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Last data update: 2014.03.03

R: Bartels Rank Test of Randomness

Bartels

R Documentation

Bartels Rank Test of Randomness

Description

Performs Bartels rank test of randomness. The default method for testing the null hypothesis of randomness is two.sided. By using the alternative left.sided, the null hypothesis is tested against a trend. By using the alternative right.sided, the null hypothesis of randomness is tested against a systematic oscillation in the observed data.

Usage

Bartels(x, alternative = "two.sided", pvalue = "normal")

## Default S3 method:
Bartels(x, alternative = "two.sided", pvalue = "normal")

Arguments

`x`	a numeric vector of data values.
`alternative`	a character string for hypothesis testing method; must be one of `two.sided` (default), `left.sided` or `right.sided`.
`pvalue`	A method for asymptotic aproximation used to compute the p-value.

Details

Missing values are by default removed.

The RVN test statistic is

RVN=∑(R_i-R_{i+1})^2 / ∑(R_i-(n+1)/2)^2

where R_i=rank(X_i), i=1,...,n. It is known that (RVN-2)/σ is asymptotically standard normal, where σ^2=[4(n-2)(5n^2-2n-9)]/[5n(n+1)(n-1)^2].

Value

`statistic`	The value of the RVN statistic test and the theoretical mean value and variance of the RVN statistic test.
`n`	the sample size, after the remotion of consecutive duplicate values.
`p.value`	the asymptotic p-value.
`method`	a character string indicating the test performed.
`data.name`	a character string giving the name of the data.
`alternative`	a character string describing the alternative.

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

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)

 # See it graphically
 qplot(factor(years), tourists)+ geom_point()

# Test the null against a trend
 Bartels(tourists, alternative="left.sided", pvalue="beta")

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(SciencesPo)
Loading required package: ggplot2
initializing ... done

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/SciencesPo/Bartels.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Bartels
> ### Title: Bartels Rank Test of Randomness
> ### Aliases: Bartels Bartels.default
> ### Keywords: Tests
> 
> ### ** 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)
> 
>  # See it graphically
>  qplot(factor(years), tourists)+ geom_point()
> 
> # Test the null against a trend
>  Bartels(tourists, alternative="left.sided", pvalue="beta")

	Bartels Ratio Test

data:  tourists
statistic = -3.6453, n = 13, p-value = 0.0000000121
alternative hypothesis: trend

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>