| Popis: |
The study of the topic of randomisation models in the field of experimental design, was initiated by R.A, Fisher. Many of his contributions to this topic and to the general subject of experimental design are included in his book "The Design of Experiments". The study of efficiencies of experimental designs was first performed by F. Yates, who is acknowledged as the originator of many of the now standard complex designs. This thesis deals with these two topics, when related to classes of incomplete block designs. Chapter I surveys the historical development of randomisation. Special attention is given to studying the development of suitable alternatives to permutation testing, an exact method of hypothesis testing available when a randomisation model has been assumed. This chapter is mainly historical in content. The second chapter contains the randomisation analysis of a balanced incomplete block design with double grouping, a design originated by Robinson (1966). The efficiency of this design is then compared to some standard designs. This chapter is an extension of a paper prepared by Folks and Kempthorne (1960), which deals with the randomisation analysis and resulting efficiencies of a class of incomplete block designs. Graybill and Seshadri (1960) have shown that under the normal model assumptions the combined estimates of treatment contrasts in a balanced incomplete block design are unbiased. This estimate is a weighted estimate of treatment differences based on both inter—block and intra—block information. Chapter III is an extension of the above, to the set of balanced incomplete block designs under the randomisation model. A refinement in the method of proving that the estimate was unbiased, was suggested by my supervisor Mr. J. Robinson. The final chapter discusses the major studies which have been performed in developing suitable methods of hypothesis testing for randomisation models. In particular I have revised the study performed by Ogawa (1963), which shows that the usual F-test based on normality is a suitable approximation to the variance ratio test criterion obtained in a randomised balanced incomplete block design under the Neyman model. Ogawa‘s result is obtained by a more elegant and less stringent approach, using a technique developed by Kumar Mitra (1960). |
