kensen.test: Test for a Trend

In USGS-R/smwrStats: R functions to support statistical methods in water resources

Test for a Trend

Description

Tests for a temporal trend using Kendall's tau and computes the Sen slope estimate of the trend.

Usage

kensen.test(y, t, n.min = 10)

Arguments

y	the data collected over time. Missing values (NAs) are allowed and removed before computations.
t	the time corresponding to each observations in y. Missing values are allowed only where y is missing. These should be expressed as Julian or decimal time and must be strictly increasing.
n.min	the minimum number of observations for adjusting the p-value for serial correlation. Used when t are uniformly spaced to adjust the p-value for serial correlation. Any value larger than the number of observations in y or Inf will suppress the adjustment.

Value

An object of class "htest" containing the following components:

method	a description of the method.
statistic	the value of Kendall's tau.
p.value	the p-value.
estimate	a named vector containing the Sen estimate of the slope in units per year, the median value of the data, the median value of time, the number of observations, and if the serial correction is applied, the effective number of observations (n*).
data.name	a string containing the actual name of the input series.
coef	a vector of an estimate of the intercept and slope.
alternative	a character string describing alternative to the test ("two.sided").
null.value	the value for the hypothesized slope (0).

Note

A straight line of the form

 ytrend = sen.slope * (
t - median.time ) + median.data

may be used as a trend line for graphically portraying or detrending the data. It goes through the point

 (t,y) = ( median.time , median.data )

with slope sen.slope.

Many tied values can cause misleading results.

The p-values for uniformly spaced data (t values unit value like years) are adjusted for lag-1 autoregressive serial correlation according to the method described by Yue and Wang (2004) that adjusts for trend. In keeping with the logic of seaken, the p-value adjustment is never performed for fewer than 10 observations. The user can suppress the adjustment by setting the value of n.min to Inf.

References

Conover, W.J., 1980, Practical nonparametric statistics (2d ed.): New York, Wiley, 512 p.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

Hirsch, R.M., Alexander, R.B. , and Smith, R.A., 1991, Selection of methods for the detection and estimation of trends in water quality: Water Resources Research, v. 27 p. 803–813.

Kendall, M.G., 1938, A new measure of rank correlation: Biometrika v. 30, p. 81–89.

Kendall, M.G., 1976, Rank correlation methods (4th ed.): London, Griffin, 202 p.

Sen, P.K., 1968, Estimates of regression coefficient based on Kendall's tau: Journal of the American Statisical Association, v. 63, p. 1379–1389.

Yue, S. and Wang. C., 2004, The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series: Water Resources Management v. 18, p. 201-218.

See Also

dectime, seaken

Examples

## Not run: 
library(smwrData)
data(SaddlePeaks)
with(SaddlePeaks, kensen.test(Flow, Year))

## End(Not run)

USGS-R/smwrStats documentation built on Oct. 11, 2022, 6:15 a.m.