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. ______________________________________________ [email protected] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide https://www.r-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [email protected] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide https://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
