# The power of visualizing distributional differences: Formal graphical n-sample tests

arXiv: https://arxiv.org/abs/2403.01838 · HTML: https://mlsanity.com/paper/2403.01838/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Conformal Data Contamination Tests for In-distribution Data Acquisition](https://mlsanity.com/paper/2507.13835/) (2025)

## Abstract (arXiv)

Classical tests are available for the two-sample test of correspondence of distribution functions. From these, the Kolmogorov-Smirnov test provides also the graphical interpretation of the test results, in different forms. Here, we propose modifications of the Kolmogorov-Smirnov test with higher power. The proposed tests are based on the so-called global envelope test which allows for graphical interpretation, similarly as the Kolmogorov-Smirnov test. The tests are based on rank statistics and are suitable also for the comparison of n samples, with n ≥ 2. We compare the alternatives for the two-sample case through an extensive simulation study and discuss their interpretation. Finally, we apply the tests to real data. Specifically, we compare the height distributions between boys and girls at different ages, the sepal length distributions of different flower species, and distributions of standardized residuals from a time series model for different exchange courses using the proposed methodologies.