# Talk:Regression toward the mean

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## Confusion about what is being implied

It says in this article, in the "Other statistical phenomena" section, "For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10..." but what does that actually mean? Because, the odds of throwing 10 heads in a row haven't change at all due to that rare first event. The odds of throwing 10 heads in a row is still as it always was 1/1024 and those odds don't change over time, previous experience is completely irrelevant to any future probability. There is no God evening-out things, trying to make things fairer. It is true that the chance of throwing a run of 10 heads on a flip of a fair coin is a rare event and so if you keep throwing the coin it is highly probable that you will not throw another 10 heads in a row, but the probability of that same rare event happening again has not changed at all, the odds for the second time of a run of 10 heads on a flip of a fair coin are exactly the same as they were on the first. When you look at all the throws of the coins, say a couple hundred times later, the ratio of head to tail is highly likely, but only highly likely, to be close to 50/50 but that definitely does not mean that the probability in the second run of throwing 10 coins was less likely to end up with 10 heads than the first, which seems to be what is being subtly implied in this Wikipedia article. It is true that following a run of 10 heads on a flip of a fair coin (a rare, extreme event), the next run of heads will likely be less than 10, but your chance of throwing 10 heads on a flip of a fair coin (a rare, extreme event) was always less than 10, even before the first run, so what is significantly being said there?! The probability for the second run of throwing the coins hasn't been changed, the odds are still the same as they were for the first time, 1/1024 of them all turning out to be heads. Even if you did by chance throw another 10 heads the second time, then if you were to consider throwing the coin a third 10 times your calculated odds for the third time are still exactly the same as they were for the very first run, 1/1024 chance of getting 10 heads in a row! Once an extreme pure chance event happens it does not lessen the likelihood of another extreme pure chance event happening, it is perhaps less likely that you'll get two extreme pure chance events happening rather than just one but once an extreme pure chance event has happened it will have absolutely no effect on the future probability of another extreme pure chance event happening. The "Other statistical phenomena" section confuses me, what on Earth is it implying!? It almost sounds like a confidence trick, a scam is being marketed.

## First sentence

"[...] 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)

## Picking nits - 'regression AWAY from the mean'

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)

## Change of Lede – old was false, misleading or irritating

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)

## When did "reversion to the mean" become historical?

I was under the impression that "reversion to the mean" was a common name for this, almost as common if not just as common as "regression." For instance, Wolfram lists reversion to the mean as the preferred term. (https://mathworld.wolfram.com/ReversiontotheMean.html) However, in this article, it is presented as a former name. I think this should be changed, but don't feel confident enough to do it myself; do others agree?

## Why is there no mention of the Central Limit Theorem in the entire page?

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)