DescTools (version 0.99.43)

VonNeumannTest: 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.

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.

Details

The VN test statistic is in the unbiased case $$VN=\frac{\sum _{i=1}^{n-1}(x_i-x_{i+1}{)}^2\cdot n}{\sum _{i=1}^n{(x_i-\overline{x})}^2\cdot (n-1)}$$ 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 $$VN=\frac{\sum _{i=1}^{n-1}(x_i-x_{i+1}{)}^2}{\sum _{i=1}^n{(x_i-\overline{x})}^2}$$ 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.

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

# NOT RUN {
VonNeumannTest(d.pizza$temperature)
# }