Talk:Regression toward the mean

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Different use in finance[edit]

I added a note to the end of the introduction, because I'm almost certain that "mean reversion" as used in finance is fundamentally different from "reversion to the mean" or "regression to the mean" as described here. I don't think the Wikipedia article on Mean reversion (finance) is clear on this. As I understand it, as used in science and statistics, mean reversion is an effect that shows up when genuinely independent random samples are drawn successively from a fixed population having a constant frequency distribution.

As used in finance, it seems to be referring to a situation in which performance over successive time periods is not independent, but shows a negative correlation from one time period to the next. A fluke period of low returns is not followed by a typical period of average returns, simply due to the nature of a random process. On the contrary, a period of low returns has an actual tendency to be followed by a compensating period of high returns. Thus, the average return as holding periods increase decreases faster than it would if the process were a random walk.

The law of large numbers says that if you throw 10 heads in a row, then flip a coin 100 times more, the average number of heads for the whole 110 throws will be closer to 50/50, not because there's any tendency to throw more tails after a long series of heads, but simply because the maximum likelihood is that the 100 additional throws will be split 50/50 and the percentage for the whole series will decline from 10/10 = 100% heads to (10 + 50) / 110 = 55%. I've talked to a couple of financial specialists who have been quite definite that in finance, "mean reversion" does not just mean swamping out an unusual run with a series that simply has the mean value, it means active compensation--a run of low stock returns will (supposedly) tend to be followed, not by a run with mean-value stock returns, but by a run of higher-than-mean stock returns.

In the article, I'm doing my best to present this by paraphrasing what Jeremy Siegel says, but I admit that I'm going just a little farther by using the word "compensation." Dpbsmith (talk) 15:33, 22 December 2011 (UTC)

Cross-Cultural Differences in recognizing and adjusting to a regression toward the mean.[edit]

A recent study performed by Roy Spina et al. found that there are cultural differences in being able to account for the regression toward the mean, and I think that this may be found in other studies and would add to this article. Here is the citation for his article. Spina, R. R., Ji, L., Ross, M., Li, Y., & Zhang, Z. (2010). Why best cannot last: Cultural differences in predicting regression toward the mean. Asian Journal Of Social Psychology, 13(3), 153-162. doi:10.1111/j.1467-839X.2010.01310.x Fotherge (talk) 21:19, 7 February 2012 (UTC)

Please select non-controversial examples illustrating regression to mean.[edit]

Have removed a reference to alleged criticism of UK speed cameras partly because it appeared to argue an unrelated point about speed cameras being an unproductive use of road safety funds. A good illustrative example of regression to the mean should be clear & easy to understand and should not drag in any secondary issues which could detract from the idea being explained.

Noel darlow (talk) 21:46, 23 October 2013 (UTC)

Reinserted with offending sentence removed and two additional references. Qwfp (talk) 19:30, 24 October 2013 (UTC)
Great :) It does make a good, topical example of R2M when it's worded to be camera-neutral. Noel darlow (talk) 01:07, 25 October 2013 (UTC)

Why is it MORE likely that high performers are unlucky the next day?[edit]

Seems like they should be just as likely to be unlucky (or lucky) the next day as they were on the first day. Danielx (talk) 02:44, 20 December 2013 (UTC)

They aren't. However, if they are a high scorer for this event, then it's more likely that they have been lucky this time and entirely probable they won't be next time. Alpha3031 (talk) 13:17, 3 April 2015 (UTC)

Regression effect/fallacy[edit]

The explanation given of regression towards mediocrity seems plausible. But it does not explain why this phenomenon also occurs with entirely random data. Generate (x, y) pairs from a bivariate normal distribution with the same marginal distributions and correlation 0.5. The regression effect will show up, and no genetic theory will account for it.

This is already discussed in the article, I'm just wondering if the example from genetics really explains something that is not already an artifact of the definition of the regression line.TerryM--re (talk) 22:52, 24 May 2016 (UTC)