{"id":"https://openalex.org/W2108570932","doi":"https://doi.org/10.1155/2011/748580","title":"A Nonparametric Two-Sample Wald Test of Equality of Variances","display_name":"A Nonparametric Two-Sample Wald Test of Equality of Variances","publication_year":2011,"publication_date":"2011-01-05","ids":{"openalex":"https://openalex.org/W2108570932","doi":"https://doi.org/10.1155/2011/748580","mag":"2108570932"},"language":"en","primary_location":{"id":"doi:10.1155/2011/748580","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/748580","pdf_url":"https://downloads.hindawi.com/archive/2011/748580.pdf","source":{"id":"https://openalex.org/S104792724","display_name":"Advances in Decision Sciences","issn_l":"2090-3359","issn":["2090-3359","2090-3367"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Decision Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2011/748580.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023827919","display_name":"David Allingham","orcid":"https://orcid.org/0000-0002-4173-2852"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David Allingham","raw_affiliation_strings":["Centre for Computer-Assisted Research Computation and Its Applications, School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Computer-Assisted Research Computation and Its Applications, School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015245481","display_name":"J. C. W. Rayner","orcid":"https://orcid.org/0000-0003-4987-0026"},"institutions":[{"id":"https://openalex.org/I204824540","display_name":"University of Wollongong","ror":"https://ror.org/00jtmb277","country_code":"AU","type":"education","lineage":["https://openalex.org/I204824540"]},{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"J. C. W. Rayner","raw_affiliation_strings":["Centre for Statistical and Survey Methodology, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia","School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Statistical and Survey Methodology, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia","institution_ids":["https://openalex.org/I204824540"]},{"raw_affiliation_string":"School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia","institution_ids":["https://openalex.org/I78757542"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"USD","value_usd":200},"apc_paid":{"value":200,"currency":"USD","value_usd":200},"fwci":1.0951,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7988186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2011","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11235","display_name":"Statistical Methods in Clinical Trials","score":0.9520999789237976,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11235","display_name":"Statistical Methods in Clinical Trials","score":0.9520999789237976,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wald-test","display_name":"Wald test","score":0.8797047138214111},{"id":"https://openalex.org/keywords/f-test-of-equality-of-variances","display_name":"F-test of equality of variances","score":0.8075535893440247},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.7584277987480164},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.7431275844573975},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7096344232559204},{"id":"https://openalex.org/keywords/goldfeld\u2013quandt-test","display_name":"Goldfeld\u2013Quandt test","score":0.6830658912658691},{"id":"https://openalex.org/keywords/levenes-test","display_name":"Levene's test","score":0.6632854342460632},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.5813606381416321},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5694210529327393},{"id":"https://openalex.org/keywords/test","display_name":"Test (biology)","score":0.5581677556037903},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5389400720596313},{"id":"https://openalex.org/keywords/normality-test","display_name":"Normality test","score":0.5110905766487122},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4519462585449219},{"id":"https://openalex.org/keywords/sign-test","display_name":"Sign test","score":0.44923004508018494},{"id":"https://openalex.org/keywords/heteroscedasticity","display_name":"Heteroscedasticity","score":0.4443942904472351},{"id":"https://openalex.org/keywords/f-test","display_name":"F-test","score":0.42154672741889954},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.41451460123062134},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.40501341223716736},{"id":"https://openalex.org/keywords/z-test","display_name":"Z-test","score":0.29678022861480713},{"id":"https://openalex.org/keywords/test-statistic","display_name":"Test statistic","score":0.16772300004959106},{"id":"https://openalex.org/keywords/wilcoxon-signed-rank-test","display_name":"Wilcoxon signed-rank test","score":0.16096585988998413},{"id":"https://openalex.org/keywords/mann\u2013whitney-u-test","display_name":"Mann\u2013Whitney U test","score":0.1405065655708313},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.07809862494468689},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06933245062828064}],"concepts":[{"id":"https://openalex.org/C203274628","wikidata":"https://www.wikidata.org/wiki/Q748664","display_name":"Wald test","level":3,"score":0.8797047138214111},{"id":"https://openalex.org/C29447264","wikidata":"https://www.wikidata.org/wiki/Q5423649","display_name":"F-test of equality of variances","level":4,"score":0.8075535893440247},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.7584277987480164},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.7431275844573975},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7096344232559204},{"id":"https://openalex.org/C122379554","wikidata":"https://www.wikidata.org/wiki/Q3519047","display_name":"Goldfeld\u2013Quandt test","level":5,"score":0.6830658912658691},{"id":"https://openalex.org/C184310629","wikidata":"https://www.wikidata.org/wiki/Q1821748","display_name":"Levene's test","level":3,"score":0.6632854342460632},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.5813606381416321},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5694210529327393},{"id":"https://openalex.org/C2777267654","wikidata":"https://www.wikidata.org/wiki/Q3519023","display_name":"Test (biology)","level":2,"score":0.5581677556037903},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5389400720596313},{"id":"https://openalex.org/C85031952","wikidata":"https://www.wikidata.org/wiki/Q3026029","display_name":"Normality