Mann-Kendall Trend Test with Sen's Slope

The Mann-Kendall trend test is a rank-based test for a monotonic trend in a time series, usually reported with Sen's slope, the median of all pairwise slopes, and its confidence interval.

Mann-Kendall 추세 검정은 시계열의 단조 추세를 순위로 검정하는 방법으로, 모든 두 점 기울기의 중앙값인 Sen 기울기와 그 신뢰구간을 함께 보고한다.

Has annual rainfall at this station increased over the last 40 years?

이 관측소의 연강수량이 지난 40년 동안 늘었는지 검정하고 싶어요.

The Mann-Kendall statistic S counts how many later observations exceed earlier ones minus how many fall below them, with a variance corrected for ties. Sen's slope gives the size of the trend in outcome units per time step and is robust to outliers.

When to use Mann-Kendall Trend Test with Sen's Slope

• You want to test for a monotonic (not necessarily linear) trend.
• The data are skewed or contain outliers.
• You need a robust estimate of the rate of change, as in hydrology or climate records.

When to use something else

• The series is strongly autocorrelated; use a prewhitened or variance-corrected Mann-Kendall test.
• You need to adjust for covariates or seasonality; use regression with time terms or the seasonal Kendall test.

Assumptions and requirements

• Observations are serially independent.
• A monotonic trend is the alternative of interest.
• Measurements are comparable over time.

What the analysis reports

• S, tie-corrected variance and continuity-corrected Z
• Two-sided p-value and Kendall's τ
• Sen's slope with confidence interval
• Lag-1 autocorrelation check

How to report it

A Mann-Kendall test indicated a monotonic trend, S = [value], Z = [value], p = [value]; Sen's slope was [value] per year, 95% CI [[value], [value]].

Related methods

• Kendall's Tau Correlation
• Change Point Detection (Binary Segmentation)
• Interrupted Time Series (ITS)

Run Mann-Kendall Trend Test with Sen's Slope on Quorant