This is what “power = .06” looks like (visualized by Art Owen).

Statistical Modeling, Causal Inference, and Social Science 2023-09-07

Art Owen writes:

Here’s a figure you might like. I generated a bunch of data sets constructed to have true effect size 1 and power equal to 0.06. The first 100 confidence intervals that exclude 0 are shown. Their endpoints come close to the origin and their centers have absolute value far from 1. Just over 1/4 of them have the wrong sign.

When the CI endpoint is a full CI width away from zero, then you’d be pretty safe regarding the sign. Details are in this article.

I do like the above figure. It’s a very vivid expression of This is what “power = .06” looks like. Get used to it. Somebody should send it to the University of Chicago economics department.