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Is there a criteria to say a statistical confidence interval is wide or narrow? Is there any formula to know?

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  • $\begingroup$ Are you referring to the question of whether the actual coverage is the stated level, or if your CI will be useful for your application? $\endgroup$ May 20 '15 at 16:32
  • $\begingroup$ Suppose, in analogy, someone were to ask you whether there were (universal) criteria to determine whether an apple is large or small. How would you answer that without first inquiring as to the context of the question, the potential use of the apple, and to what alternatives it might be compared? $\endgroup$
    – whuber
    May 20 '15 at 22:00
  • $\begingroup$ Is my piece of string long, or short? It depends on what length I might expect my piece of string to be, or what purpose I have in mind for it. A three-inch length may be short if I'm trying to tie a medium-size parcel but such a stringette is possibly ideal for attaching notes to pigeons' legs or flogging small household pests, such as ants. $\endgroup$
    – Glen_b
    May 20 '15 at 22:35
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Whether or not a confidence interval is "wide" depends on why you collected the data, and how you will interpret the parameter for which you computed the confidence interval. What is too-wide-to-be-useful in one context might be considered narrow-enough-to-make-a-useful-conclusion in another context. So no general answer would be useful.

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