A new rank test for the K-Sample problem
The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made...
Gespeichert in:
| Veröffentlicht in: | Communications in statistics. Theory and methods 1985-01, Vol.14 (6), p.1471-1484 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1484 |
|---|---|
| container_issue | 6 |
| container_start_page | 1471 |
| container_title | Communications in statistics. Theory and methods |
| container_volume | 14 |
| creator | Barbour, A. D. Cartwright, D.I. Donnelly, J.B. Eagleson, G.K. |
| description | The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution |
| doi_str_mv | 10.1080/03610928508828988 |
| format | Article |
| fullrecord | <record><control><sourceid>pascalfrancis_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1080_03610928508828988</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>8396905</sourcerecordid><originalsourceid>FETCH-LOGICAL-c279t-e5e77aef6ef4aefd1962379cb4b2e68203355b1584f4c4e414cf4b052d80ad213</originalsourceid><addsrcrecordid>eNp1j0tLxDAUhYMoWEd_gLssXLip3rzaBNwMg6PigAsV3JU0vcFqXySFYf69HapuxNVZ3POdy0fIOYMrBhquQWQMDNcKtObaaH1AEqYETyVTb4ck2d_TqZAdk5MYPwCYyrVIyOWSdrilwXafdMQ4Ut8HOr4jfUyfbTs0SIfQlw22p-TI2ybi2XcuyOv69mV1n26e7h5Wy03qeG7GFBXmuUWfoZdTVMxkXOTGlbLkmGkOQihVMqWll06iZNJ5WYLilQZbcSYWhM27LvQxBvTFEOrWhl3BoNirFn9UJ-ZiZgYbnW38ZOPq-AtqYTIDaqrdzLW6myxbu-1DUxWj3TV9-GHE_1--AFgUZCU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A new rank test for the K-Sample problem</title><source>Taylor & Francis Journals Complete</source><creator>Barbour, A. D. ; Cartwright, D.I. ; Donnelly, J.B. ; Eagleson, G.K.</creator><creatorcontrib>Barbour, A. D. ; Cartwright, D.I. ; Donnelly, J.B. ; Eagleson, G.K.</creatorcontrib><description>The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution</description><identifier>ISSN: 0361-0926</identifier><identifier>EISSN: 1532-415X</identifier><identifier>DOI: 10.1080/03610928508828988</identifier><identifier>CODEN: CSTMDC</identifier><language>eng</language><publisher>Philadelphia, PA: Marcel Dekker, Inc</publisher><subject>analysis of variance of ranks ; asymptotic normality ; dissociated random variance ; Exact sciences and technology ; k-sample problem ; Mathematics ; Nonparametric inference ; Probability and statistics ; Sciences and techniques of general use ; Statistics</subject><ispartof>Communications in statistics. Theory and methods, 1985-01, Vol.14 (6), p.1471-1484</ispartof><rights>Copyright Taylor & Francis Group, LLC 1985</rights><rights>1986 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/03610928508828988$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/03610928508828988$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,776,780,4009,27902,27903,27904,59623,60412</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=8396905$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Barbour, A. D.</creatorcontrib><creatorcontrib>Cartwright, D.I.</creatorcontrib><creatorcontrib>Donnelly, J.B.</creatorcontrib><creatorcontrib>Eagleson, G.K.</creatorcontrib><title>A new rank test for the K-Sample problem</title><title>Communications in statistics. Theory and methods</title><description>The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution</description><subject>analysis of variance of ranks</subject><subject>asymptotic normality</subject><subject>dissociated random variance</subject><subject>Exact sciences and technology</subject><subject>k-sample problem</subject><subject>Mathematics</subject><subject>Nonparametric inference</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><issn>0361-0926</issn><issn>1532-415X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1985</creationdate><recordtype>article</recordtype><recordid>eNp1j0tLxDAUhYMoWEd_gLssXLip3rzaBNwMg6PigAsV3JU0vcFqXySFYf69HapuxNVZ3POdy0fIOYMrBhquQWQMDNcKtObaaH1AEqYETyVTb4ck2d_TqZAdk5MYPwCYyrVIyOWSdrilwXafdMQ4Ut8HOr4jfUyfbTs0SIfQlw22p-TI2ybi2XcuyOv69mV1n26e7h5Wy03qeG7GFBXmuUWfoZdTVMxkXOTGlbLkmGkOQihVMqWll06iZNJ5WYLilQZbcSYWhM27LvQxBvTFEOrWhl3BoNirFn9UJ-ZiZgYbnW38ZOPq-AtqYTIDaqrdzLW6myxbu-1DUxWj3TV9-GHE_1--AFgUZCU</recordid><startdate>19850101</startdate><enddate>19850101</enddate><creator>Barbour, A. D.</creator><creator>Cartwright, D.I.</creator><creator>Donnelly, J.B.</creator><creator>Eagleson, G.K.</creator><general>Marcel Dekker, Inc</general><general>Taylor & Francis</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19850101</creationdate><title>A new rank test for the K-Sample problem</title><author>Barbour, A. D. ; Cartwright, D.I. ; Donnelly, J.B. ; Eagleson, G.K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c279t-e5e77aef6ef4aefd1962379cb4b2e68203355b1584f4c4e414cf4b052d80ad213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1985</creationdate><topic>analysis of variance of ranks</topic><topic>asymptotic normality</topic><topic>dissociated random variance</topic><topic>Exact sciences and technology</topic><topic>k-sample problem</topic><topic>Mathematics</topic><topic>Nonparametric inference</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Barbour, A. D.</creatorcontrib><creatorcontrib>Cartwright, D.I.</creatorcontrib><creatorcontrib>Donnelly, J.B.</creatorcontrib><creatorcontrib>Eagleson, G.K.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Communications in statistics. Theory and methods</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Barbour, A. D.</au><au>Cartwright, D.I.</au><au>Donnelly, J.B.</au><au>Eagleson, G.K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new rank test for the K-Sample problem</atitle><jtitle>Communications in statistics. Theory and methods</jtitle><date>1985-01-01</date><risdate>1985</risdate><volume>14</volume><issue>6</issue><spage>1471</spage><epage>1484</epage><pages>1471-1484</pages><issn>0361-0926</issn><eissn>1532-415X</eissn><coden>CSTMDC</coden><abstract>The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution</abstract><cop>Philadelphia, PA</cop><pub>Marcel Dekker, Inc</pub><doi>10.1080/03610928508828988</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0361-0926 |
| ispartof | Communications in statistics. Theory and methods, 1985-01, Vol.14 (6), p.1471-1484 |
| issn | 0361-0926 1532-415X |
| language | eng |
| recordid | cdi_crossref_primary_10_1080_03610928508828988 |
| source | Taylor & Francis Journals Complete |
| subjects | analysis of variance of ranks asymptotic normality dissociated random variance Exact sciences and technology k-sample problem Mathematics Nonparametric inference Probability and statistics Sciences and techniques of general use Statistics |
| title | A new rank test for the K-Sample problem |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T21%3A43%3A07IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-pascalfrancis_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20new%20rank%20test%20for%20the%20K-Sample%20problem&rft.jtitle=Communications%20in%20statistics.%20Theory%20and%20methods&rft.au=Barbour,%20A.%20D.&rft.date=1985-01-01&rft.volume=14&rft.issue=6&rft.spage=1471&rft.epage=1484&rft.pages=1471-1484&rft.issn=0361-0926&rft.eissn=1532-415X&rft.coden=CSTMDC&rft_id=info:doi/10.1080/03610928508828988&rft_dat=%3Cpascalfrancis_cross%3E8396905%3C/pascalfrancis_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |