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Even though I read my lecture notes and PP-plots vs. QQ-plots carefully, I'm still confused.

So Probability plot is a plot of samples vs theoretical quantiles. There we can find a or some parameters when there is some 'linear' relationship.

And QQ plot is a plot of sample1 vs sample2, and sample2 can be replaced by theoretical one.

So QQ plot is a larger concept which includes Probability plot.

This is what I thought, but https://en.wikipedia.org/wiki/P%E2%80%93P_plot says that Probability plot also means the plot between two empirical datasets. And it states that these two can be confused.

So what are these???

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    $\begingroup$ Probability plot is the oldest term here and one that survives and even thrives. Even in the definitive 1968 paper by Wilk and Gnanadesikan jstor.org/stable/2334448 the title and much of the discussion perpetuate a wide sense of the term. But strictly Q-Q plots plot quantiles versus quantiles and probability is not explicit. I'd summarize usage as (a) probability plot is a broad term which covers all these cases and some more; (b) Q-Q plots is a strict term and implies quantiles on both axes with probability implicit (c) P-P plots is another strict term and the opposite of (b). $\endgroup$
    – Nick Cox
    Jun 30, 2017 at 16:52
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    $\begingroup$ Thanks for the great and clear summary! The opposite of (b) at the last part means not quantile but probability, right? $\endgroup$
    – HyeonPhil Youn
    Jun 30, 2017 at 17:16
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    $\begingroup$ Yes, P-P plots have probabilities on both axes and quantiles are implicit. $\endgroup$
    – Nick Cox
    Jun 30, 2017 at 17:18

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Answered in comments by Nick Cox:

Probability plot is the oldest term here and one that survives and even thrives. Even in the definitive 1968 paper by Wilk and Gnanadesikan https://www.jstor.org/stable/2334448 the title and much of the discussion perpetuate a wide sense of the term. But strictly Q-Q plots plot quantiles versus quantiles and probability is not explicit. I'd summarize usage as (a) probability plot is a broad term which covers all these cases and some more; (b) Q-Q plots is a strict term and implies quantiles on both axes with probability implicit (c) P-P plots is another strict term and the opposite of (b).

P-P plots have probabilities on both axes and quantiles are implicit.

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  • $\begingroup$ Take checking for normal distributions as a prominent example. In my reading "normal probability plot" is in slow decline and "normal quantile plot" in slow increase for the same plot, i.e. observed values versus expected normal quantiles from either a normal distribution with mean 0 and SD 1 or a normal distribution with the same mean and SD as the data or something else with similar flavour. $\endgroup$
    – Nick Cox
    Jul 27, 2022 at 9:43

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