| VonNeumannTest {DescTools} | R Documentation |
Von Neumann's Successive Difference Test
Description
A popular statistic to test for independence is the von Neumann ratio.
Usage
VonNeumannTest(x, alternative = c("two.sided", "less", "greater"), unbiased = TRUE)
Arguments
x |
a numeric vector containing the observations |
alternative |
a character string specifying the alternative hypothesis, must be one of |
unbiased |
logical. In order for VN to be an unbiased estimate of the true population value, the calculated value is multiplied by |
Details
The VN test statistic is in the unbiased case
VN=\frac{\sum_{i=1}^{n-1}(x_i-x_{i+1})^2 \cdot n}{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2 \cdot (n-1)}
It is known that (VN-\mu)/\sigma is asymptotically standard normal, where \mu=\frac{2n}{n-1} and \sigma^2=4\cdot n^2 \frac{(n-2)}{(n+1)(n-1)^3}.
The VN test statistic is in the original (biased) case
VN=\frac{\sum_{i=1}^{n-1}(x_i-x_{i+1})^2}{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}
The test statistic (VN-2)/\sigma is asymptotically standard normal, where \sigma^2=\frac{4\cdot(n-2)}{(n+1)(n-1)}.
Missing values are silently removed.
Value
A list with class "htest" containing the components:
statistic |
the value of the VN statistic and the normalized statistic test. |
parameter, n |
the size of the data, after the remotion of consecutive duplicate values. |
p.value |
the p-value of the test. |
alternative |
a character string describing the alternative hypothesis. |
method |
a character string indicating the test performed. |
data.name |
a character string giving the name of the data. |
Author(s)
Andri Signorell <andri@signorell.net>
References
von Neumann, J. (1941) Distribution of the ratio of the mean square successive difference to the variance. Annals of Mathematical Statistics 12, 367-395.
See Also
Examples
VonNeumannTest(d.pizza$temperature)