Extending the Mann-Kendall test to allow for measurement uncertainty

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.