HodgesLehmann {DescTools} | R Documentation |

## 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 |

### 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 <andri@signorell.net>

### 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

### 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
```

*DescTools*version 0.99.55 Index]