Von Neumann's Successive Difference Test
A popular statistic to test for independence is the von Neumann ratio.
VonNeumannTest(x, alternative = c("two.sided", "less", "greater"), unbiased = TRUE)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 n/(n-1). Default is TRUE. |
The VN test statistic is in the unbiased case
VN=∑(x_i-x_{i+1})^2 / ∑(x_i-mean(x)^2 * n/n-1
It is known that (VN-μ)/σ is asymptotically standard normal, where μ=2n/(n-1) and σ^2=[4*n^2 * (n-2)]/[(n+1)(n-1)^3].
The VN test statistic is in the original (biased) case
VN=∑(x_i-x_{i+1})^2 / ∑(x_i-mean(x)^2
The test statistic (VN-2)/σ is asymptotically standard normal, where σ^2=[4*(n-2)]/[(n+1)(n-1)].
Missing values are silently removed.
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. |
Andri Signorell <andri@signorell.net>
von Neumann, J. (1941) Distribution of the ratio of the mean square successive difference to the variance. Annals of Mathematical Statistics 12, 367-395.
VonNeumannTest(d.pizza$temperature)
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