مقابله هاي تيماري در طرح هاي تصادفي مقيد ترتيبي

چكيده انگليسي :

Treatment contrasts in order restricted randomised designs Marziye Rozbahani m rouzbahani@math iut ac ir February 20 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Saeid Pooladsaz spooladsaz@cc iut ac irAdvisor Dr Reyhaneh Rikhtehgaran r rikhtegaran@cc iut ac ir2000 MSC 62K10 62J10 62J05Keywords Contrast parameter ranked set sample subjective ranking judgment post stratified sample rank sum test Abstract In the design of experiments it is necessary to allocate treatments to experimental units in order to find an efficientdesign in which the performance of the design is more than the other designs in the same class and with the samesize Finally the comparisons of the treatments of the efficient design gives more information to the researcher andalso usually when two designs are compared in terms of quality the criterion of superiority is the ability of thatdesign to minimize total variation This means that the design is efficient if it reduces the total variance one of themain principles in design of experiment is to use blocking factors whenever it is possible In many studies blockinginformation is not precisely defined or may be subjective in nature In this thesis order restricted randomized designs ORRD have been used to compare the effects of a randomizedblock factor and also the comparisons are based on the information from a small set of experimental units EUs Using this design we first select a small set of experimental units and then the order of each units specified byordering from smallest to largest based on inherent variation In many studies blocking information is not preciselydefined or may be subjective in nature Hence it is usually discarded in the construction of the design and in theanalysis of a data set By ORR designs a random method is used to assign treatment levels to experimental units ineach block This Thesis uses a special design an order restricted randomized design ORRD which uses availablesubjective information in a small set of experimental units to create a judgment ranked blocking factor Underthe design we then use a randomization scheme to assign the treatment levels to the ranked experimental units Such an assignment with certain restrictions on the randomization scheme which keeps the design to be balanced translates the within set positive dependence structure into a variance reduction technique in the estimation of acontrast parameter Analysis of variance for ORRD can be obtained using two methods test of linear assumptionsand ranked regression of linear models that is necessary to do some reforms on ranked regression before analyzing inorder to estimate the exact parameters In Chapter 1 we provide a review and description of existing designs that are closely related to ORRD in literature We also introduce two designs Design 1 and Design 2 where Design 1 emphasizes all pairwise comparisons andDesign2 emphasizes all possible contrasts We have defined some trivial conceptions in chapter 2 In Chapter 3 themodel is introdued in detail and the asymptotic distribution of the estimator Is developed The ORR design for twotreatments which minimizes the asymptotic variance of the contrast parameters is discussed Also we introduce anadditive model to analyze data of ORRD In chapter 4 we construct consistent estimators for the scale parameterand the covariance matrix and provides empirical evidence to investigate properties of the tests and estimators Alsoin Chapter 4 discusses the simulation results to evaluate the empirical size and power of the tests is discussed Alsowe develop testing procedures for general linear hypotheses Tests include the score drop and Wald tests it is shownthat in general Design 2 is more efficient thas Design 1 under a wide range of judgment ranking information

روزبهاني، مرضيه

مقابله هاي تيماري در طرح هاي تصادفي مقيد ترتيبي

طرح هاي تصادفي مقيد ترتيبي(ORR) , نمونه گيري مجموعه رتبه دار (RSS) , آزمون والد , كارايي نسبي مجانبي , طرح بلوكي كامل , طرح مربع لاتين , مدل خطي تعميم يافته