Talk:Regression toward the mean

message: "[...] the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the mean or average on its second measurement, and if it is extreme on its second measurement, it will tend to have been closer to the average on its first." 
Put another way, this sentence says that if you measure something twice, one of the measurements would be closer to the mean than to other, which is a rather meaningless sentence. Or one could understand it as saying that if one measurement is extreme, then the two measurements would be different from each other. This of course depends on the measurement in question. Not a very good way to start an article. I would have corrected it but I came here to learn about the concept, so I don't really have what it takes to make this correction. --178.8.24.240 (talk) 15:44, 28 November 2018 (UTC)
thread_title:  First sentence 

message: Regarding this:  individuals that measure very close to the mean should expect to move away from the mean. I found a couple of references to 'regression away from the mean' online, but someting's wrong here. A person who scores 1oo on an IQ test (the mean, by definition), may indeed have a different score in a retest, and so, would have moved 'away from the mean.' But is this 'regression? 
The word regression implies a return to an expected value. In the case of normally distributed IQ scores, the most probably score of a random test-taker (also the mean) is given the value of 100. So a test-taker who does, in fact, score 100 on a first test is already at the most probably value. So when, after a second test, a score of 98 results, to what has the test-taker 'regressed' to? 
The only way this makes sense is if each test score is considered a single outcome in a sample of test results - the sample representing a part of all possible test results. So if the testee took 100 tests, we might find a range of scores (error on IQ tests is within 4 points, I believe). If the mean of the 100 test scores were 102, then the first score of 100 would, in later tests, regress toward the mean value of all possible test results. 
In this case, there is some logic to a regression away from the population mean, but only in the sense that the first score of 100 was away from the test-takers true ability, and thus, what we really have is a regression of the test-taker's score to his or her personal mean test score. 
The other way to think of it - the only other way I can think of - is that the movement away from the mean after a first score is not a regression at all, but simply error variance. Thus, if a testee's true IQ were 100, we would expect later test scores to be different, but only because test results are not perfect measures of intelligence - there is error in the testing process. 
Another way to think if the first case is also for IQ. If two parents each have an IQ of 100, we do not expect their children to 'regress away from the mean.' In fact, their children will be expected to have IQs normally distributed with a mean of ... 100. The fact that sibilings have a mean IQ difference of about 11 points does not come from any regression away from the mean. It is simply the result of the probably distribution of IQ, centered on the mean, with lesser probabilities as you move out from the mean. 
MarkinBoston (talk) 18:50, 17 April 2019 (UTC)
thread_title:  Picking nits - 'regression AWAY from the mean'  

message: It states “In statistics, regression toward (or to) the mean is the phenomenon that arises if a random variable is extreme on its first measurement but closer to the mean or average on its second measurement and if it is extreme on its second measurement but closer to the average on its first.” That doesn’t make sense at all. Everything beginning from “and” can be cut off. Also there’s nothing inherently special about the very first measurement only being extreme. It should say “In statistics, regression toward (or to) the mean is the phenomenon that arises if a random variable is extreme on its first or first few measurements but closer to the mean or average on further measurements.” I edited like so. Correct me if I’m wrong, though. Zyzzyvy (talk) 17:53, 15 June 2020 (UTC)
thread_title:  Change of Lede – old was false, misleading or irritating 

message: I am not sure if these two concepts are mathematically related but to me they seem highly similar. Should the Central Limit Theorem not at least be a "See Also"?
Nickfury95 (talk) 18:31, 6 October 2021 (UTC)
thread_title:  Why is there no mention of the Central Limit Theorem in the entire page?