Is there a colloquial way of saying "small but significant"? I sometimes speak about statistical results to a popular audience, and the term "significant" can (understandably) be misunderstood. I sometimes want to say something like "the likelihood of seeing these results under the null hypothesis is small enough that there probably is something going on here, however the effect size is small enough that it's probably not worth worrying too much about."
Among technical audiences, I believe this could be summarized as "small but significant". Is there a short way I can communicate this to a non-technical audience?
 A: I would use something like, "We notice a difference that is extremely likely to be there and not a fluke. However, the difference has no practical meaning. They are effectively the same, like the distance to the sun versus the distance to the sun plus an inch."
The acknowledges the statistical significance ("not a fluke") while acknowledging the lack of practical significance ("no practical meaning").
A: If the audience knows what "statistical significant" and $p \le 0.05$ means, there is not much that can go wrong. But otherwise, I really like the fantastic suggestion by Jordan Ellenberg as an alternative to "statistically significant" in general:
[...] "statistically noticeable” or statistically detectable" instead of “statistically significant”! That would be truer to the meaning of the method [...] - Jordan Ellenberg in his book "How Not to Be Wrong: The Power of Mathematical Thinking"
Edit based on the short discussion in the comments: Note this answer does not specifically address the "small effect" situation but rather proposes an apt word for statistical significance in general where you don't have to fear that people take "statistically significant" as "relevant". In this way, you can distinguish in a clean and understandable way the two topics "hypothesis testing" and "effect size".
A: I have found the distinction between statistically significant and physically significant is often useful when communicating results to non-statisticians. The phrases clinically significant or practically significant may be preferred in some fields (thanks @Jelsema). You are describing a situation where the effect may be statistically significant, but physically insignificant.

As an aside, there is actually a push right now to stop (or limit) using the phrase "statistically significant" altogether. Some relevant reading:
Moving to a World Beyond "p < 0.05"
The Difference Between "Significant" and "Not Significant" is Not Itself Statistically Significant
Scientists rise up against statistical significance
References
Wasserstein, Ronald L., Allen L. Schirm, and Nicole A. Lazar. "Moving to a world beyond “p< 0.05”." (2019): 1-19.
Gelman, Andrew, and Hal Stern. "The difference between “significant” and “not significant” is not itself statistically significant." The American Statistician 60.4 (2006): 328-331.
Amrhein, Valentin, Sander Greenland, and Blake McShane. "Scientists rise up against statistical significance." (2019): 305-307.
A: Referring to the tale of "The Princess and the Pea", you could say :
"There seems to be a pea under all these mattresses."
See also:
https://en.wikipedia.org/wiki/The_Princess_and_the_Pea
