  The rank envelope test (Myllym\"aki et al., Global envelope tests for spatial
processes, arXiv:1307.0239 [stat.ME]) is proposed as a solution to multiple
testing problem for Monte Carlo tests. Three different situations are
recognized: 1) a few univariate Monte Carlo tests, 2) a Monte Carlo test with a
function as the test statistic, 3) several Monte Carlo tests with functions as
test statistics. The rank test has correct (global) type I error in each case
and it is accompanied with a $p$-value and with a graphical interpretation
which shows which subtest or which distances of the used test function(s) lead
to the rejection at the prescribed significance level of the test. Examples of
null hypothesis from point process and random set statistics are used to
demonstrate the strength of the rank envelope test. The examples include
goodness-of-fit test with several test functions, goodness-of-fit test for one
group of point patterns, comparison of several groups of point patterns, test
of dependence of components in a multi-type point pattern, and test of Boolean
assumption for random closed sets.

Methodology