R: Von Neumann's Successive Difference Test

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 `"two.sided"` (default), `"greater"` or `"less"`. You can specify just the initial letter.
`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.

### Details

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.

### 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

`BartelsRankTest`

### Examples

    VonNeumannTest(d.pizza$temperature)

[Package DescTools version 0.99.32 Index]