What does it mean to have a high p value but a very very low effect size? What can I conclude? Is it necessary to report the effect size when p=0.998?

  • 2
    $\begingroup$ Have you constructed a confidence interval for the effect size? That may be helpful. $\endgroup$
    – wzbillings
    Commented Oct 31, 2023 at 15:05
  • 4
    $\begingroup$ Why the "but" between "high p value" and "very very low effect size"?? Wouldn't a high p-value be expected to go with a low effect size? There's no hint of a contradiction that would suggest "but". $\endgroup$
    – Glen_b
    Commented Oct 31, 2023 at 15:13
  • 1
    $\begingroup$ A high $p$-value is telling you the observations are close to those predicted by the null hypothesis, while a low $p$-value would suggest that the observations appear more extreme under that hypothesis. Seeing $99999$ heads when flipping a possibly biased coin $200000$ times ($p=0.9982$) does not guarantee the coin is unbiased, but does suggest that the extent of any bias is likely to be very small. $\endgroup$
    – Henry
    Commented Oct 31, 2023 at 15:25
  • $\begingroup$ This page asks (and answers) essentially the same question: stats.stackexchange.com/questions/330713/… $\endgroup$ Commented Oct 31, 2023 at 18:11

1 Answer 1


There is a strong case for reporting effect sizes alongside p-values, as they both represent two different things. The p-value indicates certainty/uncertainty, whereas the effect size tells you about the magnitude of the effect. You can read this article for example: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/

And refer to this post:


You could report both the effect size and p-value, saying that the difference between the two levels of your variable is small and non significant for example.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.