partial.mk.test: Partial Mann-Kendall Trend Test

View source: R/partial.mk.test.R

partial.mk.testR Documentation

Partial Mann-Kendall Trend Test

Description

Performs a partial Mann-Kendall Trend Test

Usage

partial.mk.test(x, y, alternative = c("two.sided", "greater", "less"))

Arguments

x

a "vector" or "ts" object that contains the variable, which is tested for trend (i.e. correlated with time)

y

a "vector" or "ts" object that contains the variable, which effect on "x" is partialled out

alternative

character, the alternative method; defaults to "two.sided"

Details

According to Libiseller and Grimvall (2002), the test statistic for x with its covariate y is

z = \frac{S_x - r_{xy} S_y}{\left[ \left( 1 - r_{xy}^2 \right) n \left(n - 1 \right) \left(2 n + 5 \right) / 18 \right]^{0.5}}

where the correlation r is calculated as:

r_{xy} = \frac{\sigma_{xy}} {n \left(n - 1\right) \left(2 n + 5 \right) / 18}

The conditional covariance between x and y is

\sigma_{xy} = \frac{1}{3} \left[K + 4 \sum_{j=1}^n R_{jx} R_{jy} - n \left(n + 1 \right) \left(n + 1 \right) \right]

with

K = \sum_{1 \le i < j \le n} \mathrm{sgn} \left\{ \left( x_j - x_i \right) \left( y_j - y_i \right) \right\}

and

R_{jx} = \left\{ n + 1 + \sum_{i=1}^n \mathrm{sgn} \left( x_j - x_i \right) \right\} / 2

Value

A list with class "htest"

method

a character string indicating the chosen test

data.name

a character string giving the name(s) of the data

statistic

the value of the test statistic

estimate

the Mann-Kendall score S, the variance varS and the correlation between x and y

alternative

a character string describing the alternative hypothesis

p.value

the p-value of the test

null.value

the null hypothesis

Note

Current Version is for complete observations only. The test statistic is not corrected for ties.

References

Libiseller, C. and Grimvall, A., (2002). Performance of partial Mann-Kendall tests for trend detection in the presence of covariates. Environmetrics 13, 71–84, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/env.507")}.

See Also

partial.cor.trend.test,

Examples

data(maxau)
s <- maxau[,"s"]; Q <- maxau[,"Q"]
partial.mk.test(s,Q)


trend documentation built on Oct. 10, 2023, 9:06 a.m.