论文信息 - A RANDOMIZATION PROBLEM IN FORMING DESIGNS WITH SUPERIMPOSED TREATMENTS1

A RANDOMIZATION PROBLEM IN FORMING DESIGNS WITH SUPERIMPOSED TREATMENTS1

Some programmes of experimentation require the superimposition of a new set of treatments on an existing experiment. Randomization of such treatments has received little attention in the literature but merits careful consideration. The present paper examines two apparently different theoretical approaches, one in effect randomizing the experiments together and the other randomizing the second experiment without reference to any randomization used in the first. In the simplest superimpositions the two methods give identical results in practice but problems arise when one Latin square is to be superimposed on another.

H. D. Patterson | D. A. Preece | R. A. Bailey | D. Preece

[1] John A. Nelder,et al. The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2] M. Healy,et al. Restricted randomization and quasi-Latin squares , 1950 .

[3] The formation of Latin squares for use in field experiments , 1933 .

[4] G. H. Freeman. The Use of the Same Experimental Material for More than One Set of Treatments , 1959 .

[5] Restricted randomization for blocks of sixteen plots , 1964, The Journal of Agricultural Science.

[6] G. H. Freeman,et al. Some Considerations in the Design of Successive Experiments in Fruit Plantations , 1954 .

[7] S. C. Pearce,et al. The changing of treatments in a long-term trial , 1948, The Journal of Agricultural Science.

[8] John A. Nelder,et al. The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.