DescTools (version 0.99.7)

RunsTest: Runs Test for Randomness

Description

This function performs the runs test for randomness.

Usage

RunsTest(x, alternative = c("two.sided", "less", "greater"), na.rm = FALSE)

Arguments

x

a dichotomous vector of data values.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "less" or "greater".

na.rm

defines if NAs are omitted. Default is FALSE.

Value

• A list with the following components.
• statistic
  the value of the standardized runs statistic.
• p.value
  the p-value for the test.
• data.name
  a character string giving the names of the data.
• alternative
  a character string describing the alternative hypothesis.

Details

The runs test for randomness, also known as the Wald-Wolfowitz test, is used to test the hypothesis that a series of numbers is random. For a categorical variable, the number of runs correspond to the number of times the category changes, that is, where xi belongs to one category and xi+1 belongs to the other. The number of runs, is the number of sign changes plus one. For a numeric variable x, a run is a set of sequential values that are either all above or below a specified cutpoint, typically the median.

References

Wackerly, D., Mendenhall, W. Scheaffer, R. L. (1986): Mathematical Statistics with Applications, 3rd Ed., Duxbury Press, CA. Wald, A. and Wolfowitz, J. (1940): On a test whether two samples are from the same population, Ann. Math Statist. 11, 147-162.

See Also

Run Length Encoding rle

Examples

# x has to be dichotomous for the test being 
x <- c("S","S", "T", "S", "T","T","T", "S", "T")
RunsTest( x < median(x) )


x <- c(13, 3, 14, 14, 1, 14, 3, 8, 14, 17, 9, 14, 13, 2, 16, 1, 3, 12, 13, 14)
RunsTest( x < median(x) )

plot( (x < median(x)) - 0.5, type="s", ylim=c(-1,1) )
abline(h=0)

set.seed(123)
x <- sample(0:1, size=100, replace=TRUE)
RunsTest(x)
# As you would expect of values from a random number generator, the test fails to reject 
# the null hypothesis that the data are random.