{"id":"https://openalex.org/W2149836749","doi":"https://doi.org/10.1080/03610910801943735","title":"The Fisher Transform of the Pearson Product Moment Correlation Coefficient and Its Square: Cumulants, Moments, and Applications","display_name":"The Fisher Transform of the Pearson Product Moment Correlation Coefficient and Its Square: Cumulants, Moments, and Applications","publication_year":2008,"publication_date":"2008-04-14","ids":{"openalex":"https://openalex.org/W2149836749","doi":"https://doi.org/10.1080/03610910801943735","mag":"2149836749"},"language":"en","primary_location":{"id":"doi:10.1080/03610910801943735","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910801943735","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"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/A5022996665","display_name":"Rachel T. Fouladi","orcid":"https://orcid.org/0000-0002-2873-6170"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Rachel T. Fouladi","raw_affiliation_strings":["Simon Fraser University","Department of Psychology , Simon Fraser University , Burnaby, British Columbia, Canada"],"affiliations":[{"raw_affiliation_string":"Simon Fraser University","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Psychology , Simon Fraser University , Burnaby, British Columbia, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090535839","display_name":"James H. Steiger","orcid":null},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James H. Steiger","raw_affiliation_strings":["Vanderbilt University","Department of Psychology and Human Development , Vanderbilt University , Nashville, Tennessee, USA"],"affiliations":[{"raw_affiliation_string":"Vanderbilt University","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Department of Psychology and Human Development , Vanderbilt University , Nashville, Tennessee, USA","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022996665"],"corresponding_institution_ids":["https://openalex.org/I18014758"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.16530728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"37","issue":"5","first_page":"928","last_page":"944"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9961000084877014,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9961000084877014,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9660999774932861,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9567999839782715,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7364944219589233},{"id":"https://openalex.org/keywords/pearson-product-moment-correlation-coefficient","display_name":"Pearson product-moment correlation coefficient","score":0.6011918783187866},{"id":"https://openalex.org/keywords/fisher-transformation","display_name":"Fisher transformation","score":0.596939206123352},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5948553681373596},{"id":"https://openalex.org/keywords/cumulant","display_name":"Cumulant","score":0.5918326377868652},{"id":"https://openalex.org/keywords/correlation-coefficient","display_name":"Correlation coefficient","score":0.5777766704559326},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5370447039604187},{"id":"https://openalex.org/keywords/null-hypothesis","display_name":"Null hypothesis","score":0.5254057049751282},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4887070953845978},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4678391218185425},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.4310115575790405},{"id":"https://openalex.org/keywords/pearsons-chi-squared-test","display_name":"Pearson's chi-squared test","score":0.4268401861190796},{"id":"https://openalex.org/keywords/test-statistic","display_name":"Test statistic","score":0.19335466623306274},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.059649765491485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7364944219589233},{"id":"https://openalex.org/C55078378","wikidata":"https://www.wikidata.org/wiki/Q1136628","display_name":"Pearson product-moment correlation coefficient","level":2,"score":0.6011918783187866},{"id":"https://openalex.org/C106366893","wikidata":"https://www.wikidata.org/wiki/Q5454862","display_name":"Fisher transformation","level":3,"score":0.596939206123352},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5948553681373596},{"id":"https://openalex.org/C172686274","wikidata":"https://www.wikidata.org/wiki/Q746007","display_name":"Cumulant","level":2,"score":0.5918326377868652},{"id":"https://openalex.org/C2780092901","wikidata":"https://www.wikidata.org/wiki/Q3433612","display_name":"Correlation