Skew-Dependent Detection of Change of Central Tendency in Hydrologic Data
Publication: Journal of Hydrologic Engineering
Volume 5, Issue 1
Abstract
Changes in central tendency in hydrologic data are commonly evaluated with nonparametric statistics because the assumptions of parametric alternatives are not met. The Wilcoxon signed-ranks (WSR) test can be used to infer changes in central tendency in paired comparisons. Standard critical values for the WSR test assume that the data samples are drawn from distributions with equal skew, such that the differences are symmetrically distributed. When the data are drawn from distributions with unequal skews, the WSR test with the zero-skew critical values can lead to incorrect or inaccurate research decisions. This work provides critical values that can be applied to paired data with unequal skews. Skew-dependent critical values were developed by simulation. Equations are presented enabling the estimation of critical values as a function of sample size, skew, and type I error for both positively and negatively skewed data. The new critical values are applied to compare the annual maximum discharge and runoff depths measured at two small agricultural watersheds. The results show that the skew-dependent critical values provide decisions with different statistical significance than those decisions made using the traditional critical values that assume zero skew. The implication is that more rational decisions will be made, using the skew-dependent critical values, when the WSR test is applied to data characterized by unequal skews.
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References
1.
Berryman, D., Bobee, B., Cluis, D., and Haemmerli, J. (1988). “Nonparametric tests for trend detection in water quality time series.” Water Resour. Bull., 24(3), 545–556.
2.
Conover, W. J. (1980). “Practical nonparametric statistics.” 2nd ed., Wiley, New York.
3.
Coplin, L. S., Liscum, F., East, J. W., and Goldstein, L. B. (1996). “Measurement of flows for two irrigation districts in the Lower Colorado River Basin, Texas.” Water-Resources Investigations Rep., 96-4225, United States Geological Survey, Washington, D.C.
4.
Helsel, D. M., and Hirsch, R. M. (1988). “Discussion of the applicability of the t-test for detecting trends in water quality variables.” Water Resour. Bull, 24, 201–204.
5.
Helsel, D. M., and Hirsch, R. M. ( 1992). “Statistical methods in water resources.” Studies in environmental science, 49, Elsevier Science, Amsterdam.
6.
Hipel, K. W., and McLeod, A. I. ( 1994). “Chapter 45: Time series modelling of water resources and environmental systems.” Developments in water science, Elsevier Science, Amsterdam.
7.
Hipel, K. W., McLeod, A. I., and Weiler, R. R. (1988). “Data analysis of water quality time series in Lake Erie.” Water Resour. Bull., 24(3), 533–544.
8.
Hirsch, R. M., and Gilroy, E. J. (1985). “Detectability of step trends in the rate of atmospheric deposition of sulfate.” Water Resour. Bull., 21(5), 773–784.
9.
Hirsch, R. M., and Slack, J. R. (1984). “A nonparametric trend test for seasonal data with serial dependence.” Water Resour. Res., 20(6), 727–732.
10.
Hirsch, R. M., Helsel, D. M., Cohn, T. A., and Gilroy, E. J. ( 1993). “Statistical analysis of hydrologic data.” 17.1-17.55, Handbook of hydrology, D. R. Maidmont, ed., McGraw-Hill, New York.
11.
Hobbs, H. W. ( 1963). “Hydrologic data for experimental agricultural watersheds in the United States, 1956–1959.” Misc. Publ. No. 945, Agricultural Research Serv., U.S. Department of Agriculture, Washington, D.C.
12.
Hobbs, H. W., and Crammatte, F. B. ( 1965). “Hydrologic data for experimental agricultural watersheds in the United States, 1960–1961.” Misc. Publ. No. 994, Agricultural Research Serv., U.S. Department of Agriculture.
13.
Keim, B. D., and Muller, R. A. (1992). “Temporal fluctuations of heavy rainfall magnitudes in New Orleans, Louisiana: 1871–1991.” Water Resour. Bull., 28(4), 721–729.
14.
Kingman, A., and Zion, G. (1994). “Some power considerations when deciding to use transformations.” Statistics in Medicine, 13(5–7), 769–783.
15.
Lazaro, T. R. (1976). “Nonparametric statistical analyses of annual peak flow data from a recently urbanized watershed.” Water Resour. Bull., 12(1), 101–107.
16.
MacNeill, I. B. (1985). “Detecting unknown interventions with application to forecasting hydrological data.” Water Resour. Bull., 21(5), 785–796.
17.
McCuen, R. H., and Hromadka, T. V. (1988). “Flood skew in hydrologic design on ungaged watersheds.”J. Irrig. and Drain. Engrg., ASCE, 114(2), 301–310.
18.
McCuen, R. H., and James, L. D. (1972). “Nonparametric statistical methods in urban hydrologic research.” Water Resour. Bull., 8(5), 965–975.
19.
Van Belle, G., and Hughes, J. P. (1984). “Nonparametric tests for trends in water quality.” Water Resour. Res., 21(1), 127–136.
20.
Yu, Y. S., Zou, S., and Whittemore, D. (1993). “Non-parametric trend analysis of water quality data of rivers in Kansas.” J. Hydrol., 150, 61–80.
Information & Authors
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Published In
Journal of Hydrologic Engineering
Volume 5 • Issue 1 • January 2000
Pages: 43 - 51
History
Received: Jul 22, 1998
Published online: Jan 1, 2000
Published in print: Jan 2000
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