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Networks of these connections are quantitatively represented using complex structures, including matrices, functions, and graphs, which require specialized statistical techniques for estimation and inference about developmental and disorder\u2010related changes. Unfortunately, classical statistical testing procedures are not well suited to high\u2010dimensional testing problems. In the context of global or regional tests for differences in neuroimaging data, traditional analysis of variance (ANOVA) is not directly applicable without first summarizing the data into univariate or low\u2010dimensional features, a process that might mask the salient features of high\u2010dimensional distributions. In this work, we consider a general framework for two\u2010sample testing of complex structures by studying generalized within\u2010group and between\u2010group variances based on distances between complex and potentially high\u2010dimensional observations. We derive an asymptotic approximation to the null distribution of the ANOVA test statistic, and conduct simulation studies with scalar and graph outcomes to study finite sample properties of the test. Finally, we apply our test to our motivating study of structural connectivity in autism spectrum disorder.<\/jats:p>","DOI":"10.1111\/biom.13123","type":"journal-article","created":{"date-parts":[[2019,7,27]],"date-time":"2019-07-27T13:48:12Z","timestamp":1564235292000},"page":"257-269","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Distance\u2010based analysis of variance for brain connectivity"],"prefix":"10.1093","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8627-8203","authenticated-orcid":false,"given":"Russell T.","family":"Shinohara","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Informatics, Penn Statistics in Imaging and Visualization Center University of Pennsylvania Philadelphia Pennsylvania"},{"name":"Department of Radiology, Center for Biomedical Image Computing and Analytics, Perelman School of Medicine University of Pennsylvania Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haochang","family":"Shou","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Informatics, Penn Statistics in Imaging and Visualization Center University of Pennsylvania Philadelphia Pennsylvania"},{"name":"Department of Radiology, Center for Biomedical Image Computing and Analytics, Perelman School of Medicine University of Pennsylvania Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2106-0953","authenticated-orcid":false,"given":"Marco","family":"Carone","sequence":"additional","affiliation":[{"name":"Department of Biostatistics University of Washington Seattle Washington"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Schultz","sequence":"additional","affiliation":[{"name":"Center for Autism Research The Children's Hospital of Philadelphia Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Birkan","family":"Tunc","sequence":"additional","affiliation":[{"name":"Department of Radiology, Center for Biomedical Image Computing and Analytics, Perelman School of Medicine University of Pennsylvania Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Drew","family":"Parker","sequence":"additional","affiliation":[{"name":"Department of Radiology, Center for Biomedical Image Computing and Analytics, Perelman School of Medicine University of Pennsylvania Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Melissa Lynne","family":"Martin","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Epidemiology, and Informatics, Penn Statistics in Imaging and Visualization Center University of Pennsylvania Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ragini","family":"Verma","sequence":"additional","affiliation":[{"name":"Department of Radiology, Center for Biomedical Image Computing and Analytics, Perelman School of Medicine University of Pennsylvania Philadelphia Pennsylvania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,9,30]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704248"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.10609"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2003.10.021"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOS504"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1093\/nsr\/nwt032"},{"key":"e_1_2_6_7_1","first-page":"723","article-title":"A kernel two\u2010sample test","volume":"13","author":"Gretton A.","year":"2012","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2007.00631.x"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1159\/000288704"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2013.04.015"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2015.04.057"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ajhg.2007.10.010"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxs014"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pgen.1000384"},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1890\/0012-9658(2001)082[0290:FMMTCD]2.0.CO;2"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1002\/sam.11227"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btr528"},{"key":"e_1_2_6_18_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0601602103"},{"key":"e_1_2_6_19_1","unstructured":"Oksanen J. 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