MannKendallTest

The Mann-Kendall test, or Mann-Kendall trend test, is a nonparametric statistical method used to detect monotonic trends in a time-ordered sequence of measurements. It is widely applied in hydrology, climatology, and environmental sciences to identify whether a variable such as rainfall, stream flow, temperature, or pollutant concentration shows a consistent increase or decrease over time without assuming a specific distribution for the data.

The test operates by examining all pairs of observations and counting the number of pairs that show an increase, decrease, or no change. The core statistic is S, defined as the sum over all i < j of the sign of (x_j − x_i). If there is no trend, the expected value of S is zero. For large samples, S can be transformed into a Z statistic using its variance, Var(S), which accounts for ties (equal values). A positive Z indicates an increasing trend, a negative Z indicates a decreasing trend, and the resulting p-value assesses the strength of evidence against the null hypothesis of no trend. The test is nonparametric, meaning it does not assume a particular distribution for the data.

Variants and adjustments exist to handle common data characteristics. The Seasonal Mann-Kendall test extends the method to account for seasonality by performing the test within seasonal blocks and combining results. Autocorrelation in the time series can inflate the false positive rate, so methods such as prewhitening or the use of modified variance formulas (e.g., Hamed and Rao adjustments) are sometimes employed. The test also includes tie corrections when repeated values are present.

Limitations include reduced power with small samples and sensitivity to autocorrelation. The Mann-Kendall test can indicate the presence of a monotonic trend but does not quantify the magnitude of change or distinguish linear from nonlinear trends. It remains a standard tool for trend analysis in environmental data.