HodgesLehmann {DescTools}

Hodges-Lehmann Estimator of Location

Description

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, na.rm = FALSE)

Arguments

x

a numeric vector.

y

an optional numeric vector of data values: as with x non-finite values will be omitted.

conf.level

confidence level of the interval.

na.rm

logical. Should missing values be removed? Defaults to FALSE.

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 the function 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.

(The calculation of the confidence intervals is not yet implemented.)

Value

the Hodges-Lehmann estimator of location as a single numeric value if no confidence intervals are requested,
and otherwise a numeric vector with 3 elements for the estimate, the lower and the upper confidence interval

Author(s)

Cyril Flurin Moser (Cyril did the lion's share and coded Monahan's algorithm in C++), Andri Signorell <[e-mail]>

References

Hodges, J.L., and Lehmann, E.L. (1963), Estimates of location based on rank tests. The Annals of Mathematical Statistics, 34, 598–611.

Monahan, J. (1984), Algorithm 616: Fast Computation of the Hodges-Lehmann Location Estimator, ACM Transactions on Mathematical Software, Vol. 10, No. 3, pp. 265-270

See Also

wilcox.test, median, MedianCI

Examples

set.seed(1)
x <- rt(100, df = 3)
y <- rt(100, df = 5)

HodgesLehmann(x)
HodgesLehmann(x, y)

# same as
wilcox.test(x, conf.int = TRUE)$estimate