pracma (version 1.7.0)

runs.test: The Runs Test, or Wald-Wolfowitz Test

Description

The ``Runs Test", or Wald-Wolfowitz Test for Randomness

Usage

runs.test(x)

Arguments

x

vector with only two different values.

Value

• Returns a list with components $Z the test statistics, and $p.value the p-value for the null hypothesis.

Details

The Runs Test is a non-parametric test for checking the randomness of a dichotomous sequence, i.e. with only two different values. The test counts the number of `runs', subsequences consisting of the same adjacent element.

The two characteristic elements of the sequence need not have the same probability. The null hypothesis is the assumption that the elements are independently drawn from from the conditional distribution given by the frequncy distribution within the sequence.

References

The `dieharder' website at http://www.phy.duke.edu/~rgb/General/dieharder.php

See Also

chisq.test, RDieHarder::dieharder

Examples

x1 <- c('H','T','T','H','H','H','T','T','T','T','T','T','T','H','H',
        'H','T','H','T','H','H','H','T','H','H','H','T','H','T','H')
runs.test(x1)
##  $Z
##  [1] -0.1617764
##  $p.value
##  [1] 0.8714819

x2 <- rep(c(0, 1), 50)
runs.test(x2)
##  $Z
##  [1] 9.849873
##  $p.value
##  [1] 0

# Which sequence is random?
x3 <- c(1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,1,
        0,0,1,0,0,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,1,1,0,1)
x4 <- c(0,0,1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,
        1,0,1,0,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0,1,1,1,0)

runs.test(x3)   # null hypotheses rejected at 0.05 level
##  $Z
##  [1] 2.05555
##  $p.value
##  [1] 0.03982587

runs.test(x4)   # randomness is very probable
##  $Z
##  [1] 0.002947558
##  $p.value
##  [1] 0.9976482