Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [regression-to-the-mean]

The phenomenon that on repeated testing a high value tends to be lower, and a low value higher.

There is an extensive set of examples and explanations in the Wikipedia article https://en.wikipedia.org/wiki/Regression_toward_the_mean. The concept originates with Galton in genetics but arises on many fields of application.

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Regression to the mean vs gambler's fallacy

On the one hand, I have the regression to the mean and on the other hand I have the gambler´s fallacy. Gambler’s fallacy is defined by Miller and Sanjurjo (2019) as “the mistaken belief that random sequences have a systematic tendency towards…
Luis P.
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Regression to the mean in "Thinking, Fast and Slow"

In Thinking, Fast and Slow, Daniel Kahneman poses the following hypothetical question: (P. 186) Julie is currently a senior in a state university. She read fluently when she was four years old. What is her grade point average (GPA)? His intention…
Rations
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Is the Dunning–Kruger effect mostly caused by regression to the mean?

In Bland's discussion of regression to the mean, there are several sections which detail examples of regression to the mean, which I understand to be an unavoidable consequence of not taking the mean of several measurements per subject. In the…
post-hoc
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Testing change in variance over 5 time points and regression to the mean

I searched regarding change in variance over time, but everything I saw was about relatively long time series. I have a series of 5 time points, equally spaced, but with different people missing at each time point. There are about 15 variables I…
Peter Flom
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Can I use the early response to a treatment to predict the full effect? - Dealing with regression towards the mean

Suppose I have a 6 week weight-loss program, that I know is only effective in a fraction of the population. I weight the participants at baseline, after 1 week and after the full 6 weeks. $$ T_0 = Baseline $$ $$ T_1 = 1\ Week $$ $$ T_2 = 6\…
JohannesNE
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How to test whether a series data follow Ornstein-Uhlenbeck process (OU process)?

I have some measures which seems to have some mean-reverting properties and I'm wondering whether they can be modeled as Ornstein-Uhlenbeck process (OU process). And actually I quite expect it because if so, the following work will be much easier…
fisher
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backwards stepwise regression, collinearity and regression to the mean

My research paper was recently rejected and some of the feedback I received was in relation to the statistical tests done/not done. I would like help in clarifying what I could do differently as the feedback was not to informative. I am attempting…
lighthouse
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Given the same before-after differences within groups, is it relevant whether time trajectories converge or diverge?

Both drugs are associated with the same decreases in mean blood pressure in both scenarios. Given that we attach the same meaning to any blood pressure decrease of the same amount, does scenario B constitute equivalent evidence for the superiority…
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Is a normal process mean reverting

A normal process has a lot of outcomes around the mean and then fewer and fewer outcomes away from the mean. From this, can we conclude that a normal process reverts to the mean whenever it gets a certain distance away from the mean? In that sense,…
Victor
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Variance of data from small versus large countries

In considering (for example) homicide rates reported annually for each country, it occurs to me that the U.S., being larger in population, might thereby be expected to have a rate closer to the worldwide mean. However, I don't know how to evaluate…
Ralph Dratman
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Why is linear regression overestimating small values and underestimating big values?

I am trying to predict age from a couple of variables using linear regression, but when I plot predicted age against real age, I can see that small values are significantly overestimated and big values are underestimated. If I flip the axes, so my…
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How to adjust estimates to account for regression to the mean?

Let us consider an example where we have a number of runners and an estimate of speed in mph for each runner. The estimate for each runner may be based on an equal or unequal number of independent and identical experiments where that runner is timed…
Ryan Volpi
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"Regression" versus "regression to the mean"

Are The two concepts really two sides of the same coin ? The latter is often referred to simply as a regression, but surely this is just an unfortunate coincidence? The former is about predicting values of a dependent variable from a weighted…
z8080
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Reconciling regression to the mean with the independence of with-replacement sampling

Say we monitor a ski jumper's consecutive jumps (distance jumped), and we assume it is a combination (sum) of the skier's skills, + luck (modelled by a random variable). We also assume that the distance jumped at trial$_N$ is independent of that…
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Distinguishing responders and non-responders in studies of classical conditioning

I am concerned about the way "response" to certain experimental manipulations in psychology is defined and then used to claim that a specific subject did or did not "respond" to justify exclusion of "non-reponders" from the statistical analysis.…
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