The Power of Statistical Tests for Trend Detection


Abstract: The existence of a trend in a hydrological time series is detected by statistical tests. The power of a test is the probability that it will reject a null hypothesis when it is false. In this study, the power of the parametric t-test for trend detection is estimated by Monte Carlo simulation for various probability distributions and compared with the power of the non-parametric Mann-Kendall test. The t-test has less power than the non-parametric test when the probability distribution is skewed. However, for moderately skewed distributions the power ratio is close to one. Annual streamflow records in various regions of Turkey are analyzed by the two tests to compare their powers in detecting a trend.

Keywords: Trend detection, Power of a test, t-test, Mann-Kendall test

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