Transcription
Chi-Square Tests forIndependence and HomogeneityChapter 8
Chi-Square Test for IndependenceLevels of thesecond variableLevels of the first variableTotalTotalVariables are independent.Variables are not independent.Variables are unrelated.Variables are not unrelated.Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.2
Chi-Square Test for Independence𝑐𝑟𝑗 1 𝑖 1𝑂𝑖𝑗 𝐸𝑖𝑗𝐸𝑖𝑗2 𝜒 2𝑟 1𝑐 1The number of columnsThe number of rowsDecision rule2If 𝜒𝑐𝑎𝑙𝑐. 𝜒 2𝑟 1𝑐 1 ,𝛼reject 𝐻022If 𝜒𝑐𝑎𝑙𝑐. 𝜒𝑐 𝑘 1,𝛼do not reject 𝐻0Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.3
ExampleNationalityThe expenditurelevel ( /day)Less than 5051-100More than 100TotalGermanBritishItalianAmericanOtherTotalThe expenditure level and nationality are independent.The expenditure level and nationality are not independent (dependent).The expenditure level and nationality are unrelated.The expenditure level and nationality are not unrelated (related).Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.4
ExampleNationalityThe expenditurelevel ( /day)Less than 50GermanBritishItalianAmericanOtherTotal51-100More than 100Total2𝜒𝑐𝑎𝑙𝑐. 95.4171𝜒 2𝑟 1𝑐 1 ,𝛼2 𝜒8,0.05 15.50722Since 𝜒𝑐𝑎𝑙𝑐. 𝜒8,0.05, we reject the null hypothesis.Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.5
Cramer’s V2𝜒𝑐𝑎𝑙𝑐.The estimated coefficient of relationship.The sample size.The minimum of 𝑐 1 and 𝑟 1.Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.6
ExampleParametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.7
SPSS SolutionChi-Square TestsPearson Chi-SquareLikelihood RatioFisher's Exact TestLinear-by -LinearAssociationN of Valid CasesValue95,417a96,692.b6,24688Asy mp. Sig.(2-sided),000,0001,012dfExact Sig.(2-sided).b.b.b.Exact Sig.(1-sided)b.b400a. 0 cells (,0%) hav e expected count less than 5. The minimum expected count is11,50.b. Cannot be computed because there is insuf f icient memory .Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.8
Chi-Square Test for HomogeneitySamples are taken from the same population.Samples are not taken from the same population.𝑐𝑟𝑗 1 𝑖 1𝑂𝑖𝑗 𝐸𝑖𝑗𝐸𝑖𝑗2If 𝜒𝑐𝑎𝑙𝑐. 𝜒 2𝑟 12 𝜒 2𝑟 1𝑐 1 ,𝛼𝑐 1reject 𝐻0Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.9
ExampleMachineABTotalQualityQualified Not qualified TotalSamples are taken from the same population.Samples are not taken from the same population.2𝜒𝑐𝑎𝑙𝑐.Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.10
Example22 Since 𝜒𝑐𝑎𝑙𝑐. 12.5 𝜒1,0.05 3.841, wereject the null hypothesis. Therefore, samples are taken from differentpopulations. Hence, the quality level of twomachines are different.Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.11
SPSS SolutionChi-Square TestsPearson Chi-SquareContinuity CorrectionaLikelihood RatioFisher's Exact TestLinear-by -LinearAssociationN of Valid CasesValue12,500b11,28112,972c12,438111Asy mp. Sig.(2-sided),000,001,000Exact Sig.(2-sided),001Exact intProbability,000200a. Computed only f or a 2x2 tableb. 0 cells (,0%) hav e expected count less than 5. The minimum expected count is 20,00.c. The standardized statistic is 3,527.Parametrik Olmayan Yöntemler 4. BaskıGamgam, H. & Altunkaynak BEdited by Güler, H.12
SPSS Solution Parametrik Olmayan Yöntemler 4. Baskı Gamgam, H. & Altunkaynak B Edited by Güler, H. Chi-Square Tests 12,500b 1 ,000 ,001 ,000 11,281 1 ,001 12,972 1 ,000 ,001 ,000,001 ,000 12,438 c 1 ,000 ,001 ,000 ,000 200 Pearson Chi-Square Continuity Correctiona Likelihood Ratio Fisher's Exact Test Linear-by-Linear Association N of Valid .
