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I'm vaguely familiar with normal probability plots (non-statistician who knows enough to get by). The graph in this article:

What are the two dotted curves called, what do they signify, and how are they calculated?


(source: wrstephe at www.public.iastate.edu)

edit: My question is software-independent. I just want to know what side bands used in a typical normal probability plot are called and how they are defined.


I don't have a good answer but after stabbing around in the dark on Google I finally found this lecture notes on quantile-quantile plots:

https://www.stat.auckland.ac.nz/~ihaka/787/lectures-quantiles2-handouts.pdf

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    $\begingroup$ My guess is they're intended to be bands within which 95% of the QQ plot points should lie, if the normal assumption were true. Without knowing exactly how Minitab implements its plots, I can't say for certain what they represent. $\endgroup$
    – Glen_b
    Mar 2, 2014 at 2:19
  • $\begingroup$ Thanks... I don't really care what Minitab does. I don't use it; I have access to Python + NumPy + SciPy. I've seen these types of plots with side bands before and I just want to know what they are in a mathematical sense. You're saying they're 95% bands? What does that mean, quantitatively? (and how do I calculate the curve values myself?) $\endgroup$
    – Jason S
    Mar 2, 2014 at 17:27
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    $\begingroup$ You can't generalize with certainty. If you show a plot from program A and think you're also getting an answer that relates to program B, unless they both explicitly state what they're actually plotting (or you run a bunch of examples to check), there's a fair chance they're not actually the same thing. So you can say "I don't care what Minitab does" -- well why link to an article that's explicitly discussing Minitab? I've seen this problem a bunch of times with other kinds of display. You have to check, because there's a good chance they don't all plot the same thing. ...(ctd) $\endgroup$
    – Glen_b
    Mar 2, 2014 at 22:23
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    $\begingroup$ (ctd) ... Second, I don't say "they are 95% bands". First, note that I said "guess" -- and that's what it is. Second, I defined what I meant in what I did guess fairly precisely already. If you have Python + NumPy + SciPy and care what they have, can't you look at the source code to see what they do? $\endgroup$
    – Glen_b
    Mar 2, 2014 at 22:29
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    $\begingroup$ It depends on what they are exactly, e.g. do you want simultaneous or pointwise bands? The method used in creating them can also matter. I like to create such bands using resampling, but the ones you show are too regular for that. $\endgroup$ Mar 5, 2014 at 13:46

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What Ross Ihaka is discussing is (as he explains) a simultaneous confidence band for the points in the QQ-plot based on a Komogorov-Smirnov interval for $F$; a point falling outside the band would correspond to rejection by the KS-test.

However, note that the bound from the KS-test is predicated on $\mu$ and $\sigma$ being known. The existence of some value for $\mu$ and $\sigma$ laying within the bands is equivalent to estimating those quantities (whence the test is no longer distribution free, and the bounds too wide -- for which then values from a Lilliefors test would be necessary).

So if Ihaka is actually doing what he says, the interval would be too wide to be interpreted as a CI with the claimed coverage.

What Ihaka discusses there may or may not be the same thing as what's in the plot you show in your question.

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