Mann-Kendall-Test

The Mann-Kendall-Test is a test on monotonic trends. The Null hypothesis

• \(H_0\): No Monotonic Trend (f.e. unchanging climate)

is tested against the alternative

• \(H_1\) : Monotonic trend

with the test statistic for the observations \(y_1, ...,y_n\)

\(S=\sum\limits_{k=1}^{n-1}\sum\limits_{j=k+1}^{n} sgn(y_j-y_k)\)

\(S>0\) means that observations made later in time tend to be larger than observations made earlier$

\(z=\left\{ \begin{array}{ll} (S-1)/Std & \quad if \; S > 0\\ 0 & \quad if \; S = 0\\ (S+1)/Std & \quad if \; S < 0\\ \end{array} \right.\)

• \(H_0\) is rejected if \(\vert z\vert > z_{\alpha/2}\)

• \(\alpha\): significance level

• \(z_{\alpha}\): \((1-\alpha)\)-percentile of the standard normal distribution

• Std: Standard deviation (without tied groups)

Source: Pacific Northwest National Laboratory

Code: Chad A. Greene et al. (2019) The Climate Data Toolbox for MATLAB.