Serious question. How do *you* interpret a confidence interval in a way that is both true to the definition *and* helpful to the readers understanding?

Two common approaches, that are painful to read.... One is using vague language "the CI expresses our uncertainty about the true value" the other is straight-up ignoring the definition "the CI is a range of values that contains the true value"

It feels like a trick question. A CI is a technical concept and may simply require a technical interpretation. I'm curious how others think about and communicate this.

Ok maybe the original tweet wasn't quite clear enough. The question is really how do you interpret a *specific* interval. Not how do you explain the concept of confidence intervals. Although I'm interested in the latter too, I don't think it's as difficult.

I wish I remembered more stat theory!

'a range of plausible values'

I like this the best. Is it true? I guess a CIs could occasionally have insanely wrong values, but on average still have the right coverage. Can that happen?