# What does it mean for a statement to be "dichotomous"?

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.

• I think more context is needed to allow a proper answer. Feb 5, 2017 at 21:44
• I would take "dichotomous statement" as double-talk for "double-talk". Feb 5, 2017 at 21:53
• Hot Licks, I would agree, without additional information. Feb 5, 2017 at 21:58
• The quote is from a paper discussing common misunderstandings about confidence Intervals. Here is a snapshot of relevant passages, the quoted sentence is highlighted: LINK TO IMAGE Feb 5, 2017 at 22:01

## 2 Answers

The passage appears to have been written by someone with less than perfect command of the English language. In addition to grammar mistakes (e.g. "an procedure"), it contains a logical contradiction in the last two sentences.

Judging from the context, the author most likely meant to say that the statement is an unequivocal, true-or-false proposition.

c. State that L < θ < U - that is, that θ is in the interval

"It is merely a dichotomous statement that is meant to have a specified probability of being true, in the long-run."

You are correct in your assumption that this does have to do with two parts.

### Dichotomous

• Involving two completely opposing ideas or things

(CD)

The author is not using this word in any special way; he/she is simply saying that statement (c) is nothing special. Statement (c) is merely a statement that is split into two parts, L & U, which are opposing values (they are opposites, as state in the original).

• In the given context, it appears to mean exactly the opposite of contradictory. Feb 5, 2017 at 22:18