DescTools (version 0.99.19)

BartelsRankTest: Bartels Rank Test

Description

Performs the Bartels rank test of randomness.

Usage

BartelsRankTest(x, alternative = c("two.sided", "trend", "oscillation"), method = c("normal", "beta", "auto"))

Arguments

x

a numeric vector containing the observations

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "trend" or "oscillation".

method

a character string specifying the method used to compute the p-value. Must be one of normal (default), beta or auto.

Value

A list with class "htest" containing the components: A list with class "htest" containing the components:

Details

Missing values are removed.

The RVN test statistic is $$RVN=\frac{\sum_{i=1}^{n-1}(R_i-R_{i+1})^2}{\sum_{i=1}^{n}\left(R_i-(n+1)/2\right)^2}$$ where $R_i=rank(X_i), i=1,...,n$. It is known that $(RVN-2)/\sigma$ is asymptotically standard normal, where $\sigma^2=[4(n-2)(5n^2-2n-9)]/[5n(n+1)(n-1)^2]$.

By using the alternative "trend" the null hypothesis of randomness is tested against a trend. By using the alternative "oscillation" the null hypothesis of randomness is tested against a systematic oscillation.

References

Bartels, R. (1982). The Rank Version of von Neumann's Ratio Test for Randomness, Journal of the American Statistical Association, 77(377), 40-46.

Gibbons, J.D. and Chakraborti, S. (2003). Nonparametric Statistical Inference, 4th ed. (pp. 97-98). URL: http://books.google.pt/books?id=dPhtioXwI9cC&lpg=PA97&ots=ZGaQCmuEUq

See Also

rank.test

Examples

## Example 5.1 in Gibbons and Chakraborti (2003), p.98.
## Annual data on total number of tourists to the United States for 1970-1982.

years <- 1970:1982
tourists <- c(12362, 12739, 13057, 13955, 14123,  15698, 17523, 18610, 19842,
      20310, 22500, 23080, 21916)
plot(years, tourists, pch=20)

BartelsRankTest(tourists, alternative="trend", method="beta")

#  Bartels Ratio Test
#
# data:  tourists
# statistic = -3.6453, n = 13, p-value = 1.21e-08
# alternative hypothesis: trend


## Example in Bartels (1982).
## Changes in stock levels for 1968-1969 to 1977-1978 (in $A million), deflated by the
## Australian gross domestic product (GDP) price index (base 1966-1967).
x <- c(528, 348, 264, -20, - 167, 575, 410, -4, 430, - 122)

BartelsRankTest(x, method="beta")