  The Mann-Kendall test for trend has gained a lot of attention in a range of
disciplines, especially in the environmental sciences. One of the drawbacks of
the Mann-Kendall test when applied to real data is that no distinction can be
made between meaningful and non-meaningful differences in subsequent
observations. We introduce the concept of partial ties, which allows inferences
while accounting for (non)meaningful difference. We introduce the modified
statistic that accounts for such a concept and derive its variance estimator.
We also present analytical results for the behavior of the test in a class of
contiguous alternatives. Simulation results which illustrate the added value of
the test are presented. We apply our extended version of the test to some real
data concerning blood donation in Europe.
