SURVO MM Help System (web edition)

Q-Q plots

COMPARE <Sample_1>,<Sample_2>,L / TEST=Q-Q
computes the quantiles of both samples, saves them in a Survo data
file _QQ.SVO, and generates a GPLOT scheme (from the line L onwards)
for making a quantile-quantile (q-q) plot.
This scheme may be refined by the user according to his/her needs.

If 0<p<1, and the fraction of values below x(p) is p, x(p) is the
p-quantile in the (empirical) distribution of x.
In the q-q plot the x(p)-values of both samples are plotted against
each other. If the sample sizes are not equal, the x(p)-values of
the smaller sample are plotted against corresponding values in the
greater sample obtained by linear interpolation.
Hence if the samples come from the same distribution, the quantile
points are approximately on the line y=x.

More generally, if samples 1 and 2 are generated from distributions
of independent variables X and Y and the Y distribution is obtained
from the X distribution by a linear mapping Y=a*X+b, then in the q-q
plot we have the same dependence.
For example, if the samples are drawn from distributions N(m1,s1^2) and
N(m2,s2^2), the quantile points are roughly on the line
(y-m2)/s2=(x-m1)/s1. Thus mere linearity of a q-q graph does not imply
a common distribution.
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