{"id":"https://openalex.org/W7123336210","doi":"https://doi.org/10.3934/math.2026042","title":"Statistical reproducibility of correlation tests: Pearson, Spearman, and Kendall","display_name":"Statistical reproducibility of correlation tests: Pearson, Spearman, and Kendall","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7123336210","doi":"https://doi.org/10.3934/math.2026042"},"language":"en","primary_location":{"id":"doi:10.3934/math.2026042","doi":"https://doi.org/10.3934/math.2026042","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2026042","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/1/PDF/math-11-01-042.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.aimspress.com/aimspress-data/math/2026/1/PDF/math-11-01-042.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140199298","display_name":"Norah D. Alshahrani","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210136004","display_name":"University of Bisha","ror":"https://ror.org/040548g92","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210136004"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Norah D. Alshahrani","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Bisha, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Bisha, Saudi Arabia","institution_ids":["https://openalex.org/I4210136004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5140199298"],"corresponding_institution_ids":["https://openalex.org/I4210136004"],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":7.2398,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.96798652,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"11","issue":"1","first_page":"957","last_page":"976"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14406","display_name":"Multidisciplinary Science and Engineering Research","score":0.36250001192092896,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T14406","display_name":"Multidisciplinary Science and Engineering Research","score":0.36250001192092896,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T13500","display_name":"Probability and Statistical Research","score":0.2379000037908554,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.11680000275373459,"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/pearson-correlation","display_name":"Pearson correlation","score":0.6790000200271606},{"id":"https://openalex.org/keywords/spearman-s-rank-correlation","display_name":"Spearman correlation","score":0.9089999794960022},{"id":"https://openalex.org/keywords/kendall-s-rank-correlation","display_name":"Kendall's rank correlation","score":0.8849999904632568},{"id":"https://openalex.org/keywords/correlation-test","display_name":"correlation test","score":0.7620000243186951},{"id":"https://openalex.org/keywords/sample-size-effects","display_name":"sample size effects","score":0.7870000004768372},{"id":"https://openalex.org/keywords/noise-level","display_name":"noise level","score":0.6620000004768372},{"id":"https://openalex.org/keywords/nonlinear-dependence","display_name":"nonlinear dependence","score":0.7390000224113464},{"id":"https://openalex.org/keywords/monte-carlo-simulation","display_name":"Monte Carlo simulation","score":0.7239999771118164}],"concepts":[{"id":"https://openalex.org/C9893847","wikidata":"https://www.wikidata.org/wiki/Q1425625","display_name":"Reproducibility","level":2,"score":0.8895999789237976},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.7409999966621399},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6643999814987183},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.6525999903678894},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4781000018119812},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.4528000056743622},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C55078378","wikidata":"https://www.wikidata.org/wiki/Q1136628","display_name":"Pearson product-moment correlation coefficient","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C96608239","wikidata":"https://www.wikidata.org/wiki/Q1199823","display_name":"Statistical power","level":2,"score":0.3953999876976013},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.37229999899864197},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C104709138","wikidata":"https://www.wikidata.org/wiki/Q1671540","display_name":"Intraclass correlation","level":3,"score":0.3314000070095062},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C2986587452","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical analysis","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C154020017","wikidata":"https://www.wikidata.org/wiki/Q520171","display_name":"Repeatability","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/math.2026042","doi":"https://doi.org/10.3934/math.2026042","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2026042","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/1/PDF/math-11-01-042.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/math.2026042","doi":"https://doi.org/10.3934/math.2026042","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2026042","pdf_url":"http://www.aimspress.com/aimspress-data/math/2026/1/PDF/math-11-01-042.