{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T05:56:08Z","timestamp":1789192568080,"version":"build-2803163510"},"reference-count":65,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:00:00Z","timestamp":1782172800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100007249","name":"University of Minnesota","doi-asserted-by":"publisher","award":["DMS-2152746"],"award-info":[{"award-number":["DMS-2152746"]}],"id":[{"id":"10.13039\/100007249","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Marsden","award":["VUW1616"],"award-info":[{"award-number":["VUW1616"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Thousands of experiments are analysed, and papers are published each year involving the statistical analysis of grouped data. While this area of statistics is often perceived\u2013somewhat naively\u2013as saturated, several misconceptions still affect everyday practice, and new frontiers have so far remained unexplored. Researchers must be aware of the limitations affecting their analyses and what new possibilities are at their hands. The article introduces a unifying approach to the analysis of divisible statistics\u2013that includes Pearson\u2019s \u03c72, the likelihood ratio, and spectral statistics, as special cases\u2013 when a statistician deals with a large number of bins\/groups, thus leading to a large number of small or moderate frequencies. Performance of the tests is analysed against the class of contiguous (local) alternatives. Perhaps the most surprising result here is that, in this \u2018sparse\u2019 regime, most of the tests proposed in the literature can be modified to produce more powerful tests, and no single test based on a divisible statistic leads to a goodness-of-fit test. Distribution-free goodness-of-fit tests are also constructed.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag084","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T11:46:13Z","timestamp":1781178373000},"source":"Crossref","is-referenced-by-count":1,"title":["On the statistical analysis of grouped data: when Pearson \u03c72 and other divisible statistics are not goodness-of-fit"],"prefix":"10.1093","author":[{"given":"Sara","family":"Algeri","sequence":"first","affiliation":[{"name":"School of Statistics, University of Minnesota , Minneapolis, MN ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Estate V","family":"Khmaladze","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Victoria University of Wellington , Wellington ,","place":["New 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