ÇOKLU KARŞILAŞTIRMALARDA DAĞILIŞLA VE VARYANS YAPISIYLA İLGİLİ FARAZİYELERDEN AYRILIŞLARIN TEST ÖZELLİKLERİNE ETKİLERİ ÜZERİNDE BİR ARAŞTIRMA
ÇOKLU KARŞILAŞTIRMALARDA DAĞILIŞLA VE VARYANS YAPISIYLA İLGİLİ FARAZİYELERDEN AYRILIŞLARIN TEST ÖZELLİKLERİNE ETKİLERİ ÜZERİNDE BİR ARAŞTIRMA
Yazar: Okur, Mehmet Cudi
Dergi: Atatürk Üniversitesi Ziraat Fakültesi Dergisi, Vol. 5 No. 4, 2010

OZETÇoklu karşılaştırma testlerinde,n en fazla kullanılan LSD,Duncan, SNK ve Tukey testlerinin teorik özelliklerJ mc'elenerektemel fıa.raziyelerdeki aksamaların bu testleri nasıl etkileyeceğiincelenmiştir. Simulasyon teknikleriyle teşkil tadilen .de&middot;nemeler yeter sayıda1ekrarlanarak teıst!erin h:a.ta seviyeleri değişik'populasyonlarve örnek genişlikleri ,esas alınarak tesbitedilmiştir. Normal şartlar için beklenen hata seviyeleri normaldağıliş ve homojen varyans faraziyelerininbozulduğu çeşitlidurumlarda ortaya çıkan hata seviyeleriyle karşılaştırılarakhangi testlerin ne ölçüde etkilendiği incelenmiştir. Böylece,testlerin sağlamlık yönünden genel ve birbirlerine katşı durumlarıortaya konmuştur.SUMMARYA Researoh on the Effects of Nonnormality and Variance Heterogeneity on the, Structure of Multiple Comparison Tests.When tıhe fixed model is u-sed,the aim of the analysis of varianceis to determine the differencesbetween the pQpulation means.As the F, test used for generalnulI hypotıheses is not sufficient,the analysis of variance has got. to be completed by the multiplecomparison tests. in order todetect tıhe differences among thepopulation means, 'some parametricand non parametric test procedureshave been developed. Inthis researah some properties ofthe parametric tests, s'llchas L.s.d., Duncan, SNK and Tukey, wereinvestigated by using sampiingexperiments.Multiple comparison testsare the main coİnponents of theanalysis of variance. For this rea~son, the validity of the comparisonsdepends on the accuracy ofthe knowledge thaıt is essentialfor the analysis of variance. Therefore the assuımptioll's,of theaınalysiş of vaPİance can also 1?e.extended for the multiple compariısontests. The oecurance ofsome departures from the underlyingassu,mptions invıalidates themultiple compadsçm tests as theF tests, and causes wrong decisions.The error rate and theoreti&middot;cal s;tıruoture of multiple comparisıonprocedures are 'different/from eamother. Therefore : :tJlıelevels of type i and type 11 errOrsand their powers are not theSMTle. Because of the differencesin tıhe error rates, the decisionsand the results obtained by theuse of these tests are different.In tlüs researc,h the sampling.experiments obtained by usingMonte-Car1o methods. The errorrates of the multiple comparison'te9ts were investigated nderdifferent conditiQns. The errorrates obtained for the nonnalcase have been taken as a crlterionto compare the other caseswhere some departures from theunderlyıing assumptions.Taking two poission distributionwitth the' parametres L = 2'and L = 3, the departures from'the nonnal1ty were considered.'57Taking the samples of 5 groups,each with sample sizes of 3 and7, type i error rates were estimatedaccording to various errorrate cri:teria. With the departuresfrom the nQrmality the errorrates of the Duncan, SNK, andTukey's niethods were mareased.Th1s prıaotically arises when thesample sizes are smaIl.Effeots of the heterogeneityof the variances were also mvestigatedfor various combinamonsof the group variançes. On eachsampling, 4 and 5 groups ea'.chhaving 3 and 7 observations wereohosen, Applying the analysis ofv:ariance and the multiple 'comparisontests, type i error rateswere calculated it has been revealedthat high heterogeneity ofvariance ended up with the increaseof type T error mates ofmultiple comparison tests exceptL.S.D.. In the case of low heterogeneity,however, did not proveaccordingly giying slightly decreasingerror rates.

