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From these, the Kolmogorov\u2013Smirnov test provides also the graphical interpretation of the test results, in different forms. Here, we propose modifications of the Kolmogorov\u2013Smirnov 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\u2013Smirnov test. The tests are based on rank statistics and are suitable also for the comparison of <jats:italic>n<\/jats:italic> samples, with <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$n \\ge 2$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>\u2265<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>. 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.<\/jats:p>","DOI":"10.1007\/s00180-024-01569-z","type":"journal-article","created":{"date-parts":[[2024,11,7]],"date-time":"2024-11-07T12:04:40Z","timestamp":1730981080000},"page":"2553-2582","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The power of visualizing distributional differences: formal graphical n-sample tests"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3549-5851","authenticated-orcid":false,"given":"Konstantinos","family":"Konstantinou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tom\u00e1\u0161","family":"Mrkvi\u010dka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mari","family":"Myllym\u00e4ki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"issue":"8","key":"1569_CR1","first-page":"1","volume":"1","author":"H Abdi","year":"2010","unstructured":"Abdi H (2010) Holm\u2019s sequential Bonferroni procedure. 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