HodgesLehmann | R Documentation |
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).
HodgesLehmann(x, y = NULL, conf.level = NA, na.rm = FALSE)
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 |
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.)
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
Cyril Flurin Moser (Cyril did the lion's share and coded Monahan's algorithm in C++), Andri Signorell <andri@signorell.net>
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
wilcox.test
, median
, MedianCI
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
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