# 03 - bivariate analysis - ordinal

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• Senin, 21 Februari 2011

• Variabel 1Variabel 2Nominal Ordinal Interval Nominal Chi Quare 2Phi CoefficientCoefficient Contingency CCramers (nu)Lambda simetrikLambda asimetrikSpearman rst test (hypothesis of difference)Z test (hypothesis of difference)Eta Ordinal Kendalls Gamma Spearman rsSommers D asimetrikInterval Pearsons rRegression asimetrik

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• Nominal Bivariate Analysis - continued

• ...is a proportional reduction in error statistics ...it reflects the degree to which knowledge of the independent variable reduces errors in predicting where cases will fall on the dependent variable...it tells us how much, proportionally, knowledge of the independent variable improves our ability to guess the dependent category

• N = Total number of casesLy = The number of cases in the modal Y category, ignoring XLyx = the number of cases in the largest cell within given X categoryLx = The number of cases in the modal X category, ignoring YLxy = the number of cases in the largest cell within given Y category

xy = ( Lyx Ly) / (N Ly)yx = ( Lxy Lx) / (N Lx)

Bidang Kerja (Y)Gaya Hidup (X)AchieverAnxiousPusher Manufaktur 324754133Jasa326039131Pemerintahan23419515987148188423

• xy = ( Lyx Ly) / (N Ly) = (32+60+95) - 159/ (423 159) = 0.11yx = ( Lxy Lx) / (N Lx) = (54+60+95) - 188/ 423 188) = 0.09

Bidang Kerja (Y)Gaya Hidup (X)AchieverAnxiousPusher Manufaktur 324754133Jasa326039131Pemerintahan23419515987148188423

• Ly = The number of cases in the modal Y categoryLx = The number of cases in the modal X categoryLyx = the number of cases in the largest cell within given X categoryLxy = the number of cases in the largest cell within given Y category

yx = ( Lyx + lxy Ly - Lx)/ 2N - Ly - Lxyx = (32+60+95)+(54+60+95) 159 - 188)/ 2(423) 159 188

Bidang Kerja (Y)Gaya Hidup (X)AchieverAnxiousPusher Manufaktur 324754133Jasa326039131Pemerintahan23419515987148188423

• Bandingkan korelasi symmetric dengan korelasi asymmetric yang diperhitungkan sebelumnyaBila symmetric lebih besar (>) daripada asymmetric, berarti:

Mungkin ada variabel ketiga (intervening variable)Hubungan x y tidak bersifat kausal

• In practice

• Measures Greek SymbolType of DataHigh AssociationLambdaNominal 1 - 0GammaOrdinal+1.0 , -1.0Tau (Kendalls)Ordinal +1.0 , -1.0RhoInterval, Ratio+1.0 , -1.0Chi - square2Nominal, Ordinal Infinity

• Bivariate AnalysisStatistical SignificanceStrengthDirectionFormNon SpuriousnessDirection of InfluenceTheoretical Status of IVSufficientNecessaryContributoryReciprocalAsymmetricSymmetric

• Related to Differences

• An unsophisticated forecaster uses statistics as a drunken man uses lamp-posts - for support rather than for illumination (Andrew Lang)Facts are stubborn, but statistics are more pliable (Mark Twain)

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