An answer to a FAQ notes:

The effect size of a covariate may be high, even if it is not significant.

Does anyone know of papers I can reference to support that assertion?

FWIW, I do understand why it's true, i.e. I am not looking for an argument explaining why that fact is true. A citation to a published paper is useful to convince some non-mathematicians of it in a space-limited context.

The specific context is that I'm working with researchers in a field where it's normal to test a potential covariate for significance and then drop it if it's not significant. (Worse, the test is usually a univariable test.) The discussion in Harrell's RMS is excellent, but I'd prefer to cite short papers on the topic if they are out there.


1 Answer 1


A little googling found:

One issue (and one reason that I didn't immediately turn up something in, say, American Statistician) is that this is very well known and also rather evident to anyone who has had elementary statistics (at least, if they had it from a decent professor).

It's also discussed in many books, but you didn't want those.

  • 3
    $\begingroup$ Kalinowski (2010) is perfect, thank you. The fact should indeed be well known but you would be shocked at how much of a mess the stats is in some fields... $\endgroup$
    – Mohan
    Dec 9, 2023 at 18:50
  • $\begingroup$ Although one caveat: that focuses on 'significant does not imply large effect size'. 'insignificant does not imply small effect size' is logically distinct. [P => Q, ~P => ~Q] $\endgroup$
    – Mohan
    Dec 9, 2023 at 19:17
  • 1
    $\begingroup$ Oh, I wouldn't be shocked. I was a consultant for a long time. No amount of ignorance of stats shocks me. $\endgroup$
    – Peter Flom
    Dec 9, 2023 at 19:26

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