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Detection of trends in water quality data from records with dependent observations
Author(s) -
Lettenmaier Dennis P.
Publication year - 1976
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr012i005p01037
Subject(s) - nonparametric statistics , statistics , mathematics , sample size determination , series (stratigraphy) , independence (probability theory) , dimensionless quantity , parametric statistics , sample (material) , lag , statistical hypothesis testing , econometrics , computer science , paleontology , computer network , physics , chemistry , chromatography , mechanics , biology
Classical statistical tests for trend, both parametric and nonparametric, assume independence of observations, a condition rarely encountered in time series obtained by using moderate to high sample frequencies. A method is developed for summarizing the power of the parametric t tests and the nonparametric Spearman's rho test and Mann‐Whitney's test against step and linear trends in a dimensionless ‘trend number’ which is a function of trend magnitude, standard deviation of the time series, and sample size. For the case of dependent observations, use of an equivalent independent sample size rather than the actual sample size is shown to enable use of the same trend number developed for the independent case. An important related result is the existence of an upper limit on power (trend detectability) over a fixed time horizon, regardless of the number of samples taken, for a lag 1 Markov process.