an opportunity to attack the U.S. shipping going to England and the Soviet Union while we were distracted elsewhere. In addition, he was tired of letting his own navy get harrassed in the Atlantic, while not being able to retaliate.

Oddly, you make a good point. Bush hasn't been shy about expanding the power of the executive branch himself.

Without measurement error, there could be no luck in taking the test. Someone with an I.Q. of 130 would always score a 130 on an I.Q. test. They'd never get lucky and score a 140, nor unlucky and score a 120.

First, FDR got us into WWII through his escalating provocations against Germany and Japan. Then he conducted WWII in such a manner that the Soviets got the heart of Europe. This could have been avoided by giving the German generals a good reason to overthrow Hitler. They realized their nation couldn't win, and they wanted to avoid hostile foreign occupation (especially Soviet occupation). They would gladly have accepted any fair deal FDR had cared to offer. With the European war over several years early, the lion's share of Europe would have been out of Soviet hands. Jews would have been spared several years of concentration camps; and the nations of Europe and North America would have been spared several years of horrible war. FDR's refusal to even pursue this possibility wasn't just a minor slip-up. It was an outright disaster. Nor is that the only problem with FDR's presidency. He moved the country toward a much more centrally planned economy. He had little respect for private property rights. He eliminated some of the constraints on the executive, and attempted to eliminate even more constraints. Had he not been constrained by external political forces, he would have become this nation's first dictator.

I'm sorry, but I know exactly what I'm doing. Yes, the subset I'm retesting has an overwhelming net positive error bias. You think I don't know that? When I retest the Threshold members, that net positive error bias goes away; which causes the scores of the Threshold members to mildly regress toward the mean. But guess what? The same thing happens in real life. People who've obtained above-the-mean scores on I.Q. tests are disproprortionately lucky; while those who've obtained below-the-mean scores are disproportionately unlucky. Ask a group of people who obtained a high score on an I.Q. test to retake it, and guess what? The group's net luck goes away, and their average scores fall a little. The more luck based the test, the more strongly this group will regress toward the mean upon being retested.

Your post is intelligently written, eloquently expressed, but nonetheless wrong. For instance, a normally distributed population is not required for regression toward the mean to take place. Consider a population where everyone had an I.Q. of 100; and where people took an error-prone I.Q. test. Those who scored significantly above or below the mean on their first I.Q. test would, on average, appear to regress toward the mean upon retaking the test. I agree that regression toward the mean wouldn't take place in a uniformly distributed population; except at the very extreme edges. For example, if there were equal numbers of people with I.Q.s of 140, 150, and 160, then a score of 150 on an I.Q. test would be just as likely to indicate an unlucky 160 as a lucky 140. Therefore, someone who scored a 150 on an I.Q. test the first time around would, on average, score a 150 upon retaking the test. Regression toward the mean would still exist at the extreme edge of this distribution. Suppose there were equal numbers of 170s, 180s, and 190s, but zero 200s. Those who got lucky and scored a 200 on the I.Q. test would, on average, score 10 points closer to the mean upon retaking the test. You are correct to point to the shape of the distribution as a relevant factor in regression toward the mean. However, your take on measurement error seems to miss what this discussion is about. Someone who gets a high score on an I.Q. test will, on average, obtain a slightly lower score upon being retested. This phenomenon could not take place unless there was measurement error. As for the height example, I'm not "attempting to restate" anything. I was merely pointing out the rather obvious fact that if a height measurement system involved error, those who obtained extreme height measurements would appear to regress toward the mean upon being remeasured. The height example you're thinking of is important, but not relevant to the discussion of this particular statistical phenomenon.

I was hoping the regression toward the mean discussion could stay confined to that thread, instead of bleeding over onto the whole PPP board.

Instead of responding in kind to these insults (and thus hijacking the thread), I'm going to say something about the original article. On the one hand, I'm glad solar power is apparently being developed. On the other hand, I'd rather see it developed here than in China. Once an industry gets going in a particular place, it's tough to transplant it to some other place. For example, think of how nicely set up Silicon Valley is if you want to start a high tech firm. You've got lots of talented, motivated people right there, venture capitalists ready to fund high tech firms, suppliers, customers, everything all right there. Suppose this same support structure were to be built for solar companies in China, but not for solar companies in the U.S. Do you think that if we fell behind early on, we could catch up later? It'd be awfully difficult.

In my Monte Carlo simulation, I began by creating a population with a normally distributed I.Q. To assign each member an I.Q., I started with a random number, and used the norminv command to convert this to a point on the normal distribution. I then measured the I.Q.s of each member of the population. Measurement was based on their true I.Q.s, plus a normally distributed error term with a mean of zero and a standard deviation 1/4 as large as the standard deviation of the underlying population's normal I.Q. distribution. Those who scored above the Threshold level on the I.Q. test were given a second I.Q. test. The second test was based on the same underlying I.Q. as the first test; as well as on the same error formula. As a group, Threshold members consistently scored slightly worse on the retest than they did on the initial test. If you removed measurement error from the test, this phenomenon would disappear.

You know what we need around here? Fewer threads about solar cells, emerging industries, and the environment. We also need more threads about eugenics, regression toward the mean, and generally throwing insults at each other. I thank you for moving this thread from the badness of the first group of things toward the goodness of the second group. You're really on top of things today, aren't you Ramius? I'm sure RTDB appreciates your efforts to hijack his thread.

Unfortunately, you haven't understood them.

Yes it is. Suppose an error-prone height measurement system. The average person who's initially measured at 7'6" will, upon being remeasured, appear to slightly regress toward the mean.

I've found plenty of evidence with which to support my position--various links, thought experiments, my Monte Carlo simulation, even the opinion of someone who does stats for a living (Wraith). The only evidence I've seen you show to support your position is your ability to throw insults at people. In looking for those extra links on regression toward the mean, I didn't see a single one which supported your view, or hinted at such support. Not one. I've never seen anyone support your view, outside of these forums.

Wraith's metaphor was a good one, but was only beneficial for those capable of understanding it.

You're wrong. Take a ruler, and measure the height of everyone in the U.S. population. Use a nice, accurate ruler to avoid measurement error. Now consider 100 people who measured 7'6". Put them in a room, and have them be remeasured. What's the expected value of the remeasurement? Right: 7'6". No regression toward the mean here. Now keep the example the same, except that your measurement method allows you to be off by an inch. Someone who's initially measured at 7'6" might be a lucky 7'5", or an unlucky 7'7". Of those two possibilities, the 7'5" one is more likely, because there are more 7'5"s than 7'7"s. Someone who got measured at 7'6" the first time around will, on average, get a slightly shorter measurement upon being remeasured. The presence of measurement error is necessary for this form of regression toward the mean to occur.