coefficient","level":2,"score":0.5777766704559326},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5370447039604187},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.5254057049751282},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4887070953845978},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4678391218185425},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.4310115575790405},{"id":"https://openalex.org/C66924754","wikidata":"https://www.wikidata.org/wiki/Q2336256","display_name":"Pearson's chi-squared test","level":4,"score":0.4268401861190796},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.19335466623306274},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059649765491485596},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610910801943735","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910801943735","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W271007954","https://openalex.org/W404240460","https://openalex.org/W1964605289","https://openalex.org/W1986214614","https://openalex.org/W1991567646","https://openalex.org/W2004955987","https://openalex.org/W2007356270","https://openalex.org/W2007943671","https://openalex.org/W2008750707","https://openalex.org/W2014461446","https://openalex.org/W2021721631","https://openalex.org/W2021861826","https://openalex.org/W2022261649","https://openalex.org/W2027666102","https://openalex.org/W2036720031","https://openalex.org/W2041993782","https://openalex.org/W2042925556","https://openalex.org/W2043337501","https://openalex.org/W2044233129","https://openalex.org/W2078839703","https://openalex.org/W2079614233","https://openalex.org/W2085248495","https://openalex.org/W2089115119","https://openalex.org/W2097137621","https://openalex.org/W2120004901","https://openalex.org/W2120062331","https://openalex.org/W2129109788","https://openalex.org/W2144242878","https://openalex.org/W2144288836","https://openalex.org/W2157721549","https://openalex.org/W2319030420","https://openalex.org/W2321283766","https://openalex.org/W2462634734","https://openalex.org/W2801118113","https://openalex.org/W2905060314","https://openalex.org/W2986057930","https://openalex.org/W3022255685","https://openalex.org/W3119264854","https://openalex.org/W3141640847","https://openalex.org/W3212834860","https://openalex.org/W4230941884","https://openalex.org/W4231379694","https://openalex.org/W4231949113","https://openalex.org/W4237268041","https://openalex.org/W4239801559","https://openalex.org/W4243725744","https://openalex.org/W4246026492"],"related_works":["https://openalex.org/W2946560178","https://openalex.org/W3030957661","https://openalex.org/W2560331580","https://openalex.org/W4232364410","https://openalex.org/W4245967523","https://openalex.org/W2146096861","https://openalex.org/W2963320501","https://openalex.org/W4242395546","https://openalex.org/W1549917086","https://openalex.org/W2149836749"],"abstract_inverted_index":{"This":[0],"paper":[1],"extends":[2],"results":[3,115,132,158],"on":[4,83,167],"the":[5,8,12,25,54,67,84,93,108,111,119,125,136,160],"distribution":[6],"of":[7,11,28,31,53,72,92,110,121,124,130,138,156,164],"Fisher":[9,17,55,112,126],"transform":[10,56],"correlation":[13,32,85],"coefficient":[14,30,86],"(Fisher,":[15],"1921":[16,22],",":[18,76],"R.":[19],"A.":[20],"(":[21,78],").":[23,80],"On":[24],"\u201cprobable":[26],"error\u201d":[27],"a":[29,35,146],"deduced":[33],"from":[34],"small":[36,161],"sample":[37,162],".":[38,45,90,104],"Metron":[39],"1":[40,42],":":[41,100],"\u2013":[43,102],"32":[44],"[Google":[46,105],"Scholar]).":[47],"Approaches":[48],"to":[49,152],"obtain":[50],"exact":[51],"moments":[52,109],"for":[57,107],"both":[58],"null":[59],"and":[60,87,142,145],"non-null":[61],"correlations":[62],"are":[63,116,133],"presented.":[64],"We":[65],"extend":[66],"classic":[68],"series":[69],"expansion":[70],"formulae":[71],"Hotelling":[73,75],"(1953":[74],"H.":[77],"1953":[79],"New":[81],"light":[82],"its":[88],"transforms":[89],"Journal":[91],"Royal":[94],"Statistical":[95],"Society,":[96],"Ser.":[97],"B":[98],"15":[99],"192":[101],"232":[103],"Scholar])":[106],"transform.":[113,127],"These":[114],"considered":[117],"in":[118,135],"context":[120,137],"quadratic":[122],"functions":[123],"Some":[128],"applications":[129],"these":[131,157],"discussed":[134],"correlational":[139],"hypothesis":[140],"tests":[141,166],"confidence":[143],"intervals,":[144],"Monte":[147],"Carlo":[148],"experiment":[149],"is":[150],"used":[151],"demonstrate":[153],"how":[154],"application":[155],"impact":[159],"performance":[163],"select":[165],"correlations.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
