Taro T

That sucks.

In his extremely simplistic original example, you would be correct. However, there are going to be other variables (time of day, alertness, mental state, health, medication, etc.) that will effect the "true IQ". A "perfect test", as he has mentioned in his description at varying times, would detect the subject's "true IQ" at the time the person took the test without any measurement error. As these regressors change for an individual subject upon a retest, even a "perfect test" would/could end up resulting in a different "true IQ" even though the error term in the regression was 0 both times. So, even with an IQ test, you can have variation in an individual's test results without measurement error. I guess I am having a hard time with agreeing that a "perfect test" would have measurement error. If the test IS perfect in design, implementation, and execution; there would not be measurement error.

After this post, I'm pretty sure I'm out of the whole discussion. But, 1st, one final question: why do you insist upon stating that IF you have measurement error, extreme scores will tend to move closer to the mean? While measurement error can be a factor, this will occur whether or not there is measurement error (at least as most of the world would define measurement error). (Also, depending upon the magnitude and the form of the measurement error, the effect you are expecting might not be observable.) You have stated that you agree with this, and then you go and continue to repost that you don't agree with it (as in the post I am quoting). Either you are as obtuse as CTM/BJ states, in which case there is no reason to continue this discussion; or you are jerking our chains, in which case there is no reason to continue this discussion. Or quite possibly both, in which case there is definitely no reason to continue the discussion. Wraith seems to suggest a 4th possibility, that you actually understand what you are trying to say but don't have the statistical background to state it properly. I doubt the likelihood of that possibility, but even if that is the case, your continual insistance to continue using your own vernacular makes continuing this discussion too frustrating to bother with.

All the Great Society legislation passed under his watch. So I wouldn't exactly say he did "nothing else".

I did not state what you think I did on point 2. I said you would expect an INDIVIDUAL that scored a 180 on the test to get it again the 2nd time. Especially, if you assume that you have a "perfect test" and the magnitude of the individual variation is small, then MOST of the people that scored a 180 would have done so because that is what their underlying score should be. There would be a few "true 170's" that scored the 180 on the 1st test and fewer "true 190's" that scored 180 on the 1st test. So, upon retesting, the majority of the people that scored 180 the 1st time would score 180 AGAIN. You would get a few 170's, and fewer 190's. Thus, a SINGLE INDIVIDUAL would be expected to get the 180 again. But the AVERAGE score of the subpopulation as a whole would be expected to be lower than 180. I thought stating to be clear and straight forward. Also, and I think you already realize this, but am not positive of that; some of the people that get 160's and 170's on the 2nd test will be people whose "true score" is in fact 180 (there may even be some 190's going there on the 2nd one as well) and conversely for the 2nd test 190's. EDIT: You do realize that the "average" score for an INDIVIDUAL is that individual's score? That is NOT necessarily the "average" score for the subpopulation that you are referring to. Although a particular individual WOULD be expected to get a 180 on the perfect retest, the average score of the individuals taking that perfect retest would be less than 180.

Losman is definitely playing better this season. Playing well at the beginning of games and at the end is a start. And to be honest, if at this stage in his development he's only going to be successful for part of the game, those are the parts that I want him to be successful in. If the defense were stronger, with the special teams the Bills have, that would be enough to win a few more games. Heck, it was the formula they often used when Flutie was at the helm. Score early, have the D keep it close, and then turn it on in the 4th.

Actually, that just reinforces my point. Thanks for playing.

No, even with a "perfect test" there will STILL be variation in what individuals within the population will score. It won't be a function of measurement error as most would define measurement error, it will be due to the variance within the test subjects themselves. By definition, a perfect test would exhibit NO measurement error. Actually, you would expect a single someone who scored a 180 (especially on a perfect test) to score a 180 upon retaking the test. You would expect the average score of the entire population that scored 180 on the original test to have an average score that is slightly lower. I guarantee you, if we bet $1,000 on what score each person that took the original test will score on the 2nd test that you will owe me a lot of money betting that those 180's will turn into 170's. At least you realize that measurement error is not required for your observations to occur. Especially, because in your example (a perfect test) there would be NO measurement error.

You keep using that word. I do not think it means what you think it means.

Nope, there'll just be a run on Thomas Jeffersons.

So NOW you're point is "regression toward the mean happens", and not "regression toward the mean happens because of measurement error, just like when you don't roll a 3.5 with a single die..." like it has been for the past month. Do you honestly think you can blather on for fifty or so pages, and then suddenly wake up one day and claim you were saying something else? 860859[/snapback] Wow, deja vu.

So darn close. That is the 2nd best album ever. Wish You Were Here did not sell as much, but was a better album. Shine On (all 9 parts) puts it over the top. (Pretty much anything by Floyd except the Soundtract to More is incredible. Gilmour's 1st solo album is incredible as well.) AJ, don't fully know your tastes (seems that you like darn near any style), but you can rarely go wrong with Dire Straits. Love Over Gold is my favorite (Telegraph Road is fantastic), but Making Movies, Dire Straits, and Communique are all excellent. Knopfler's solo stuff is good too (at least the early stuff). The soundtrack to Local Hero is very good, but has very little vocals in it. I saw him play just outside of Filly about a week after the Sabres smoked them in '01. The locals didn't seem to appreciate my Sabres sweater. Skynyrd's 1st album (self titled) and Street Survivors are great too. On a slightly less beaten path, the following self titled (and nearly self titled) albums have at least 1 excellent song and the rest are good as well: The Men, Toy Matinee, and The Kings (Are Here). Church of Logic, Sin, and Love by The Men is the all time greatest song to warm up for a hockey game to, Last Plane out by Toy Matinee is a great song, and to the best of my knowledge the only one about the 1st Gulf War that got regular radio play, and you can never go wrong with This Beat Goes On / Switching to Glide. Bought far more DVD's than CD's since the kids started showing up (amazing how few non-animated movies you make it to in the theater after that) so I won't even attempt to suggest "new" stuff.

