Wald-Wolfowitz Runs Test
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 n1 and n2. |
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. http://projecteuclid.org/euclid.aoms/1177731909
## ## 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)
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