kendallTrendTest {WRTDStidal}

Kendall trend test

Description

Nonparametric test for monotonic trend based on Kendall's Tau statistic

Usage

kendallTrendTest(y, ...)

## Default S3 method:
kendallTrendTest(
  y,
  x = seq(along = y),
  alternative = "two.sided",
  correct = TRUE,
  ci.slope = TRUE,
  conf.level = 0.95,
  warn = TRUE,
  data.name = NULL,
  data.name.x = NULL,
  parent.of.data = NULL,
  subset.expression = NULL,
  ...
)

## S3 method for class 'formula'
kendallTrendTest(y, data = NULL, subset, na.action = na.pass, ...)

Arguments

y

an object containing data for the trend test. In the default method, the argument y must be numeric vector of observations. In the formula method, y must be a formula of the form y ~ 1 or y ~ x. The form y ~ 1 indicates use the observations in the vector y for the test for trend and use the default value of the argument x in the call to kendallTrendTest.default. The form y ~ x indicates use the observations in the vector y for the test for trend and use the specified value of the argument x in the call to kendallTrendTest.default. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.

...

methods passed to or from other methods

x

numeric vector of "predictor" values. The length of x must equal the length of y. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed. The default value of x is the vector of numbers 1, 2, ..., n where n is the number of elements in y.

alternative

character string indicating the kind of alternative hypothesis. The possible values are "two.sided" (tau not equal to 0; the default), "less" (tau less than 0), and "greater" (tau greater than 0).

correct

logical scalar indicating whether to use the correction for continuity in computing the z-statistic that is based on the test statistic S'. The default value is TRUE.

ci.slope

logical scalar indicating whether to compute a confidence interval for the slope. The default value is TRUE.

conf.level

numeric scalar between 0 and 1 indicating the confidence level associated with the confidence interval for the slope. The default value is 0.95.

warn

logical scalar indicating whether to print a warning message when y does not contain at least two non-missing values, or when x does not contain at least two unique non-missing values. The default value is TRUE.

data.name

character string indicating the name of the data used for the trend test. The default value is deparse(substitute(y)).

data.name.x

character string indicating the name of the data used for the predictor variable x. If x is not supplied this argument is ignored. When x is supplied, the default value is deparse(substitute(x)).

parent.of.data

character string indicating the source of the data used for the trend test.

subset.expression

character string indicating the expression used to subset the data.

data

specifies an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which kendallTrendTest is called.

subset

specifies an optional vector specifying a subset of observations to be used.

na.action

specifies a function which indicates what should happen when the data contain NAs. The default is na.pass.

Details

kendallTrendTest performs Kendall's nonparametric test for a monotonic trend, which is a special case of the test for independence based on Kendall's tau statistic (see cor.test). The slope is estimated using the method of Theil (1950) and Sen (1968). When ci.slope=TRUE, the confidence interval for the slope is computed using Gilbert's (1987) Modification of the Theil/Sen Method.

Kendall's test for a monotonic trend is a special case of the test for independence based on Kendall's tau statistic. The first section below explains the general case of testing for independence. The second section explains the special case of testing for monotonic trend. The last section explains how a simple linear regression model is a special case of a monotonic trend and how the slope may be estimated.

Value

A list object with elements for results of the test

References

Hirsch, R.M., Slack, J.R., Smith, R.A. 1982. Techniques of trend analysis for monthly water quality data. Water Resources Research, 18:107-121.

Millard, S. P. 2013. EnvStats: An R Package for Environmental Statistics. Springer, New York.

Examples

kendallTrendTest(res ~ dec_time, tidfitmean)