Hodges-Lehmann Estimator
Computes the Hodges-Lehmann estimator of a sample's location, a robust alternative to both the mean and the median. It's defined as the median of all pairwise averages (the so-called Walsh averages) among the values, including each value with itself. The result combines the median's resistance to outliers with greater efficiency when the data are nearly normal. It's the estimator associated with the Wilcoxon signed-rank test. Enter the sample of values.
Resultado
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Hodges-Lehmann Estimator
Computes the Hodges-Lehmann estimator of a sample's location, a robust alternative to both the mean and the median. It's defined as the median of all pairwise averages (the so-called Walsh averages) among the values, including each value with itself. The result combines the median's resistance to outliers with greater efficiency when the data are nearly normal. It's the estimator associated with the Wilcoxon signed-rank test. Enter the sample of values.
The best of both worlds between mean and median
The mean is efficient but gets dragged by a single outlier; the median is robust but throws away a lot of information. The Hodges-Lehmann estimator occupies a remarkable middle ground: it resists extreme values almost as well as the median, but uses the data far more efficiently when the distribution is reasonably symmetric.
The construction is ingenious. Instead of looking at the values one by one, it forms all possible averages between pairs of observations, including each value with itself — the so-called Walsh averages. The location estimate is simply the median of that collection of averages. That process of averaging before taking the median is what gives the estimator its rare combination of robustness and efficiency.
Enter the sample of values. The tool returns the Hodges-Lehmann estimate of location. Not by chance, it's the estimator naturally associated with the Wilcoxon signed-rank test: just as that test is the robust alternative to the t-test, this is the robust alternative to the sample mean that accompanies it.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.