# Questions tagged [regression-to-the-mean]

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

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### How control for a pre-treatment outcome $Y_0$ if is a strong confounder while avoiding regression to the mean bias for treatment effect on $Y_1$?

I'm facing a dilemma in a pre/post cohort matching analysis for a healthcare intervention: Matching on the pre-treatment outcome $Y_0$ (a continuous variable) will likely lead to regression to the ...
1 vote
197 views

### How does the law of large numbers relate to regression to the mean?

Intuitively, these two important statistical principles appear to describe two facets of the same phenomenon, namely that in the long run, any extreme occurrences get counter-balanced, and things tend ...
2k views

### What's complicated about regression to the mean?

Note: I am a bit of a novice when it comes to statistics and data analysis. Reading the chapter on regression to the mean in Kahneman's Thinking Fast and Slow, I came across the following passage: ...
201 views

### Matching on pre-treatment outcome $z$-score in diff-in-diff analysis to avoid regression toward the mean bias in $ATT$ estimates?

There have been many articles (e.g., Chabé-Ferret (2017), Daw & Hatfield (2018), Zeldow & Hatfield (2021)) discussing the perils of matching on pre-treatment outcomes (such as patient's ...
116 views

### 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 ...
150 views

### 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 = ...
6k views

### 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 ...
1k views

### 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 ...
1 vote
32 views

### "Regression" versus "regression to the mean" [duplicate]

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 ...
73 views

### 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 ...
1 vote
151 views

### 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 "...
1 vote
60 views

### Regression to the mean: multiple predictors

Let's say I want to predict the value of Y using the value on my predictor X. X is correlated with Y with some strength $r$ (let's say 0.5). In order to correct for regression towards the mean I ...
14k views

### 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 ...
2k views

### 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. ...
275 views

### Control for regression to the mean effects when comparing propensity score matched observations?

I'm working on a project where I'm comparing the % change in total annual health care expenditures among patients who did or did not participate in a cost reduction intervention program. We're ...
26 views

### 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 ...
1 vote
59 views

### Does ridge regression adequately control for regression to the mean effects in my outcome variable?

I've been asked how to control for regression to the mean effects in a difference of differences analysis on health insurance data. We're measuring a utilization outcome both pre- and post-...
636 views

### 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 ...
1k views

### 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 ...
2k views

### 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 ...
108 views

### 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 ...