OZETÇoklu karşılaştırma testlerinde,n en fazla kullanılan LSD,Duncan, SNK ve Tukey testlerinin teorik özelliklerJ mc'elenerektemel fıa.raziyelerdeki aksamaların bu testleri nasıl etkileyeceğiincelenmiştir. Simulasyon teknikleriyle teşkil tadilen .de&middot;nemeler yeter sayıda1ekrarlanarak teıst!erin h:a.ta seviyeleri değişik'populasyonlarve örnek genişlikleri ,esas alınarak tesbitedilmiştir. Normal şartlar için beklenen hata seviyeleri normaldağıliş ve homojen varyans faraziyelerininbozulduğu çeşitlidurumlarda ortaya çıkan hata seviyeleriyle karşılaştırılarakhangi testlerin ne ölçüde etkilendiği incelenmiştir. Böylece,testlerin sağlamlık yönünden genel ve birbirlerine katşı durumlarıortaya konmuştur.SUMMARYA Researoh on the Effects of Nonnormality and Variance Heterogeneity on the, Structure of Multiple Comparison Tests.When tıhe fixed model is u-sed,the aim of the analysis of varianceis to determine the differencesbetween the pQpulation means.As the F, test used for generalnulI hypotıheses is not sufficient,the analysis of variance has got. to be completed by the multiplecomparison tests. in order todetect tıhe differences among thepopulation means, 'some parametricand non parametric test procedureshave been developed. Inthis researah some properties ofthe parametric tests, s'llchas L.s.d., Duncan, SNK and Tukey, wereinvestigated by using sampiingexperiments.Multiple comparison testsare the main coİnponents of theanalysis of variance. For this rea~son, the validity of the comparisonsdepends on the accuracy ofthe knowledge thaıt is essentialfor the analysis of variance. Therefore the assuımptioll's,of theaınalysiş of vaPİance can also 1?e.extended for the multiple compariısontests. The oecurance ofsome departures from the underlyingassu,mptions invıalidates themultiple compadsçm tests as theF tests, and causes wrong decisions.The error rate and theoreti&middot;cal s;tıruoture of multiple comparisıonprocedures are 'different/from eamother. Therefore : :tJlıelevels of type i and type 11 errOrsand their powers are not theSMTle. Because of the differencesin tıhe error rates, the decisionsand the results obtained by theuse of these tests are different.In tlüs researc,h the sampling.experiments obtained by usingMonte-Car1o methods. The errorrates of the multiple comparison'te9ts were investigated nderdifferent conditiQns. The errorrates obtained for the nonnalcase have been taken as a crlterionto compare the other caseswhere some departures from theunderlyıing assumptions.Taking two poission distributionwitth the' parametres L = 2'and L = 3, the departures from'the nonnal1ty were considered.'57Taking the samples of 5 groups,each with sample sizes of 3 and7, type i error rates were estimatedaccording to various errorrate cri:teria. With the departuresfrom the nQrmality the errorrates of the Duncan, SNK, andTukey's niethods were mareased.Th1s prıaotically arises when thesample sizes are smaIl.Effeots of the heterogeneityof the variances were also mvestigatedfor various combinamonsof the group variançes. On eachsampling, 4 and 5 groups ea'.chhaving 3 and 7 observations wereohosen, Applying the analysis ofv:ariance and the multiple 'comparisontests, type i error rateswere calculated it has been revealedthat high heterogeneity ofvariance ended up with the increaseof type T error mates ofmultiple comparison tests exceptL.S.D.. In the case of low heterogeneity,however, did not proveaccordingly giying slightly decreasingerror rates.