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First off, let me say that I'm extremely poorly versed in statistics, and this is a question purely about terminology.

I have a distribution for some quantity (height of person, say) and the most likely 95% of outcomes are within some range $h_0$ to $h_1$. I want to know what to call (ideally a 2 or 3 word phrase) this range. It is not the case that the distribution is normal, though we can safely assume that it is unimodal.

Clarification:

Let's say I have a coin, which I think is biased for heads with $p_h=0.6$. Now I toss it $n$ times and I get $a$ heads. I want to write a sentence which basically states that the result is in some 95% "likelihood region", (something like "middle 95 percentile" seems a little clunky, if not ambiguous --- I'm not taking a region about some median!). Now, it might be that my $p_h$ is actually a prediction based on some data, and I have some uncertainties in it, but I don't want to include those uncertainties! I want a term that refers to the fact that because I didn't toss the coin an infinite number of times, there is some variance in the ratio $a/n$.

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I'm not sure the middle 95% has a name, but the middle 50% does: "interquartile range".

The middle 80% does as well: interdecile range.

...

Actually, a bit of poking around on google turned up "95% interpercentile range" and "2.5-97.5 interpercentile range."

I hadn't heard those terms before (they don't seem to be common), but if I saw them in a paper, especially the second one, I would immediately know what the author meant. So I think you should be just fine using them.

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    $\begingroup$ As I mentioned in the edit, I don't think this is quite correct because I'm not taking a range about the median. It's what I first reached for too, before being corrected. $\endgroup$
    – genneth
    Commented Jul 3, 2011 at 15:40
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This is interval estimation and it sounds like a "prediction interval".

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  • $\begingroup$ The corresponding Wikipedia page certainly looks like it is close to what I mean. But what if there is no estimation occurring? So if I just know somehow the true distribution, and I want to convey the range of the middle 95% (percentile?)? $\endgroup$
    – genneth
    Commented Jul 2, 2011 at 12:53
  • $\begingroup$ "Prediction interval" is not quite right. An interval, estimated from data, that is intended to contain a specified proportion of a population is called a tolerance interval. $\endgroup$
    – whuber ♦
    Commented Jul 2, 2011 at 18:44
  • $\begingroup$ @whuber: so I actually thought that prediction interval is what I wanted --- even after reading that page. On the other hand, I'm also unable to really understand what tolerance intervals are from that page :-/ (which I'm sure is my fault, not the page's). Specifically, what I wanted to do was to say "I expect that 95% of the time, the measurement will be between A and B, and we got C, so that's consistent." What do you call that range, A-B? $\endgroup$
    – genneth
    Commented Jul 2, 2011 at 19:54
  • $\begingroup$ @Genneth It sounds like you're trying to interpret a tolerance interval as a prediction interval :-). The distinction is this: the TI estimates a range for the underlying distribution. The PI estimates a range in which one (or more) additional independent observations can be expected to lie. That range is typically wider than you might think because there are now two sources of uncertainty: (i) uncertainty in the underlying distribution and (ii) uncertainty in the additional values. That second source of uncertainty is irrelevant to tolerance intervals. $\endgroup$
    – whuber ♦
    Commented Jul 2, 2011 at 21:04
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    $\begingroup$ @genneth - you have put additional information in these comments which makes my answer not really applicable - you should update your question (and "unaccept" my answer) to indicate where your uncertainty is, and what you want to use the interval for. $\endgroup$
    – probabilityislogic
    Commented Jul 3, 2011 at 0:56

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