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I often see QQ-plots with a confidence interval:

like this

For my application, I have a QQ plot of test p-values against a uniform distribution. I want to add the 95% CI of the observed p-values on the plot, but I don't know how to compute them.

In other words, I am not sure:

  1. That I correctly understand what the CI represents on QQ plots.
  2. How they are computed.
whuber
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legaultmarc
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    I cannot comment on whether your interpretation of the confidence interval is correct as you did not tell us what your interpretation is. For how the confidence interval is computed see the comments in this question. – Maarten Buis Jul 15 '15 at 07:21

1 Answers1

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I'm trying to figure this out myself, but from my stats training, if your qqplot points fall within the confidence interval bounds, then the data are fairly Normal (this is what you want for linear models, such as linear regression or ANOVA).

$H_0:$ Data is Normal vs $H_A:$ Data is not Normal

You want to fail to reject the null hypothesis.

However, if your qqplot points are really not mostly within the CI, then your data is not Normal. You may want to then consider nonparametric methods.

The plot above looks fairly Normal; problems at the tails, so you may want to look out for outliers. Real world data is never perfect.

If I come across a solution for methods of CI construction, I'll edit this post.

kjetil b halvorsen
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Jon
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