About the Book
The book is meant for a wide-spectrum of readership-empirical scientists, consultants, technocrats, advertisers, researchers and students learning Data Science for conducting small replicated or non-replicated experiments / demonstrations.
It deals with two-factor three-level designs to be conducted only in six experimental units. For this an exhaustive set of 9c6=9c3 = 84 designs have been generated. Least Square algorithm has been applied for estimating separate effect of each component and their interaction along with fitting of response surface; meeting both the objectives for any factorial experiment. Of them seventy-six could be found as valid or estimable designs and the rest as non-estimable ones. Value of the determinant obtained for Least Square Matrix for each such design has been the indicator of its D-optimality status: the same could also be obtained from geometric structure of the designs.
Such exhaustive search ascertains (8+4) D-optimal designs; of them only (1+3) are hitherto known. Also, rotatable feature of any such design does not affect its D-optimality status.
A simple method SAME has been devised to meet the said twin objectives, thus escaping matrix formation and related operations.
Each such design could be combined to form pair of replicates or blocks of an experiment so as to fetch statistical significance test based on ANOVA and fitting the response surface.
About the Author
N. C. Das is former Professor-cum-Chief Scientist at the Department of Statistics and Computer Science, Birsa Agricultural University, Ranchi, India. He has over six decades of teaching- and research-experience in the field of Statistical Inference, Design of Experiments, Operations Research and Computer Science. These are now essential components of Data Science.
He intensively devoted his time in advising and guiding a wide-spectrum of students, doctoral-and postdoctoral-scholars and research specialists from various institutions, corporate organizations, core-sector industrial outfits and various consulting bodies on statistical aspects of research problems.
He, as a Research Fellow of the International Development Agency at I.I.T. Kharagpur, had developed software BIVNOR which was required to be applied in successfully solving long aspired and awaited problem of “Bivariate Joint Chance-Constrained Programming Problem”. Later it was found to be of much wider use which culminated in publication of his monograph entitled “Decision Processes by Using Bivariate Normal Quantile Pairs” by Springer (2015). The said text also offers high probability joint confidence intervals to the much aspired measure (MAM) of Higgs Boson’s particle, popularly called God particle, in case BEC (the magnitude of Bose-Einstein Correlation) is made available. He also established recurrence relation to get backward Markov Chain for 2×2 stochastic matrix and developed his software library for most of the basic computations required for Data Science.
He remained Academic Secretary-cum-Editor of the Bihar Journal of Mathematics during 1994-1998 and is currently President, Jharkhand Society of Mathematical Sciences.
During his career in the State Government and in Agriculture University he remained deeply associated with Adaptive Trials in Farmers’ Fields. It was here that he felt the requirement of “Saturated Experimental Designs” for large-scale smaller Upgraded Technology Trials (UTT) to be conducted in small and marginal farmers’ fields. It is found beneficially applicable to corporate industrial sectors with interest in Product and Process Research (PaPR) with Minimal Designs. The same has culminated into publication of the present text. The same may prove to be major operational tool in the hands Data Scientists to delve into vast Field of Experimental World (FEW).