test","level":3,"score":0.5110905766487122},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4519462585449219},{"id":"https://openalex.org/C165793278","wikidata":"https://www.wikidata.org/wiki/Q2301904","display_name":"Sign test","level":4,"score":0.44923004508018494},{"id":"https://openalex.org/C101104100","wikidata":"https://www.wikidata.org/wiki/Q1063540","display_name":"Heteroscedasticity","level":2,"score":0.4443942904472351},{"id":"https://openalex.org/C110460608","wikidata":"https://www.wikidata.org/wiki/Q1386253","display_name":"F-test","level":3,"score":0.42154672741889954},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.41451460123062134},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.40501341223716736},{"id":"https://openalex.org/C117661179","wikidata":"https://www.wikidata.org/wiki/Q897827","display_name":"Z-test","level":4,"score":0.29678022861480713},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.16772300004959106},{"id":"https://openalex.org/C206041023","wikidata":"https://www.wikidata.org/wiki/Q1751970","display_name":"Wilcoxon signed-rank test","level":3,"score":0.16096585988998413},{"id":"https://openalex.org/C12868164","wikidata":"https://www.wikidata.org/wiki/Q1424533","display_name":"Mann\u2013Whitney U test","level":2,"score":0.1405065655708313},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.07809862494468689},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06933245062828064},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C142259097","wikidata":"https://www.wikidata.org/wiki/Q5891314","display_name":"Homogeneity (statistics)","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1155/2011/748580","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/748580","pdf_url":"https://downloads.hindawi.com/archive/2011/748580.pdf","source":{"id":"https://openalex.org/S104792724","display_name":"Advances in Decision Sciences","issn_l":"2090-3359","issn":["2090-3359","2090-3367"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Decision Sciences","raw_type":"journal-article"},{"id":"pmh:oai:ro.uow.edu.au:cssmwp-1082","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/cssmwp/82","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Centre for Statistical & Survey Methodology Working Paper Series","raw_type":"text"},{"id":"pmh:oai:ro.uow.edu.au:infopapers-2284","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/infopapers/1264","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty of Informatics - Papers (Archive)","raw_type":"article"},{"id":"pmh:oai:doaj.org/article:c6db50ea76de4415b17820110b97498c","is_oa":false,"landing_page_url":"https://doaj.org/article/c6db50ea76de4415b17820110b97498c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Decision Sciences, Vol 2011 (2011)","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/27748971","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_nonparametric_two-sample_wald_test_of_equality_of_variances/27748971","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:figshare.com:article/27776010","is_oa":true,"landing_page_url":"https://figshare.com/articles/preprint/A_nonparametric_two-sample_wald_test_of_equality_of_variances/27776010","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:figshare.com:article/28979987","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_nonparametric_two-sample_Wald_test_of_equality_of_variances/28979987","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:uon:12858","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.13/939683","pdf_url":null,"source":{"id":"https://openalex.org/S4306401391","display_name":"NOVA (University of Newcastle, Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78757542","host_organization_name":"University of Newcastle Australia","host_organization_lineage":["https://openalex.org/I78757542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1155/2011/748580","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/748580","pdf_url":"https://downloads.hindawi.com/archive/2011/748580.pdf","source":{"id":"https://openalex.org/S104792724","display_name":"Advances in Decision Sciences","issn_l":"2090-3359","issn":["2090-3359","2090-3367"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Decision Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2108570932.pdf","grobid_xml":"https://content.openalex.org/works/W2108570932.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1971423289","https://openalex.org/W1983274359","https://openalex.org/W1987122296","https://openalex.org/W2004802791","https://openalex.org/W2014296507","https://openalex.org/W2022261649","https://openalex.org/W2334023846","https://openalex.org/W2993862185","https://openalex.org/W4247225573"],"related_works":["https://openalex.org/W4300811756","https://openalex.org/W2949331055","https://openalex.org/W2108570932","https://openalex.org/W165548701","https://openalex.org/W4247036622","https://openalex.org/W2062512628","https://openalex.org/W1964474044","https://openalex.org/W2108416717","https://openalex.org/W310894710","https://openalex.org/W2000427441"],"abstract_inverted_index":{"We":[0,103],"develop":[1],"a":[2,105],"test":[3,16,48,71,76,84,95,110,138,145],"for":[4,56,96],"equality":[5],"of":[6,13,43,70,108],"variances":[7,34],"given":[8],"two":[9],"independent":[10],"random":[11],"samples":[12],"observations.":[14],"The":[15,47],"can":[17,79],"be":[18,66,73,80],"expected":[19],"to":[20,38,65],"perform":[21],"well":[22],"when":[23,59,121,129],"both":[24,60,122,130],"sample":[25,33,131],"sizes":[26,132],"are":[27,35,63,124,133],"at":[28,134],"least":[29,135],"moderate":[30],"and":[31,52,82,111,146],"the":[32,39,44,57,74,93,97,100,114,137,151],"asymptotically":[36],"equivalent":[37],"maximum":[40],"likelihood":[41],"estimators":[42],"population":[45,101],"variances.":[46,102],"is":[49,53,88,92,139],"motivated":[50],"by":[51],"here":[54],"assessed":[55],"case":[58],"populations":[61,123],"sampled":[62],"assumed":[64,81],"normal.":[67],"Popular":[68],"choices":[69],"would":[72],"two-sample":[75],"if":[77,85],"normality":[78],"Levene\u2019s":[83,144],"this":[86,109],"assumption":[87],"dubious.":[89],"Another":[90],"competitor":[91],"Wald":[94],"difference":[98],"in":[99],"give":[104],"nonparametric":[106],"analogue":[107],"call":[112],"it":[113],"test.":[115,152],"In":[116],"an":[117],"indicative":[118],"empirical":[119],"study":[120],"normal,":[125],"we":[126],"find":[127],"that":[128],"25":[136],"nearly":[140,147],"as":[141,143,148,150],"robust":[142],"powerful":[149]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}