It is merely a dichotomous statement that is meant to have a specified probability of being true, in the long-run.
I understand that dichotomous means "dividing into two sharply distinguished parts", but I am not sure I understand what a "dichotomous statement" means? Literally it might mean something like "a statement that divides into sharply distinguished parts", but that doesn't really make sense.
Does it mean a polarizing statement? Or does it mean something completely different?
Edit: The context of the quote
The theory of confidence intervals
In a classic paper, Neyman (1937) laid the formal foundation for confidence intervals. It is easy to describe the practical problem that Neyman saw CIs as solving. Suppose a researcher is interested in estimating a parameter, which we may call θ. This parameter could be a population mean, an effect size, a variance, or any other quantity of interest. Neyman suggests that researchers perform the following three steps:
a. Perform an experiment, collecting the relevant data.
b. Compute two numbers – the smaller of which we can call L, the greater U – forming an interval (L, U ) according to a specified procedure.
c. State that L < θ < U – that is, that θ is in the interval.
This recommendation is justified by choosing an procedure for step (b) such that in the long run, the researcher’s claim in step (c) will be correct, on average, X% of the time.
A confidence interval is any interval computed using such a procedure. We first focus on the meaning of the statement that θ is in the interval, in step (c). As we have seen, according to CI theory, what happens in step (c) is not a belief, a conclusion, or any sort of reasoning from the data. Furthermore, it is not associated with any level of uncertainty about whether θ is, actually, in the interval. It is merely a dichotomous statement that is meant to have a specified probability of being true, in the long-run.