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Hodges-Lehmann Estimator of Location

Source: R/hodgesLehmann.R
hodgesLehmann.Rd

Function to compute the Hodges-Lehmann estimator of location in the one and two sample case following a clever fast algorithm by John Monahan (1984).

Usage

hodgesLehmann(
  x,
  y = NULL,
  conf.level = NA,
  sides = c("two.sided", "left", "right"),
  na.rm = FALSE,
  ...
)

Arguments

x

numeric vector

y

optional numeric vector

conf.level

confidence level of the interval. If set to NA (the default), only the point estimate is returned.

sides

character string specifying the sidedness of the confidence interval (one of "two.sided" (default), "left" or "right"). See ConfidenceIntervals().

na.rm

logical; whether to remove missing values

...

additional arguments passed to bootstrap procedures

Value

if conf.level = NA, a numeric scalar. Otherwise a named numeric vector with elements:

est

point estimate of the Hodges-Lehmann location

lci

lower confidence interval bound

uci

upper confidence interval bound

Details

The Hodges-Lehmann estimator is the median of the combined data points and Walsh averages.

It is the same as the pseudo median returned as a by-product of wilcox.test() (which however does not calculate correctly as soon as ties are present).

Note that in the two-sample case the estimator for the difference in location parameters does not estimate the difference in medians (a common misconception) but rather the median of the difference between a sample from x and a sample from y.

sides names the side on which the finite bound lies: "left" yields \([lci, \infty)\), "right" yields \((-\infty, uci]\). The estimator is unbounded, so the open side is reported as \(\pm\infty\).

x and y are not modified.

Note

C++ port of Monahan’s algorithm by Cyril Flurin Moser

Random number generation

A confidence level triggers a bootstrap and therefore advances R's global random number generator. Call base::set.seed() beforehand for reproducible intervals. The point estimate itself is deterministic: the compiled routine picks its pivots from a local generator and does not touch R's stream.

See also

stats::wilcox.test()

Other location: gmean(), hmean(), huberM(), meanX(), medianX(), modeX(), tukeyBiweight()

Examples

x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
hodgesLehmann(x)
#> [1] 1.725

# the input is left alone
v <- c(3, 1, 2)
hodgesLehmann(v)
#> [1] 2
v
#> [1] 3 1 2

# two-sample: median of the pairwise differences, NOT the difference
# of the medians
y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)
hodgesLehmann(x, y)
#> [1] 0.56

set.seed(1)
hodgesLehmann(x, conf.level = 0.95)
#>      est      lci      uci 
#> 1.725000 1.425000 2.211442