runs.test | R Documentation |

Performs the Wald-Wolfowitz runs test of randomness for continuous data.

runs.test(x, alternative, threshold, pvalue, plot)

`x` |
a numeric vector containing the observations |

`alternative` |
a character string with the alternative hypothesis. Must be one of " |

`threshold` |
the cut-point to transform the data into a dichotomous vector |

`pvalue` |
a character string specifying the method used to compute the p-value. Must be one of normal (default), or exact. |

`plot` |
a logic value to select whether a plot should be created. If 'TRUE', then the graph will be plotted. |

Data is transformed into a dichotomous vector according as each values is above or below a given `threshold`

. Values equal to the level are removed from the sample.

The default `threshold`

value used in applications is the sample median which give us the special case of this test with *n1 = n2*, the runs test above and below the median.

The possible `alternative`

values are "`two.sided`

", "`left.sided`

" and "`right.sided`

" define the alternative hypothesis. By using the alternative "`left.sided`

" the null of randomness is tested against a trend. By using the alternative "`right.sided`

" the null hypothesis of randomness is tested against a first order negative serial correlation.

A list with class "htest" containing the components:

`statistic` |
the value of the normalized statistic test. |

`parameter` |
a vector with the sample size, and the values of |

`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. |

`runs` |
the total number of runs (not shown on screen). |

`mu` |
the mean value of the statistic test (not shown on screen). |

`var` |
the variance of the statistic test (not shown on screen). |

Frederico Caeiro

Brownlee, K. A. (1965). *Statistical Theory and Methodology in Science and Engineering*, 2nd ed. New York: Wiley.

Gibbons, J.D. and Chakraborti, S. (2003). *Nonparametric Statistical Inference*, 4th ed. (pp. 78–86).
URL: http://books.google.pt/books?id=dPhtioXwI9cC&lpg=PA97&ots=ZGaQCmuEUq

Wald, A. and Wolfowitz, J. (1940). On a test whether two samples are from the same population, *The Annals of Mathematical Statistics* **11**, 147–162. doi:10.1214/aoms/1177731909. https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-11/issue-2/On-a-Test-Whether-Two-Samples-are-from-the-Same/10.1214/aoms/1177731909.full

## ## Example 1 ## Data from example in Brownlee (1965), p. 223. ## Results of 23 determinations, ordered in time, of the density of the earth. ## earthden <- c(5.36, 5.29, 5.58, 5.65, 5.57, 5.53, 5.62, 5.29, 5.44, 5.34, 5.79, 5.10, 5.27, 5.39, 5.42, 5.47, 5.63, 5.34, 5.46, 5.30, 5.75, 5.68, 5.85) runs.test(earthden) ## ## Example 2 ## Sweet potato yield per acre, harvested in the United States, between 1868 and 1937. ## Data available in this package. ## data(sweetpotato) runs.test(sweetpotato$yield)

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.