In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter ρ {\displaystyle ...Spearman'srankcorrelationcoefficientFromWikipedia,thefreeencyclopediaJumptonavigationJumptosearchNonparametricmeasureofrankcorrelationASpearmancorrelationof1resultswhenthetwovariablesbeingcomparedaremonotonicallyrelated,eveniftheirrelationshipisnotlinear.Thismeansthatalldatapointswithgreaterxvaluesthanthatofagivendatapointwillhavegreateryvaluesaswell.Incontrast,thisdoesnotgiveaperfectPearsoncorrelation.Whenthedataareroughlyellipticallydistributedandtherearenoprominentoutliers,theSpearmancorrelationandPearsoncorrelationgivesimilarvalues.TheSpearmancorrelationislesssensitivethanthePearsoncorrelationtostrongoutliersthatareinthetailsofbothsamples.ThatisbecauseSpearman'sρlimitstheoutliertothevalueofitsrank.Instatistics,Spearman'srankcorrelationcoefficientorSpearman'sρ,namedafterCharlesSpearmanandoftendenotedbytheGreekletterρ{\displaystyle\rho}(rho)orasrs{\displaystyler_{s}},isanonparametricmeasureofrankcorrelation(statisticaldependencebetweentherankingsoftwovariables).Itassesseshowwelltherelationshipbetweentwovariablescanbedescribedusingamonotonicfunction.TheSpearmancorrelationbetweentwovariablesisequaltothePearsoncorrelationbetweentherankvaluesofthosetwovariables;whilePearson'scorrelationassesseslinearrelationships,Spearman'scorrelationassessesmonotonicrelationships(whetherlinearornot).Iftherearenorepeateddatavalues,aperfectSpearmancorrelationof+1or−1occurswheneachofthevariablesisaperfectmonotonefunctionoftheother.Intuitively,theSpearmancorrelationbetweentwovariableswillbehighwhenobservationshaveasimilar(oridenticalforacorrelationof1)rank(i.e.relativepositionlabeloftheobservationswithinthevariable:1st,2nd,3rd,etc.)betweenthetwovariables,andlowwhenobservationshaveadissimilar(orfullyopposedforacorrelationof−1)rankbetweenthetwovariables.Spearman'scoefficientisappropriateforbothcontinuousanddiscreteordinalvariables.[1