| bartels.test {trend} | R Documentation |
Bartels Test for Randomness
Description
Performes a rank version of von Neumann's ratio test as proposed by Bartels. The null hypothesis of randomness is tested against the alternative hypothesis
Usage
bartels.test(x)
Arguments
x |
a vector of class "numeric" or a time series object of class "ts" |
Details
In this function, the test is implemented as given by Bartels (1982),
where the ranks r_1, \ldots, r_n of
the X_i, \ldots, X_n are used for the statistic:
T = \frac{\sum_{i=1}^n (r_i - r_{i+1})^2}{\sum_{i=1}^n (r_i - \bar{r})^2}
As proposed by Bartels (1982), the p-value is calculated
for sample sizes in the range of (10 \le n < 100) with
the non-standard beta distribution for the range 0 \le x \le 4
with parameters:
a = b = \frac{5 n \left( n + 1\right) \left(n - 1\right)^2}
{2 \left(n - 2\right) \left(5n^2 - 2n - 9\right)} - \frac{1}{2}
For sample sizes n \ge 100 a normal approximation with
N(2, 20/(5n + 7)) is used for p-value calculation.
Value
A list with class "htest"
data.name |
character string that denotes the input data |
p.value |
the p-value |
statistic |
the test statistic |
alternative |
the alternative hypothesis |
method |
character string that denotes the test |
Note
The current function is for complete observations only.
References
R. Bartels (1982), The Rank Version of von Neumann's Ratio Test for Randomness, Journal of the American Statistical Association 77, 40–46.
See Also
Examples
# Example from Schoenwiese (1992, p. 113)
## Number of frost days in April at Munich from 1957 to 1968
##
frost <- ts(data=c(9,12,4,3,0,4,2,1,4,2,9,7), start=1957)
bartels.test(frost)
## Example from Sachs (1997, p. 486)
x <- c(5,6,2,3,5,6,4,3,7,8,9,7,5,3,4,7,3,5,6,7,8,9)
bartels.test(x)
## Example from Bartels (1982, p. 43)
x <- c(4, 7, 16, 14, 12, 3, 9, 13, 15, 10, 6, 5, 8, 2, 1, 11, 18, 17)
bartels.test(x)