A comparison of the power of the t test, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des tests t de Student, de Mann-Kendall et du bootstrap pour la détection de tendance

Abstract Abstract Monte Carlo simulation is applied to compare the power of the statistical tests: the parametric t test, the non-parametric Mann-Kendall (MK), bootstrap-based slope (BS-slope), and bootstrap-based MK (BS-MK) tests to assess the significance of monotonic (linear and nonlinear) trends. Simulation results indicate that (a) the t test and the BS-slope test, which are slope-based tests, have the same power; (b) the MK and BS-based MK tests, which are rank-based tests, have the same power; (c) for normally-distributed data, the power of the slope-based tests is slightly higher than that of the rank-based tests; and (d) for non-normally distributed series such as time series with the Pearson type III (P3), Gumbel, extreme value type II (EV2), or Weibull distributions, the power of the rank-based tests is higher than that of the slope-based tests. The power of the tests is slightly sensitive to the shape of trend. Practical assessment of the significance of trends in the annual maximum daily flows of 30 Canadian pristine river basins demonstrates a similar tendency to that obtained in the simulation studies.

[1]  S. T. Buckland,et al.  Computer Intensive Statistical Methods: Validation, Model Selection, and Bootstrap , 1993 .

[2]  P. Sen.  Estimates of the Regression Coefficient Based on Kendall's Tau , 1968 .

[3]  D. Burn,et al.  Detection of hydrologic trends and variability , 2002 .

[4]  H. Theil.  A Rank-Invariant Method of Linear and Polynomial Regression Analysis , 1992 .

[5]  J. R. Wallis,et al.  Hydro-Climatological Trends in the Continental United States, 1948-88 , 1994 .

[6]  Richard M. Vogel,et al.  Trends in floods and low flows in the United States: impact of spatial correlation , 2000 .

[7]  H. B. Mann.  Nonparametric Tests Against Trend , 1945 .

[8]  C. Nicolis,et al.  Onset of sahelian drought viewed as a fluctuation-induced transition , 1990 .

[9]  D. Helsel,et al.  Statistical analysis of hydrologic data. , 1992 .

[10]  S. Yue,et al.  Canadian streamflow trend detection: impacts of serial and cross-correlation , 2003 .

[11]  S. Yue,et al.  Power of the Mann–Kendall and Spearman's rho tests for detecting monotonic trends in hydrological series , 2002 .

[12]  Jim C. Loftis,et al.  Testing for Trend in Lake and Ground Water Quality Time Series , 1989 .

[13]  Jeanne S. Yulianti,et al.  INVESTIGATING LINKS BETWEEN CLIMATIC WARMING AND LOW STREAMFLOW IN THE PRAIRIES REGION OF CANADA , 1998 .

[14]  M. Kendall,et al.  Rank Correlation Methods , 1949 .

[15]  Dennis P. Lettenmaier,et al.  Detection of trends in water quality data from records with dependent observations , 1976 .

[16]  R. Vogel,et al.  The moving blocks bootstrap versus parametric time series models , 1996 .

[17]  Donald O. Whittemore,et al.  Non-parametric trend analysis of water quality data of rivers in Kansas , 1993 .

[18]  H. Toutenburg,et al.  Lehmann, E. L., Nonparametrics: Statistical Methods Based on Ranks, San Francisco. Holden‐Day, Inc., 1975. 480 S., $ 22.95 . , 1977 .

[19]  Upmanu Lall,et al.  A Nearest Neighbor Bootstrap For Resampling Hydrologic Time Series , 1996 .

[20]  V. Ferro,et al.  Applying the bootstrap technique for studying soil redistribution by caesium-137 measurements at basin scale , 2000 .

[21]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[22]  Paul Dunne,et al.  Bootstrap Position Analysis for Forecasting Low Flow Frequency , 1997 .

[23]  Keith W. Hipel,et al.  Trend assessment of water quality time series , 1983 .

[24]  Keith W. Hipel,et al.  Data analysis of water quality time series in Lake Erie , 1988 .

[25]  Eric R. Ziegel,et al.  Handbook of Nonlinear Regression Models , 1991 .

[26]  G. Cavadias,et al.  Application of a Nonparametric Approach for Monitoring and Detecting Trends in Water Quality Data for the St , 1986 .

[27]  Bootstrap confidence intervals for design storms from exceedance series , 1989 .

[28]  Donald H. Burn,et al.  Hydrologic effects of climatic change in west-central Canada , 1994 .

[29]  Thian Yew Gan,et al.  Hydroclimatic trends and possible climatic warming in the Canadian Prairies , 1998 .

[30]  S. Yue,et al.  Detecting climate-related trends in streamflow data. , 2002, Water science and technology : a journal of the International Association on Water Pollution Research.

[31]  A. El-Shaarawi,et al.  A Statistical Evaluation of Trends in the Water Quality of the Niagara River , 1983 .

[32]  Harry F. Lins,et al.  Streamflow trends in the United States , 1999 .

[33]  Gary S. Wasserman,et al.  Computer Intensive Statistical Methods: Validation, Model Selection and Bootstrap , 1995 .

[34]  S. Yue,et al.  Assessment of the Significance of Sample Serial Correlation by the Bootstrap Test , 2002 .

[35]  K. Hipel,et al.  Time series modelling of water resources and environmental systems , 1994 .

[36]  J. Stedinger.  Frequency analysis of extreme events , 1993 .

[37]  Gerald van Belle,et al.  Nonparametric Tests for Trend in Water Quality , 1984 .

[38]  Julian L. Simon,et al.  Resampling: A Tool for Everyday Statistical Work , 1991 .

[39]  G. Cavadias,et al.  APPLICATION OF A NONPARAMETRIC APPROACH FOR MONITORING AND DETECTING TRENDS IN WATER QUALITY DATA OF THE ST. LAWRENCE RIVER. , 1986 .

[40]  Lena Zetterqvist.  Statistical estimation and interpretation of trends in water quality time series , 1991 .

[41]  T. McMahon,et al.  Detection of trend or change in annual flow of Australian rivers , 1993 .

[42]  M. Kendall.  Rank Correlation Methods , 1949 .

[43]  R. Sneyers.  On the statistical analysis of series of observations. , 1991 .