Detect monotonic trends in time-series data without assuming a specific distribution shape.
The Mann-Kendall Trend Test is a nonparametric test for detecting monotonic (consistently increasing or decreasing) trends in time-series data. It does not assume normality or linearity — only that the trend, if present, is consistently in one direction. It is widely used in environmental science (detecting trends in temperature, rainfall, pollution), public health (trends in disease incidence), and social science (trends in survey responses over time).
Sen's slope estimator provides a robust, nonparametric estimate of the magnitude of the trend (units of change per time period). StatRyx computes the Mann-Kendall S-statistic, its variance, Kendall's τ (standardised correlation between observation rank and time rank), and Sen's slope with 95% CI.
The Mann-Kendall test asks whether a time series tends to go up or down over time, without assuming the trend is linear or the data normal. It compares every pair of observations and counts how often the later value is higher. Kendall's τ shows the direction and strength of the trend, and Sen's slope estimates its size in units per time step. Autocorrelation — consecutive values resembling each other — inflates significance, so check it for short-interval data.
| S-statistic | Variance(S) | Kendall τ | z | p | Sen's slope |
|---|---|---|---|---|---|
| −114 | 884 | −.62 | −3.84 | < .001 | −0.42 μg/m³/yr |
A Mann-Kendall trend test indicated a significant downward trend in annual PM2.5 concentrations over the 20-year study period, τ = −.62, z = −3.84, p < .001. Sen's slope estimated a reduction of −0.42 μg/m³ per year (95% CI [−0.61, −0.23]).
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Sen's slope is the median of all pairwise slopes between data points, making it robust to outliers. It gives the typical rate of change per time unit regardless of the distribution.
The Mann-Kendall test can be used with as few as 8–10 time points, though power increases with more observations. Autocorrelation (serial correlation) in the series can inflate the Type I error rate — StatRyx applies the variance correction when autocorrelation is detected.
Report τ, z (or S), p and Sen's slope with its units: "A Mann-Kendall test showed a significant downward trend in PM2.5 over 20 years, τ = −.62, z = −3.84, p < .001; Sen's slope was −0.84 μg/m³ per year."
Linear regression assumes a straight-line trend and normal residuals and is sensitive to outliers. Mann-Kendall only assumes a monotonic trend and is robust to outliers and skew, which is why it is standard in hydrology and environmental science.
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