Hi Brian, This phenomenon is sometimes known as 'distinction without a difference', with 'distinction' referring to whether a parameter (in this case the regression coefficient) is identifiable, based on the experimental design. With enough observations of high precision, even scientifically insignificant quantities can be distinguished statistically. 'Difference' refers to the science - is this difference important to the scientific process? R can't make that judgment. That's the job of the domain scientist.
David K Stevens, PhD, PE, Professor Emeritus Civil and Environmental Engineering Utah Water Research Laboratory Utah State University 8200 Old Main Hill Logan, UT 84322-8200 [email protected] (435) 797-3229 (office) On 3/8/2026 4:50 AM, Brian Smith wrote: > 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.
