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QQPLOT Statement

Construction of Quantile-Quantile and Probability Plots

Figure 10.6 illustrates how a Q-Q plot is constructed. First, the n nonmissing values of the variable are ordered from smallest to largest: 


		\(
 x_{(1)} \leq x_{(2)} \leq  ...  \leq x_{(n)}
\)
Then the i th ordered value x(i) is represented on the plot by a point whose y-coordinate is x(i) and whose x-coordinate is F-1( [(i- 0.375 )/(n + 0.25)] ), where F(·) is the theoretical distribution with zero location parameter and unit scale parameter.

capqqcon.gif (2667 bytes)

Figure 10.6: Construction of a Q-Q Plot

You can modify the adjustment constants -0.375 and 0.25 with the RANKADJ= and NADJ= options. This default combination is recommended by Blom (1958). For additional information, refer to Chambers and others (1983). Since x(i) is a quantile of the empirical cumulative distribution function (ecdf), a Q-Q plot compares quantiles of the ecdf with quantiles of a theoretical distribution. Probability plots (see Chapter 9, "PROBPLOT Statement") are constructed the same way, except that the x-axis is scaled nonlinearly in percentiles.

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