Re: Correct interpretation of a regression coefficient

Brian,
Statistical significance and biological importance are two very different concepts. A finding can be statistically significant, but of no biological importance, or of biological importance but  not statistically significant.
In the first case  I would report the finding by indicate in my discussion that the finding is of no biological importance. In the second case, I would think about the finding and as if my sample size was adequate. The path taken beyond this takes a good deal of thought. If the sample size was small, I would consider redoing the experiment with a larger sample. If the sample size is adequate I would entertain the thought that the finding represented random variation and would consider redoing the experiment in a different population.

I hope this helps.

John



John David Sorkin M.D., Ph.D.
Professor of Medicine, University of Maryland School of Medicine;
Associate Director for Biostatistics and Informatics, Baltimore VA Medical Center Geriatrics Research, Education, and Clinical Center;
Former PI Biostatistics and Informatics Core, University of Maryland School of Medicine Claude D. Pepper Older Americans Independence Center;
Senior Statistician University of Maryland Center for Vascular Research;

Division of Gerontology, Geriatrics and Palliative Medicine,
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
Cell phone 443-418-5382





________________________________________
From: R-help <[email protected]> on behalf of Brian Smith <[email protected]>
Sent: Sunday, March 8, 2026 7:50 AM
To: Ralf Goertz via R-help <[email protected]>
Subject: [R] Correct interpretation of a regression coefficient


Hi,

My question is not directly related to R, but rather a basic question
about statistics. I am hoping to receive valuable insights from the
expert statisticians in this group.

In some cases, when fitting a simple OLS regression, I obtain an
estimated beta coefficient that is very small—for example, 0.00034—yet
it still appears statistically significant based on the p-value.

I am trying to understand how to interpret such a result in practical
terms. From a magnitude perspective, such a small coefficient would
not be expected to meaningfully affect the predicted response value,
but statistically it is still considered significant.

I would greatly appreciate any insights or explanations regarding this
phenomenon.

Thanks for your time.

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