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Über dieses Buch

This textbook presents the basic concepts of linear models, design and analysis of experiments. With the rigorous treatment of topics and provision of detailed proofs, this book aims at bridging the gap between basic and advanced topics of the subject. Initial chapters of the book explain linear estimation in linear models and testing of linear hypotheses, and the later chapters apply this theory to the analysis of specific models in designing statistical experiments.

The book includes topics on the basic theory of linear models covering estimability, criteria for estimability, Gauss–Markov theorem, confidence interval estimation, linear hypotheses and likelihood ratio tests, the general theory of analysis of general block designs, complete and incomplete block designs, general row column designs with Latin square design and Youden square design as particular cases, symmetric factorial experiments, missing plot technique, analyses of covariance models, split plot and split block designs. Every chapter has examples to illustrate the theoretical results and exercises complementing the topics discussed. R codes are provided at the end of every chapter for at least one illustrative example from the chapter enabling readers to write similar codes for other examples and exercise.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Linear Estimation

Abstract
In many modeling problems, a response variable is modeled as a function of one or more independent or explanatory variables. The linear function of the explanatory variables along with a random error term has been found useful and applicable to many problems, for example, the weight of a newborn human baby as a function of the circumference of her head or shoulder, the price of crude oil as a function of currency exchange rates, the length of elongation of a weighing spring as a function of the loaded weight, and whatnot. Many such and similar problems are modeled using a linear model.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 2. Linear Hypotheses and their Tests

Abstract
The two important statistical aspects of modeling are estimation and testing of statistical hypotheses. As a sequel to the previous chapter on linear estimation, questions such as what the statistical hypotheses that can be tested in a linear model are and what the test procedures are, naturally arise. This chapter answers such questions, for example, comparison of two or more treatments/methods occurs often in real-life problems such as comparing the effect of two or more drugs for curing a particular medical condition, comparing two or more diets on the performance of athletes/sportspersons in a particular sporting event, comparing two or more training methods, and whatnot.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 3. Block Designs

Abstract
The theory of linear estimation and linear hypotheses developed in the first two chapters will be applied to specific designs in this and later chapters. We start with a discussion on general block designs in this chapter which includes both complete and incomplete block designs. If an experimenter is able to get plots which are homogeneous with respect to the yield of interest, then the CRD model discussed in Examples 1.​2.​13 and 2.​3.​7 can be used. For example, if several teaching methods have to be compared for their efficacy, then one may choose students of a particular age group who have almost similar abilities as evident from almost identical scores in a test given to them. For sub-groups of such homogeneous students, the different teaching methods to be compared can be administered. If such homogeneous plots are not available for an experiment, but a number of groups of plots are available such that the plots within a group are homogeneous but plots across groups are not, then one can go for models associated with block designs, which is the subject matter of this chapter. In many situations, homogeneous plots are not available for experimenters and block designs are very useful models in such situations. After discussing linear estimation in general block designs, testing of standard omnibus hypotheses in general block designs is discussed. The theory of general block designs is then applied to the study of randomized block design, balanced incomplete block design, and partially balanced incomplete block design.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 4. Row-Column Designs

Abstract
Row-column designs are plots arranged in arrays wherein plots in any row are homogeneous with respect to the yield under study, and plots across rows are not, and plots in any column are homogeneous with respect to the yield under study, and plots across columns are not. Including Sudoku, which is a special type of Latin square design, there are a number of applications of such designs. Apart from Latin square design, Youden square design is the other row-column design which has many applications.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 5. Factorial Experiments

Abstract
In any statistical experiment, if the number of factors affecting the yield under study is large, then standard designs cannot be used due to the nonavailability of a large number of homogeneous plots. Such situations warrant the study of factorial experiments, which can accommodate a large number of factors influencing the yield.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 6. Analysis of Covariance

Abstract
In many experiments, for each experimental unit, we may have observations on one or more supplementary variables in addition to the yield. These variables are called concomitant variables. If the concomitant variables are unrelated to treatments and influence the yield, the variation in yield caused by them should be eliminated before comparing treatments. A technique of analysis which eliminates the variation in yield due to these concomitant variables is known as Analysis of Covariance. Let us look at some examples.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 7. Missing Plot Technique

Abstract
In many statistical experiments, observations from one or more plots, possibly, are not reported, due to human or other nonassignable errors. In such instances, there is a need to find a substitution for a missing observation. It may be noted that if the observations in an experiment employing standard designs are missing, then the readily available analyses are not applicable to such data.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Chapter 8. Split-Plot and Split-Block Designs

Abstract
Split-plot and Split-block designs belong to a class of designs in which the inter-block information is utilized fully. These designs arose from agricultural experiments where there is a necessity to consider plots of different sizes, as plots of comparable sizes may not be available. In such experiments, plots of small sizes are infeasible to experiment with a factor like irrigation, but small plots are suitable to experiment with a factor like fertilizer.
N. R. Mohan Madhyastha, S. Ravi, A. S. Praveena

Backmatter

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