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319621","display_name":"University of Bisha","ror":"https://ror.org/040548g92"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7123336210.pdf","grobid_xml":"https://content.openalex.org/works/W7123336210.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1963989273","https://openalex.org/W1985514943","https://openalex.org/W1995945562","https://openalex.org/W2005825070","https://openalex.org/W2033582154","https://openalex.org/W2078483536","https://openalex.org/W2082494913","https://openalex.org/W2119303750","https://openalex.org/W2131679102","https://openalex.org/W2136634361","https://openalex.org/W2145979309","https://openalex.org/W2164092415","https://openalex.org/W2165700458","https://openalex.org/W2166121267","https://openalex.org/W2284552311","https://openalex.org/W2736848882","https://openalex.org/W2765781497","https://openalex.org/W3146351140","https://openalex.org/W3196620053","https://openalex.org/W3214887328","https://openalex.org/W3215512458","https://openalex.org/W4293095022","https://openalex.org/W4298872162","https://openalex.org/W4299627282","https://openalex.org/W4388562518","https://openalex.org/W4408557774","https://openalex.org/W4410763908","https://openalex.org/W4414050529"],"related_works":["https://openalex.org/W2762259977","https://openalex.org/W2067376384","https://openalex.org/W4414050529","https://openalex.org/W3165488922","https://openalex.org/W3215512458","https://openalex.org/W2900955236","https://openalex.org/W2341217492","https://openalex.org/W1996641043","https://openalex.org/W117569242","https://openalex.org/W2313339984"],"abstract_inverted_index":{"Reproducibility":[0],"has":[1],"become":[2],"a":[3,24,83,280],"fundamental":[4],"concern":[5],"in":[6,199,210],"modern":[7],"statistical":[8,39,91,297],"practice,":[9],"yet":[10],"its":[11,215],"quantitative":[12,85],"assessment":[13],"remains":[14],"limited":[15],"for":[16,56,144,155,260],"commonly":[17],"used":[18,59],"dependence":[19,133,291],"measures.":[20],"This":[21],"study":[22],"introduces":[23],"systematic":[25],"evaluation":[26],"of":[27,69,87,90,120,277,283,296],"the":[28,34,37,88,99,118,121,125,177,186,200,227,275,294],"reproducibility":[29,225,240,295],"probability":[30,35],"(RP),":[31],"defined":[32],"as":[33,226,279],"that":[36,98],"same":[38],"decision":[40],"would":[41],"be":[42],"reached":[43],"if":[44],"an":[45],"experiment":[46],"were":[47,190],"independently":[48],"replicated":[49],"under":[50,130,233],"identical":[51],"conditions.":[52,73],"RP":[53,78,114,139,188,209,257,267,278],"was":[54,79],"examined":[55],"three":[57],"widely":[58],"correlation":[60,123,284],"tests":[61,178,253],"(Pearson,":[62],"Spearman,":[63],"and":[64,71,106,124,150,185,236,246,287],"Kendall)":[65],"across":[66,93,270],"different":[67],"types":[68],"relationships":[70],"sample":[72,104,126,228,244],"Through":[74],"Monte":[75],"Carlo":[76],"simulations,":[77],"shown":[80],"to":[81,214,217],"provide":[82],"meaningful":[84],"measure":[86],"stability":[89,286],"decisions":[92,198],"repeated":[94],"experiments.":[95],"Results":[96],"indicated":[97],"underlying":[100,290],"relationship":[101],"between":[102],"variables,":[103],"size,":[105],"noise":[107,247,265],"level":[108],"influenced":[109,293],"reproducibility.":[110],"In":[111,231],"linear":[112,132,218],"relationships,":[113,239],"increased":[115],"with":[116],"both":[117,243],"strength":[119],"true":[122],"size.":[127],"For":[128,161,249],"example,":[129],"strong":[131],"($":[134,166],"\\rho":[135,167,173],"=":[136,147,158,168,174],"0.9":[137],"$),":[138,176],"exceeded":[140],"$":[141,143,145,149,152,154,156,170,172,182,193],"0.95":[142],"n":[146,157],"40":[148],"approached":[151],"1.00":[153],"80":[159],"$.":[160],"weak":[162],"or":[163,171,263],"null":[164],"correlations":[165],"0":[169],"0.3":[175],"typically":[179],"yielded":[180],"non-significant":[181],"p":[183],"$-values,":[184],"corresponding":[187],"values":[189,268],"generally":[191],"above":[192],"0.5":[194],"$,":[195],"reflecting":[196],"stable":[197],"nonrejection":[201],"area.":[202],"The":[203,272],"Pearson":[204],"test":[205,285],"demonstrated":[206],"slightly":[207],"higher":[208,264],"small":[211,250],"samples":[212,262],"due":[213],"sensitivity":[216],"dependence,":[219],"whereas":[220],"rank-based":[221],"methods":[222],"achieved":[223],"comparable":[224],"size":[229,245],"increased.":[230],"contrast,":[232],"nonlinear":[234],"nonmonotonic":[235],"piecewise":[237],"monotonic":[238],"depended":[241],"on":[242],"intensity.":[248],"samples,":[251],"all":[252],"displayed":[254],"highly":[255],"variable":[256],"values,":[258],"while":[259],"larger":[261],"levels,":[266],"converged":[269],"methods.":[271],"results":[273],"emphasized":[274],"role":[276],"reliable":[281],"indicator":[282],"revealed":[288],"how":[289],"patterns":[292],"results.":[298]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-01-14T00:00:00"}
