Efficient Design of Experiments for Quality Agricultural Research : Part II

Abstract

In agricultural experiments, generally data on more than one character is observed. The experiments, where corresponding to the application of a treatment, more than one response variables are recorded, are known as multi-response experiments. Analytical procedures of analysis of data from multi-response experiments conducted using block designs have been developed. A method based on Euclidean distance and J-plot has also been developed for identification of the best treatment. To tackle the problem of outlier(s) in multi-response experiments, a test statistic has been developed for identification of a single outlier observation vector in complete multi-response experiments run in a block design. A catalogue of block designs with minimally connected designs with 4, 5, 6, 7 or 8 extra observations has been prepared alongwith lower bounds to A- and D- efficiencies and block contents. Extended Group Divisible (EGD) designs for three factors that permit the estimation of all main effects with no loss of information were obtained using self-complementary GD designs with replication number less than 6 and block size less than 11. A catalogue of such designs along with efficiencies for main effects and interactions was prepared. These designs are useful for crop sequence experiments. Results on non-existence of NPBIB designs based on group divisible designs has been obtained. Methods of construction of NPBIB designs based on Latin Square association scheme and Rectangular association scheme have been obtained and catalogued. Nested block designs for nearest neighbour correlation structure within sub-blocks of a block in a nested block design set up and for zero correlation structure in bigger blocks ignoring the sub-block classification were obtained. Analytical techniques based on mixed effects models and biplots have been developed for analysis of data generated from Farmers’ participatory research trials for Resource Conservation Technologies conducted by the Rice-Wheat Consortium (RWC) for Indo-Gangetic Plains. Doubly nested partially balanced incomplete block designs have been introduced. Some general methods of construction of doubly nested partially balanced incomplete block designs are obtained using doubly nested balanced incomplete block (DNBIB) designs, nested balanced incomplete block designs and partially balanced incomplete block designs. Robustness of BIB and PBIB [Group Divisible (GD) and Cyclic] designs has been studied under correlated error structure [NN and AR(1)] for a given value of correlation coefficient in terms of A-efficiency. Binary variance balanced block designs have been shown robust in the presence of two outliers. Robust estimation procedure of treatment effects based on Least Median Squares has been developed. Developed a beta version of On-line Software for the generation of Hadamard matrices up to the order 1000. Supersaturated designs for asymmetrical factorial experiments have been obtained using resolvable orthogonal arrays and Hadamard matrices. Some criteria for comparing supersaturated designs for asymmetrical factorial experiments are also given. To disseminate the knowledge available on combinatorial aspects of designs and analytical procedures acquired to scientists engaged in research in the National Agricultural Research System. The advisory services are pursued rigorously. For the benefit of the experimenters and practicing statisticians, Design Resources Server has been strengthened by adding 6574 efficient block designs for making all possible pairwise treatment comparisons.