The Book of Why: Regression to the Mean

Regression to the mean explained by correlation

Origins of Regression to the Mean

Regression to the Mean as a Threat to Internal Validity

Which of the following best describes the statistical phenomenon of regression to the mean?

A researcher notices that participants who scored extremely high on anxiety before a stress-reduction workshop scored notably lower after it. She concludes the workshop genuinely reduced their anxiety. This conclusion is fully justified because any improvement following an extreme initial score must reflect a real treatment effect.

A researcher is studying test anxiety in a group of students. After an initial assessment, she categorizes three participants based on their scores relative to the group average. Match each participant's initial score with their most likely outcome on a follow-up test (assuming no intervention occurred) based on the phenomenon of regression to the mean.

In a clinical study on depression, researchers recruit a 'high-severity' group consisting of participants who scored in the top 5% on a baseline diagnostic scale. At a follow-up assessment, the group's average score improved, even for those who received no treatment. Arrange the logical steps that explain this outcome using the phenomenon of regression to the mean.

Under the statistical phenomenon of regression to the mean, if an individual's score on a random variable is extremely far from the average on the first measurement, what is the most likely outcome on a subsequent measurement?

According to the phenomenon of regression to the mean, if the first sample of a random variable is extremely below the average, the second sample is typically expected to be even further below the average.

A researcher claims that a new focus-enhancing technique is effective because participants who scored in the bottom $10\%$ on a baseline concentration task showed significant improvement after the intervention. To evaluate the scientific validity of this claim, a critic would point out that the improvement may not be due to the technique itself, but rather to the statistical tendency for extreme scores to naturally shift toward the average on retesting — a phenomenon known as _____.

A researcher measures a single random variable across two timepoints. Match each participant's initial score description with the expected direction of their second score under the phenomenon of regression to the mean.

A researcher notes that an extreme score on a baseline test appears much closer to the average upon a subsequent test. From a design perspective, regression to the mean is a statistical phenomenon that occurs when resampling a single _____.

Order the steps a researcher takes to evaluate whether regression to the mean has occurred when analyzing test scores across two time points.