Exact cumulative distribution function of runs test

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Description

This function calculates the exact cumulative conditional distribution of the Wald-Wolfowitz runs.

Usage

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pruns.exact(r, n1, n2, tail = c("2-sided", "lower", "upper"))

Arguments

r

Number of runs observed.

n1

Number of +1 items in the sequence.

n2

Number of -1 items in the sequence.

tail

Tail of the cumulative distribution function.
Default is the 2-tailed value.

Value

Numeric value of the cumulative distribution function according to the chosen tail.

Note

The 2-sided exact p-value is defined as P(abs(R-E(R)>=abs(r-E(R)).
The lower (left) tail p-value is defined as P(R<=r).
The upper (right) tail p-value is defined as P(R>=r).
r is the observed value of the random variable R.

Author(s)

D. Labes

Examples

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# SPSS "Exact Tests": small sample example, exact p:  0.071
# x <- c(1, 1, 1, 1, 0, 0, 0, 0, 1, 1)  
pruns.exact(r=3, n1=4, n2=6)
# 0.07142857
# left tail P(R<=3)=0.04761905
pruns.exact(r=3, n1=4, n2=6, tail="lower")
# right tail P(R>=3)=0.9904762
pruns.exact(r=3, n1=4, n2=6, tail="upper")
# or via runs.pvalue (2-sided)
x <- c(1, 1, 1, 1, 0, 0, 0, 0, 1, 1)  
runs.pvalue(x, pmethod="ex")