234 Spatial Point Patterns: Methodology and Applications with R
that is, the minimum and maximum values of the K-functions of the simulate d patterns, called the
upper and lower envelopes of the simulated functions.
The envelope plot can be interpreted as a statistical significance test, as follows. Without peeking
at the data, choose a particula r distance r, say r
∗
= 1 metre. If the swedishpines data were
completely random, then the data and simulated p a tterns would be statistically equivalent, since
they would all be completely random patterns with the same number of points. Consequently the
values of
b
K(r
∗
) for the data and simulated patter ns would be statistically equivalent numbers. By
symmetry, since there are 40 values altogether (one data ...