Runs test is a statistical test that is used to determine whether or not a dataset comes from a random process.

The null and alternative hypotheses of the test are as follows:

H₀ (null): The data was produced in a random manner.

H_a (alternative): The data was not produced in a random manner.

This tutorial explains two methods you can use to perform Runs test in R. Note that both methods lead to the exam same results.

Method 1: Run’s Test Using the snpar Library

The first way you can perform Run’s test is with the runs.test() function from the snpar library, which uses the following syntax:

runs.test(x, exact = FALSE, alternative = c(“two.sided”, “less”, “greater”))

where:

• x: A numeric vector of data values.
• exact: Indicates whether an exact p-value should be calculated. This is FALSE by default. If the number of runs is fairly small, you can change this to TRUE.
• alternative: Indicates the alternative hypothesis. The default is two.sided.

The following code shows how to perform Run’s test using this function in R:

library(snpar)

#create dataset
data <- c(12, 16, 16, 15, 14, 18, 19, 21, 13, 13)

#perform Run's test
runs.test(data)

	Approximate runs rest

data:  data
Runs = 5, p-value = 0.5023
alternative hypothesis: two.sided

The p-value of the test is 0.5023. Since this is not less than α = .05, we fail to reject the null hypothesis. We have sufficient evidence to say that the data was produced in a random manner.

Method 2: Run’s Test Using the randtests Library

The second way you can perform Run’s test is with the runs.test() function from the randtests library, which uses the following syntax:

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

where:

• x: A numeric vector of data values.
• alternative: Indicates the alternative hypothesis. The default is two.sided.

The following code shows how to perform Run’s test using this function in R:

library(randtests)

#create dataset
data <- c(12, 16, 16, 15, 14, 18, 19, 21, 13, 13)

#perform Run's test
runs.test(data)

	Runs Test

data:  data
statistic = -0.67082, runs = 5, n1 = 5, n2 = 5, n = 10, p-value =
0.5023
alternative hypothesis: nonrandomness

Once again the p-value of the test is 0.5023. Since this is not less than α = .05, we fail to reject the null hypothesis. We have sufficient evidence to say that the data was produced in a random manner.