Power of the Mann–Whitney test for detecting a shift in median or mean of hydro-meteorological data |
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| Authors: | S Yue C Y Wang |
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| Institution: | (1) Meteorological Service of Canada–Ontario Region, Environment Canada 867 Lakeshore Rd., Burlington, Ontario, L7R 4A6, Canada e-mail: sheng.yue@ec.gc.ca, CA;(2) Development Research Center of Water Resources Ministry of China, DeWai LiuPuKang, Beijing 100011, China, CN |
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| Abstract: | The non-parametric Mann–Whitney (MW) statistic test has been popularly used to assess the significance of a shift in median
or mean of hydro-meteorological time series. It has been considered that the test is more suitable for non-normally distributed
data and it may be not sensitive to the distribution type of sample data. However, no evidence has been provided to demonstrate
these. This study investigates the power of the test in various circumstances by means of Monte Carlo simulation. Simulation
results demonstrate that the power of the test is very sensitive to various properties of sample data. The power depends on
the pre-assigned significance level, magnitude of a shift, sample size, and its occurrence position within a time series;
and it is also strongly affected by the variation, skewness, and distribution type of a time series. The bigger the magnitude
of a shift, the more powerful the test is; the larger the sample size, the more powerful the test is; and the bigger the variation
within a time series, the less power the test has. The test has the highest power if a shift occurs at the midpoint of a time
series. For the samples with different distribution types, the power of the test is dramatically different. The test has the
highest power for time series with the extreme value type III (EV3) distribution while it indicates the lowest power for time
series with the lognormal distribution. |
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| Keywords: | : Mann– Whitney test Nonparametric test Shift Power of a test Trend analysis |
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