DescTools (version 0.99.13)

BartelsRankTest: Bartels Rank Test

Description

Performs the Bartels rank test of randomness.

Usage

BartelsRankTest(x, alternative, pvalue="normal")

Arguments

x
a numeric vector containing the observations
alternative
a character string with the alternative hypothesis. Must be one of "two.sided" (default), "left.sided" or "right.sided". You can specify just the initial letter.
pvalue
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:
  • statisticthe value of the normalized statistic test.
  • parameter, nthe size of the data, after the remotion of consecutive duplicate values.
  • p.valuethe p-value of the test.
  • alternativea character string describing the alternative hypothesis.
  • methoda character string indicating the test performed.
  • data.namea character string giving the name of the data.
  • rvnthe value of the RVN statistic (not show on screen).
  • nmthe value of the NM statistic, the numerator of RVN (not show on screen).
  • muthe mean value of the RVN statistic (not show on screen).
  • varthe variance of the RVN statistic (not show on screen).

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 $R_i=rank(X_i), i=1,\dots, n$. It is known that $(RVN-2)/\sigma$ is asymptotically standard normal, where $\sigma^2=\frac{4(n-2)(5n^2-2n-9)}{5n(n+1)(n-1)^2}$. The possible alternative are "two.sided", "left.sided" and "right.sided". By using the alternative "left.sided" the null hypothesis of randomness is tested against a trend. By using the alternative "right.sided" 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

Run this code
## 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="left.sided", pvalue="beta")
# output
#
#  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, pvalue="beta")

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