Trivial effect size BUT statistically significant?

Question

I am trying to compute effect size (SS predictor / SS total) is it possible to have a REALLY small effect size (0.02 no not 0.2 but 0.02) but have the effect be statistically significant?

Answer 1

Yes. For any non-zero effect size as n approaches $\infty$, p approaches 0. This is because for Wald type tests, the test statistic is $\frac{\theta}{s_{\theta}}$, and $s_{\theta}$ typically looks something like $\frac{s}{\sqrt{n}}$, where $s$ is a standard deviation (e.g., of one's data for the t test).

Further elaboration on significance and tiny effect sizes from the perspective of equivalence and relevance.