pMedian

Pseudomedian

pMedian(x, na.rm = FALSE)

Arguments

x

a numeric vector

na.rm

set to TRUE to exclude NAs before computing the pseudomedian

Value

a scalar numeric value

Details

Uses fast Fortran code to compute the pseudomedian of a numeric vector. The pseudomedian is the median of all possible midpoints of two observations. The pseudomedian is also called the Hodges-Lehmann one-sample estimator. The Fortran code is was originally from JF Monahan, and was converted to C++ in the DescTools package. It has been converted to Fortran 2018 here.

See also

https://dl.acm.org/doi/10.1145/1271.319414, https://www4.stat.ncsu.edu/~monahan/jul10/

Examples

x <- c(1:4, 10000)
pMedian(x)
#> [1] 3
# Compare with brute force calculation and with wilcox.test
w <- outer(x, x, '+')
median(w[lower.tri(w, diag=TRUE)]) / 2
#> [1] 3
wilcox.test(x, conf.int=TRUE)
#> 
#> 	Wilcoxon signed rank exact test
#> 
#> data:  x
#> V = 15, p-value = 0.06
#> alternative hypothesis: true location is not equal to 0
#> 95 percent confidence interval:
#>      1 10000
#> sample estimates:
#> (pseudo)median 
#>              3 
#>