tseries (version 0.10-58)

runs.test: Runs Test

Description

Computes the runs test for randomness of the dichotomous (binary) data series x.

Usage

runs.test(x, alternative = c("two.sided", "less", "greater"))

Value

A list with class "htest" containing the following components:

statistic

the value of the test statistic.

p.value

the p-value of the test.

method

a character string indicating what type of test was performed.

data.name

a character string giving the name of the data.

alternative

a character string describing the alternative hypothesis.

Arguments

x

a dichotomous factor.

alternative

indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". You can specify just the initial letter.

Author

A. Trapletti

Details

This test searches for randomness in the observed data series x by examining the frequency of runs. A "run" is defined as a series of similar responses.

Note, that by using the alternative "less" the null of randomness is tested against some kind of "under-mixing" ("trend"). By using the alternative "greater" the null of randomness is tested against some kind of "over-mixing" ("mean-reversion").

Missing values are not allowed.

References

S. Siegel (1956): Nonparametric Statistics for the Behavioural Sciences, McGraw-Hill, New York.

S. Siegel and N. J. Castellan (1988): Nonparametric Statistics for the Behavioural Sciences, 2nd edn, McGraw-Hill, New York.

Examples

x <- factor(sign(rnorm(100)))  # randomness
runs.test(x)

x <- factor(rep(c(-1,1),50))  # over-mixing
runs.test(x)