Spearmans-Rank-史皮尔曼等级相关系数

BasicSocialStatisticforALGeographyHOPui-singContentLevelofMeasurement(DataTypes)NormalDistributionMeasuresofcentraltendencyDependentandindependentvariablesCorrelationcoefficientSpearman’sRankReilly’sBreak-point/Reilly’sLawLinearRegressionLevelofMeasurementNominalScale:Eg.China,USA,HK,…….OrdinalScale:Eg.Low,Medium,High,VeryHigh,….IntervalScale:Eg.27oC,28oC,29oC,…..RatioScaleEg.$20,$30,$40,…..NormaldistributionWhere=mean,s=standarddeviationxMeasuresofcentraltendencyUseavaluetorepresentacentraltendencyofagroupofdata.Mode:MostFrequentMedian:MiddleMean:ArithmeticAverageMode:MostFrequentMedian:MiddleMean:ArithmeticAverageDependentandIndependentvariablesDependentvariables:valuechangesaccordingtoanothervariableschanges.Independentvariables:Valuechangesindependently.XYXisindependentvariable,andYisdependentvariableScattergramX–independentvariable(7,8)wherex=7,y=8(3,8)wherex=3,y=8Wherex=incomey=beautifulCorrelationCoefficientThecorrelationcoefficient(r)indicatestheextenttowhichthepairsofnumbersforthesetwovariableslieonastraightline.(linearrelationship)Rangeof(r):-1to+1Perfectpositivecorrelation:+1Perfectnegativecorrelation:-1Nocorrelation:0.0CorrelationCoefficientStrongpositivecorrelation(relationship)CorrelationCoefficientStrongnegativecorrelation(relationship)CorrelationCoefficientNocorrelation(relationship)CorrelationCoefficientSpearman’sRank史皮爾曼等級相關係數Comparetherankingsonthetwosetsofscores.Itmayalsobeabetterindicatorthatarelationshipexistsbetweentwovariableswhentherelationshipisnon-linear.Rangeof(r):-1to+1Perfectpositivecorrelation:+1Perfectnegativecorrelation:-1Nocorrelation:0.0Spearman’sRankwhere:rs=spearman’scoefficientDi=differencebetweenanypairofranksN=samplesizeSpearman’sRankSpearman’sRank(Examples)ThefollowingtableshowstheSOIinthemonthofOctoberandthenumberoftropicalcyclonesintheAustralianregionfrom1970to1979.YearOctoberSOINumberoftropicalcyclones1970+11121971+18171972-12101973+10161974+9111975+18131976+4111977-1371978-571979-212UsingtheSpearman’srankcorrelationmethod,calculatethecoefficientofcorrelationbetweenOctoberSOIandthenumberoftropicalcyclonesandcommenttheresultSpearman’sRank(Examples)YearOctOSINo.ofTCOSIRankNo.TCRankDiDi21970+11121971+18171972-12101973+10161974+9111975+18131976+4111977-1371978-571979-212--------------------Spearman’sRank(Examples)CalculationrsComments:Reilly’sBreak-point雷利裂點公式Reillyproposedthataformulacouldbeusedtocalculatethepointatwhichcustomerswillbedrawntooneoranotheroftwocompetingcenters.Wherej=tradingcentreji=tradingcentreix=break-point=distancebetweeniandjPi=populationsizeofiPj=populationsizeofj=break-pointdistancefromjtoxReilly’sBreak-pointijxReilly’sBreak-pointReilly’sBreak-pointReilly’sBreak-pointReilly’sBreak-pointReilly’sBreak-pointReilly’sBreak-pointExampleReilly’sBreak-pointCentrePopulationRoaddistancefromBridgewater(km)Break-pointdistancefromBridgewater(km)Bridgewater2659800Weston5079424XFrome1338446YYeovil254923216.2Minehead80633421.9Reilly’sBreak-point08.1038.2242659850794124X9.2671.1462659813384146YLinearRegressionItindicatesthenatureoftherelationshipbetweentwo(ormore)variables.Inparticular,itindicatestheextenttowhichyoucanpredictsomevariablesbyknowingothers,ortheextenttowhichsomeareassociatedwithothers.LinearRegressionLinearRegressionAlinearregressionequationisusuallywrittenY=a+bXwhereYisthedependentvariableaistheYinterceptbistheslopeorregressioncoefficient(r)Xistheindependentvariable(orcovariate)LinearRegressionLinearRegressionUsetheregressionequationtorepresentpopulationdistribution,andKnowingvalueXtopredictvalueY.Correlationcoefficient(r)isalsousetoindicatetherelationshipbetweenXandY.TheEnd