Calculator Inputs
Example Data Table
| Observation | Sample A | Sample B | Pairwise Example Difference |
|---|---|---|---|
| 1 | 12 | 10 | 2 |
| 2 | 15 | 11 | 4 |
| 3 | 17 | 13 | 4 |
| 4 | 18 | 14 | 4 |
| 5 | 21 | 16 | 5 |
Using these samples, the two-sample Hodges Lehmann estimate summarizes the typical shift between the groups with median resistance to outliers.
Formula Used
One-sample estimator: Compute all Walsh averages, (xi + xj) / 2 for every pair where i ≤ j. The Hodges Lehmann estimator is the median of those Walsh averages.
Two-sample estimator: Compute all pairwise differences, xi - yj, for every value in Sample A against every value in Sample B. The Hodges Lehmann estimator is the median of those differences.
Interval estimate in this calculator: The displayed interval is an empirical quantile interval from ordered pairwise values, based on the selected confidence level.
Why it matters: This estimator is robust because medians reduce sensitivity to extreme values and skewed data.
How to Use This Calculator
- Select one-sample location or two-sample shift mode.
- Enter numeric observations for Sample A.
- Enter Sample B values when using two-sample mode.
- Choose the confidence level and graph point limit.
- Click Calculate Estimator to generate results.
- Review the estimator, interval, summary table, and graphs.
- Export the summary with CSV or PDF buttons.
Frequently Asked Questions
1. What does the Hodges Lehmann estimator measure?
It measures a robust central location or shift. In one-sample mode, it estimates the sample’s typical location. In two-sample mode, it estimates the typical difference between groups using medians of pairwise comparisons.
2. Why use it instead of the mean difference?
It is more resistant to outliers and skewed distributions. When data contain extreme values or fail normal assumptions, this estimator often gives a more stable summary of the typical shift.
3. What are Walsh averages?
Walsh averages are averages formed from all pairs of observations in one sample, including self-pairs. Their median becomes the one-sample Hodges Lehmann estimate.
4. What do positive and negative estimates mean?
In two-sample mode, a positive value suggests Sample A is typically larger than Sample B. A negative value suggests Sample A is typically smaller than Sample B.
5. Can I use decimals and negative values?
Yes. The calculator accepts integers, decimals, and negative numbers. Separate them with commas, spaces, or semicolons.
6. Does this calculator perform a hypothesis test?
No. This tool focuses on estimation rather than formal significance testing. It reports a robust effect estimate, interval bounds, summary statistics, and graphs for interpretation.
7. Why is the graph point limit needed?
Pairwise values can become very large because every comparison is included. The graph limit keeps plotting responsive while preserving the ordered shape and distribution of results.
8. When is this estimator especially useful?
It is especially useful for skewed data, small samples, ordinal-style measurements, and analyses where a robust estimate of location or group shift is preferred.