Designs for Varietal cum Manurial Trials

Abstract

The thesis deals with two main problems. These are (1) obtaining designs which are suitable for factorial cum manorial trials and (2) a method of analysis of such and other asymmetrical designs. So long factorial experimentations and varietal trials have been dealt separately. Since, it has been often found that the varieties selected from a varietal trial conducted at an uniform level of manure lodges at a higher dose of manure, some necessity has been felt to evolve designs through which in addition to selection of varieties some knowledge regarding the interaction between the varieties and manures can also be obtained. The usual designs which are available in literature are not very suitable for this type of experiments excepting that when the number of manorial treatments is small, incompletes’ block designs augmented by associating each variety with a number of treatments, as introduced by Bose and Conor (1952), can be adopted. The designs suitable for varietal cum manurial trials will essentially be some asymmetrical design. As the number of varieties is usually large the usual asymmetrical design where no main effect is affected is not of much help, as very large block size is required for such experimentation. There for attempts have been made to evolve varietal cum manurial designs by combining a b.i.b. design and a factorial design, and thus a series of such design has been obtained. As b.i.b. designs suffer from certain limitations that they are not available for any number of treatments with a reasonable number of replications particularly when block size is small another series of designs has been obtained by combining circular designs introduced by Das (1960) with suitable block size and a factorial design. In the present thesis we have restricted ourselves to the manorial factors each at two levels. The series obtained are based on a factorial design of the form 2n+1 and on (a) circular designs in two plot blocks, the latter design being obtained by developing the initial block 1,2,3,4 mod (v), where, v is the number of varieties and varieties are numbered in natural numbers 1 to v. Kemp Thorne (1952) has given a method of analysis for a particular asymmetrical design. An attempt has been made in the present thesis to give a general method of analysis for the design v x 2n through which besides getting a complete analysis of data it can be easily known whether for any design two affected interactions are estimable mutually independently. An illustration for the above method has also been given.