A comparison of the power of the t test, Mann-Kendall and bootstrap tests for trend detection

Monte Carlo simulation is applied to compare the power of the statistical tests: the parametric t test, the non-parametric Mann-Kendall (MK), bootstrap-based slope (BS-slope), and bootstrap-based MK (BS-MK) tests to assess the significance of monotonic (linear and nonlinear) trends. Simulation results indicate that (a) the t test and the BS-slope test, which are slope-based tests, have the same power; (b) the MK and BS-based MK tests, which are rank-based tests, have the same power; (c) for normally-distributed data, the power of the slope-based tests is slightly higher than that of the rank-based tests; and (d) for non-normally distributed series such as time series with the Pearson type III (P3), Gumbel, extreme value type II (EV2), or Weibull distributions, the power of the rank-based tests is higher than that of the slope-based tests. The power of the tests is slightly sensitive to the shape of trend. Practical assessment of the significance of trends in the annual maximum daily flows of 30 Canadian pristine river basins demonstrates a similar tendency to that obtained in the simulation studies.