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Detecting changes in trends in water quality using modified Kendall's tau
Author(s) -
Darken P. F.,
Holtzman G. I.,
Smith E. P.,
Zipper Carl E.
Publication year - 2000
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/1099-095x(200007/08)11:4<423::aid-env423>3.0.co;2-l
Subject(s) - statistics , estimator , mathematics , nonparametric statistics , equivalence (formal languages) , correlation , variance (accounting) , wald test , null hypothesis , sample size determination , one way analysis of variance , autocorrelation , econometrics , statistical hypothesis testing , analysis of variance , accounting , discrete mathematics , business , geometry
A method for testing the equivalence of two modified Kendall's tau nonparametric correlation coefficients, neither necessarily equal to zero, is presented. Several estimators of the variance taû mod were evaluated using simulation. A bootstrap estimate, the standard null‐case variance estimate, and a delta method variance estimate are shown to provide reasonable estimates in different circumstances. The results of a power study are also given, including a comparison with the test of equivalence of two Pearson correlation coefficients. The variance estimators and their corresponding Wald‐type tests were studied under different conditions, including the presence of varying degrees of serial correlation, different distributions, and different percentages of tied data. The power study revealed that in the presence of serial correlation, a new method for estimating variance, called the effective sample size bootstrap , allowed the hypothesis test to consistently hold its level while no other method of estimating the variance did. Finally, through the use of an example, it is demonstrated how this test can be used to detect changes in trend of water‐quality variables over time. Copyright © 2000 John Wiley & Sons, Ltd.