I would assume the very wide CI mentioned above means that, since it includes 0, we can’t say there is a statistically significant effectiveness (it is not significantly different from 0% effectiveness).
> we can’t say there is a statistically significant effectiveness
Agreed, although to clarify and be more precise, it also doesn't prove it's not effective. It effectively says that the sample was too small to tell anything.
> (it is not significantly different from 0% effectiveness).
This statement isn't true - it means that they are 95% sure the range of possible values is between -50 and +60, but it does not mean that the average of those two values is correct. 0% effectiveness is possible, but was not shown in this study.
You’re right, semantics are everything. I left implicit the “in this study” part. As always, failing to reject the null doesn’t mean the null is true :)
This is not really correct. CI means we are 95% sure that the true result falls somewhere within the range of -50 to 60. What this really means is that the study lacks statistical power to say anything interesting at all about vaccine effectiveness.
Right. I phrased it a bit differently below. By “we can’t say” I meant that the study/researchers aren’t able to claim that the vaccine has non-zero effectiveness, i.e., they haven’t rejected the null.