## Quick Reference

A plot for comparing two probability distributions, usually the sample distribution function and a theoretical distribution function. The sample values are ranked in order: *x*_{(1)}≤*x*_{(2)}≤…≤ *x*_{(n)}. Define the sample cumulative proportion as *p** _{j}*, typically calculated as (

*j*−½)/

*n*, and denote the theoretical distribution function by F. In a q-q plot, F

^{−1}(

*p*

*) is plotted against*

_{j}*x*

_{(j)}, for all

*j*. If the sample has come from the theoretical distribution, the plotted values will lie on an approximate straight line. Specialized graph paper, that has the values of F

^{−1}marked for interesting values of

*p*is called probability paper.

The p-p plot is entirely equivalent: F(*x*_{(j)}) is plotted against *p** _{j}*. Once again, if the sample has come from the theoretical distribution, the plotted values will lie on an approximate straight line. A plot of this type is called a probability plot. See also normal probability paper.

**From:**
q-q plot
in
A Dictionary of Statistics »

*Subjects:*
Probability and Statistics.

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