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

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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. Key wordstrend detection; Student's t test; Mann-Kendall test; bootstrap test; power of a test; P value; trend shape; statistical analysis Une comparaison de la puissance des tests t de Student, de Mann-Kendall et du bootstrap pour la dtection de tendance Rsum Des simulations de Monte Carlo ont t ralises pour comparer la puissance des tests statistiques suivants pour estimer le niveau de signification de tendances monotones (linaires et non-linaires): le test paramtrique t de Student, le test nonparamtrique de Mann-Kendall (MK), le test de pente par bootstrap (BS-pente) et le test MK par bootstrap (BS-MK).Les rsultats de simulation indiquent que (a) les tests t de Student et BS-pente, bass sur la pente, ont la mme puissance; (b) les tests MK et BS-MK, bass sur le rang, ont la mme puissance; (c) pour des donnes prsentant une distribution normale, la puissance des tests bass sur la pente est lgrement suprieure celle des tests bass sur le rang; et (d) pour des sries prsentant une distribution non-normale, comme une distribution de Pearson III, de Gumbel, de valeur extrme type II, ou de Weibull, la puissance des tests bass sur le rang est suprieure celle des tests bass sur la pente.La puissance des tests est lgrement sensible la forme de la tendance.L'estimation pratique de la signification des tendances est similaire pour les tudes par simulation et pour l'analyse des donnes de maxima annuels de dbits journaliers de 30 bassins vierges canadiens.Mots clefs dtection de tendance; test t de Student; test de Mann-Kendall; test bootstrap; puissance d'un test; valeur de P; forme de tendance; analyse statistique

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The record

Venue

Hydrological Sciences Journal

Topic

Hydrology and Drought Analysis

Field

Environmental Science

Canadian institutions

—

Funders

—

Keywords

StatisticsMathematicsGumbel distributionSeries (stratigraphy)Weibull distributionType I and type II errorsExtreme value theoryGeology

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