{"id":"https://openalex.org/W2062033729","doi":"https://doi.org/10.1080/01621459.1991.10475112","title":"Interpreting Blocks and Random Factors","display_name":"Interpreting Blocks and Random Factors","publication_year":1991,"publication_date":"1991-09-01","ids":{"openalex":"https://openalex.org/W2062033729","doi":"https://doi.org/10.1080/01621459.1991.10475112","mag":"2062033729"},"language":"en","primary_location":{"id":"doi:10.1080/01621459.1991.10475112","doi":"https://doi.org/10.1080/01621459.1991.10475112","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01621459.1991.10475112","pdf_url":null,"source":{"id":"https://openalex.org/S4394736638","display_name":"Journal of the American Statistical Association","issn_l":"0162-1459","issn":["0162-1459","1537-274X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-3","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the American Statistical Association","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111435035","display_name":"Myra L. Samuels","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Myra L. Samuels","raw_affiliation_strings":["Purdue University","Department of Statistics, Purdue University, West Lafayette, IN 47907"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Statistics, Purdue University, West Lafayette, IN 47907","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080225575","display_name":"George Casella","orcid":"https://orcid.org/0000-0001-8154-8278","observed_orcids":["https://orcid.org/0000-0001-8154-8278"]},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Casella","raw_affiliation_strings":["Cornell University","Biometrics Unit, Cornell University, Ithaca, NY 14853"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Biometrics Unit, Cornell University, Ithaca, NY 14853","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043402310","display_name":"George P. McCabe","orcid":"https://orcid.org/0000-0002-0691-3113","observed_orcids":["https://orcid.org/0000-0002-0691-3113"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George P. McCabe","raw_affiliation_strings":["Purdue University","Department of Statistics, Purdue University, West Lafayette, IN 47907"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Statistics, Purdue University, West Lafayette, IN 47907","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9457,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.86297071,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"86","issue":"415","first_page":"798","last_page":"798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.47679999470710754,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.47679999470710754,"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"}},{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.45969998836517334,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T14137","display_name":"Agriculture, Soil, Plant Science","score":0.014600000344216824,"subfield":{"id":"https://openalex.org/subfields/1105","display_name":"Ecology, Evolution, Behavior and Systematics"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-effects","display_name":"random effects","score":0.5529999732971191},{"id":"https://openalex.org/keywords/linear-mixed-models","display_name":"linear mixed models","score":0.7760000228881836},{"id":"https://openalex.org/keywords/model-formulation","display_name":"model formulation","score":0.531000018119812},{"id":"https://openalex.org/keywords/hypothesis-testing","display_name":"hypothesis testing","score":0.8019999861717224},{"id":"https://openalex.org/keywords/interval-estimation","display_name":"interval estimation","score":0.7829999923706055},{"id":"https://openalex.org/keywords/statistical-efficiency","display_name":"statistical efficiency","score":0.46299999952316284},{"id":"https://openalex.org/keywords/experimental-design","display_name":"experimental design","score":0.41100001335144043}],"concepts":[{"id":"https://openalex.org/C2777146004","wikidata":"https://www.wikidata.org/wiki/Q14949826","display_name":"CLARITY","level":2,"score":0.7190623879432678},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6180064678192139},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6146122217178345},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.5494557619094849},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5357223153114319},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.49889469146728516},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.49860501289367676},{"id":"https://openalex.org/C144745244","wikidata":"https://www.wikidata.org/wiki/Q4927286","display_name":"Blocking (statistics)","level":2,"score":0.4626065194606781},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.45777982473373413},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.4356677532196045},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4232128858566284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42177510261535645},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37315547466278076},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2468525469303131},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C95190672","wikidata":"https://www.wikidata.org/wiki/Q815382","display_name":"Meta-analysis","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/01621459.1991.10475112","doi":"https://doi.org/10.1080/01621459.1991.10475112","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01621459.1991.10475112","pdf_url":null,"source":{"id":"https://openalex.org/S4394736638","display_name":"Journal of the American Statistical Association","issn_l":"0162-1459","issn":["0162-1459","1537-274X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-3","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the American Statistical Association","raw_type":"journal-article"},{"id":"doi:10.2307/2290415","doi":"https://doi.org/10.2307/2290415","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2290415","pdf_url":null,"source":{"id":"https://openalex.org/S4394736638","display_name":"Journal of the American Statistical Association","issn_l":"0162-1459","issn":["0162-1459","1537-274X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-3","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the American Statistical Association","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1515242458","https://openalex.org/W1980986733","https://openalex.org/W1981512452","https://openalex.org/W1989226857","https://openalex.org/W1989314580","https://openalex.org/W1992897439","https://openalex.org/W1997513632","https://openalex.org/W2003376707","https://openalex.org/W2005838406","https://openalex.org/W2020917893","https://openalex.org/W2021142183","https://openalex.org/W2022335745","https://openalex.org/W2022716679","https://openalex.org/W2025347456","https://openalex.org/W2038943622","https://openalex.org/W2039048709","https://openalex.org/W2048096637","https://openalex.org/W2066728241","https://openalex.org/W2069687969","https://openalex.org/W2071609452","https://openalex.org/W2075284337","https://openalex.org/W2077843346","https://openalex.org/W2091713179","https://openalex.org/W2100756824","https://openalex.org/W2113996638","https://openalex.org/W2134654456","https://openalex.org/W2154417869","https://openalex.org/W2314056335","https://openalex.org/W2314858779","https://openalex.org/W2316865730","https://openalex.org/W2324347316","https://openalex.org/W2324456953","https://openalex.org/W2331220472","https://openalex.org/W2331717141","https://openalex.org/W2509581140","https://openalex.org/W2587072524","https://openalex.org/W2593844454","https://openalex.org/W2796824299","https://openalex.org/W2798142305","https://openalex.org/W2798510847","https://openalex.org/W3109068248","https://openalex.org/W4235506169","https://openalex.org/W4245380243","https://openalex.org/W4248817242","https://openalex.org/W4298221097"],"related_works":["https://openalex.org/W2375448918","https://openalex.org/W2048130469","https://openalex.org/W2197221002","https://openalex.org/W2071814525","https://openalex.org/W2914866251","https://openalex.org/W2807401482","https://openalex.org/W2500362368","https://openalex.org/W7101016592","https://openalex.org/W2735492253","https://openalex.org/W1998197648"],"abstract_inverted_index":{"Can":[0],"blocks":[1,7,55],"be":[2],"tested":[3],"in":[4],"a":[5,45,52],"randomized":[6],"design?":[8],"It":[9],"is":[10,57],"well":[11],"known":[12],"that":[13,56],"two":[14,78],"different":[15],"formulations":[16,33,80],"of":[17,37,39,62,76,94],"the":[18,31,35,60,77,89],"linear":[19,96],"mixed":[20,95],"model":[21,32,79],"yield":[22],"conflicting":[23],"answers":[24],"to":[25,47,51,87],"this":[26],"question.":[27],"This":[28],"article":[29],"examines":[30],"from":[34,59],"point":[36],"view":[38],"statistical":[40],"relevance.":[41],"Viewing":[42],"blocking":[43],"as":[44],"device":[46],"increase":[48],"efficiency":[49],"leads":[50],"hypothesis":[53,61],"concerning":[54],"distinct":[58],"no":[63],"\u201cblock":[64],"main":[65],"effect.\u201d":[66],"Relevant":[67],"tests":[68],"and":[69,83,91],"interval":[70],"estimates":[71],"are":[72,81,85],"reviewed.":[73],"The":[74],"merits":[75],"compared,":[82],"recommendations":[84],"made":[86],"enhance":[88],"clarity":[90],"heuristic":[92],"usefulness":[93],"models.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}