Performs an approximate Cox-Stuart or Difference-Sign trend test.
trend.test(x, method = c("cox.stuart", "diff.sign"), plot = FALSE)A list with class "htest" containing the following components:
a character string giving the names of the data.
the type of test applied.
a character string describing the alternative hypothesis.
the p-value for the test.
the value of the test statistic with a name describing it.
a numeric vector or univariate time series.
test method. The default is method = "cox.stuart".
a logical value indicating to display the plot of data.
The default is FALSE.
Debin Qiu
Cox-Stuart or Difference-Sign test is used to test whether the data have a
increasing or decreasing trend. They are useful to detect the linear or nonlinear trend.
The Cox-Stuart test is constructed as follows.
For the given data \(x[1],...,x[t]\), one can divide them into two sequences with
equal number of observations cutted in the midpoint and then take the paired difference,
i.e., \(D = x[i] - x[i+c], i = 1, ..., floor(n/2)\), where \(c\) is the index of
midpoint. Let \(S\) be the number of positive or negative values in \(D\). Under the
null hypothesis that data have no trend, for large \(n\) = length(x), \(S\) is
approximately distributed as \(N(n/2,n/4)\), such that one can immediately obtain
the p value. The exact Cox-Stuart trend test can be seen in cs.test of
snpar package.
The Difference-Sign test is constructed as the similar way as Cox-Stuart test. We first let \(D = x[i] - x[i - 1]\) for \(i = 2, ..., n\) and then count the number of positive or negative values in \(D\), defined as \(S\). Under the null hypothesis, \(S\) is approximately distributed as \(N((n-1)/2,(n+1)/12)\). Thus, p-value can be calculated based on the null distribution.
D.R. Cox and A. Stuart (1955). Some quick sign tests for trend in location and dispersion. Biometrika, Vol. 42, pp. 80-95.
P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, second ed., Springer, New York, 1991. (p. 37)
x <- rnorm(100)
trend.test(x,plot = TRUE) # no trend
x <- 5*(1:100)/100
x <- x + arima.sim(list(order = c(1,0,0),ar = 0.4),n = 100)
trend.test(x,plot = TRUE) # increasing trend
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