That is true, and even with the person not having something affecting their "underlying ability to think" their score would likely vary from test to test. But that isn't what most people would consider "measurement error". That variability is what it is, the variability that is naturally inherent in a system and within the results that an individual member of a population within that system will experience. (Although there CAN be examples that DO exhibit measurement error and using what appears to be the definition of measurement error that you are using (which is FAR broader than most would use), this variability would fall within that definition.) As CTM/BJ and Wraith both stated, if a particular individual is given the test often enough and it is a well designed, fair test that doesn't have an inherent bias, you will be able to discern what that person's "true" IQ is.

If you assume a normal distribution of the sample and a normal distribution of the measurement error, the average of people who had a 140 on the test would have a lower score. But that is due to the normal distributions, not due to the measurement error. A negative bias in the error term would give you similar result. A positive bias would produce results that are contradictory to your expectations. But the reason that subsequent test scores will be lowered is due to the normal distribution of the sample. The phenomenon you are describing occurs because the sample population is normally distributed, not because error is causing the the retest scores to be lowered on average. I think the reason you appear to be confused is because you are assuming that any observed variation of a value from the "true" value must be due to error. It doesn't. There are myriad factors which can produce the variance (including pure random chance). In the classic height measurement example that you are attempting to restate, the regression toward the mean was not in the measurement of the height of men; it was in the measurement of the height of their sons. There would be microscopically small measurement error in those samples, but yet very tall men typically have sons that are shorter than they are and very short men typically have sons that are taller than them. But even then, it doesn't always occur that way. If a very tall man has a son, it is possible that the child upon reaching adulthood would be even taller than he is or if a very short man had a son the child could be even shorter than he is. There you have regression to the mean with absolutely no measurement error to speak of. You have chosen one extremely limited example and have attempted by the basis of how you have extremely narrowly defined your example to show that error causes regression to the mean in general. It doesn't. The regression to the mean is caused, as your debating partners have stated, by the normal distribution of the population and variance within the samples of the population.

I found one other Wraith quote from earlier in the discussion where he explicitly tells our friend HA that error does not cause regression to the mean. But apparently that was before Wraith fully understood that saying error causes regression to the mean doesn't mean what it appears to mean due to some metaphorical allusion to something (unfortunately, I'm not smart enough to figure out what that something is).

Wraith stated in the quote that you are so fond of: Your hero Wraith explicitly stated that if you are saying measurement error causes regression to the mean that you are wrong. WHY would you use a metaphor that you claim to know is inaccurate / wrong?

Actually, if some guy were that confused that he actually entered the competition, wouldn't he have a leg up on the competition, so to speak?

I was not referring to anything in your IQ posts in my post. I was referring specifically to your quote "(m)easurement error causes the rubber band to stretch, and remeasuring causes it to snap back into place." Measurement error does not, can not, and will not cause a rubber band to stretch. The ONLY way to get a rubberband to stretch is to apply an external force. Barring an external force acting upon it, it will remain in its normal state where it holds the least potential energy. When you apply an external force to it, it will stretch (or compress) depending upon the force. You could apply that force while measuring the rubber band, but it would not be the "measurement error" causing the rubber band to stretch. It would be the force applied to the rubber band.

Actually, I pass up the opportunity to call the abominable snot smear an abominable snot smear several times every day. That I refer to something by its rightful and proper name doesn't mean I am worked up by it. It also doesn't mitigate your penchant for hyperbole on the subject.

No, an external force applied to a rubber band would cause it to stretch. Removal of that force would cause it to contract back to its normal dimensions. Measurement error does NOT cause a rubber band to stretch. Saying measurement error causes a rubber band to stretch is analagous to stating that measurement error causes a car to travel.

Is that what they're calling it these days?

Apus, show me ONE poster (other than John Slabyk) that has even IMPLIED that the abominable snot smear has "disrupt(ed)" his life. I truly doubt you can. The extreme rhetoric coming from the slug hater haters goes a long way toward keeping this "debate" running. Most of us that find the abominable snot smear abominable have spoken our peace long ago. No one is "crying" except maybe the people that hate the slug haters. I haven't cheered any less for the Sabres simply because they are wearing one of the, if not the, most ridiculous logos in pro sports history. That doesn't change the fact that they are wearing one of the, if not the, most ridiculous logo in pro sports history. It also doesn't change the fact that the Sabres WOULD sell a LOT more merchandise if they would, in fact, sell 3rd jersey merchandise. Nor does it change the fact that the Sabres would have sold a lot more merchandise had the primary sweaters not had an abominable snot smear on it. There are many reasons why this merchandise is selling. Very few of them include the abominable snot smear NOT being a ridiculous logo that stands for nothing. I hope they do win the SC this year (and the next, and the next, etc., etc.). Hopefully, when the banner goes up they use the logo they've stated they would wear if given the chance to win it on home ice. (Hint, it isn't the abominable snot smear that you feel just needs some tweaking.)