The influence of serial correlation on the Mann–Whitney test for detecting a shift in median

The non-parametric Mann–Whitney (MW) statistical test for assessing the significance of a shift in median or mean requires a tested series to be serially independent. However, hydrological time series such as water quality, streamflow, and others may frequently display serial correlation. In such cases, the existence of serial correlation might alter the ability of the test to detect a shift in mean. This study investigates this issue by means of the Monte Carlo simulation. Simulation results indicate that: (i) when there is no shift or a moderate shift in mean, the existence of positive serial correlation will increase the possibility to reject the null hypothesis of no shift while it might be true; and the existence of negative serial correlation will reduce the possibility to detect a shift; (ii) when a bigger shift occurs in a time series, for a series with smaller sample size, the influence of serial correlation on the test is similar to that in (i), but it is much less than that in (i); while for a series with larger sample size, the influence of serial correlation on the test is opposite to (i), i.e., positive serial correlation reduces the power of the test for detecting a shift while negative serial correlation slightly increases the power of the test for identifying a shift; and (iii) removal of serial correlation by pre-whitening can effectively remove the serial correlation and eliminate the influence of the serial correlation on the test.