Selection Procedures for a problem in analysis of Variance PDF Download

Author: Shanti Swarup Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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Book Description
There are many situations in the analysis of variance where an experimenter would like to make comparisons among (and select the 'best' set) the treatments. In this paper we study the problem where the data are based on a completely randomized block design. It is shown that the subset selection approach is a useful method to make appropriate 'identification' among the hypotheses and the selected subset. We propose an optimal selection procedure which controls the error probabilities when all the parameters (treatments) are equal and which maximize the infimum of the probability of a correct selection over some preference parameter space, simultaneously. Some examples are provided to illustrate the optimal subset selection rule and its interpretation in terms of the 'identified' hypotheses. (Author).

Author: Shanti S. Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 20

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Book Description
In most of the practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means (theta sub 1), (theta sub 2), ..., (theta sub k) are not all equal, would by itself usually the insufficient to satisfy the experimenter. In fact his problems would begin at this stage. He may desire to select the 'best' population or a subset of the 'best' populations; he may like to rank the populations in order of 'bestness' or he may like to draw some other inferences about the parameters of interest to him. The authors interest lies in selecting a non-empty subset of the k populations containing the 'best' population as ranked in terms of (theta sub i's).

Author: Ronald Christensen
Publisher: CRC Press
ISBN: 9780412062919
Category : Mathematics
Languages : en
Pages : 608

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Book Description
This text presents a comprehensive treatment of basic statistical methods and their applications. It focuses on the analysis of variance and regression, but also addressing basic ideas in experimental design and count data. The book has four connecting themes: similarity of inferential procedures, balanced one-way analysis of variance, comparison of models, and checking assumptions. Most inferential procedures are based on identifying a scalar parameter of interest, estimating that parameter, obtaining the standard error of the estimate, and identifying the appropriate reference distribution. Given these items, the inferential procedures are identical for various parameters. Balanced one-way analysis of variance has a simple, intuitive interpretation in terms of comparing the sample variance of the group means with the mean of the sample variance for each group. All balanced analysis of variance problems are considered in terms of computing sample variances for various group means. Comparing different models provides a structure for examining both balanced and unbalanced analysis of variance problems and regression problems. Checking assumptions is presented as a crucial part of every statistical analysis. Examples using real data from a wide variety of fields are used to motivate theory. Christensen consistently examines residual plots and presents alternative analyses using different transformation and case deletions. Detailed examination of interactions, three factor analysis of variance, and a split-plot design with four factors are included. The numerous exercises emphasize analysis of real data. Senior undergraduate and graduate students in statistics and graduate students in other disciplines using analysis of variance, design of experiments, or regression analysis will find this book useful.

Author: Shanti S. Gupta
Publisher:
ISBN:
Category :
Languages : en
Pages : 24

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Book Description
In most practical situations to which the analysis of variance tests are applied, they do not supply the information that the experimenter aims at. If, for example, in one-way ANOVA the hypothesis is rejected in actual application of the F-test, the resulting conclusion that the true means theta sub 7 ..., theta sub K are not all equal, would by itself usually be insufficient to satisfy the experimenter. In fact his problems would begin at this stage. The experimenter may desire to select the best population or a subset of the good populations; he may like to rank the populations in order of goodness or he may like to draw some other inferences about the parameters of interest. The extensive literature on selection and ranking procedures depends heavily on the use of independence between populations (block, treatments, etc.) in the analysis of variance. In the present paper, a method was derived to construct locally best (in some sense) selection procedures to select a non empty subset of the k populations containing the best population as ranked in terms of theta sub 1's which control the size of the selected subset and which maximizes the probability of selecting the best. Also considered was the usual selection procedures in one-way ANOVA based on the generalized least squares estimates and apply the method to two-way layout case.

Author: Shanti S. Gupta
Publisher: SIAM
ISBN: 0898715326
Category : Mathematics
Languages : en
Pages : 592

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Book Description
An encyclopaedic coverage of the literature in the area of ranking and selection procedures. It also deals with the estimation of unknown ordered parameters. This book can serve as a text for a graduate topics course in ranking and selection. It is also a valuable reference for researchers and practitioners.

Author: Jean Dickinson Gibbons
Publisher: SIAM
ISBN: 0898714397
Category : Mathematics
Languages : en
Pages : 589

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Book Description
Provides a compendium of applied aspects of ordering and selection procedures.

Author: Victor Chew
Publisher:
ISBN:
Category : Analysis of variance
Languages : en
Pages : 72

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Author: Deng-Yuan Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 78

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Book Description
The report makes some contributions to the subset selection procedures - both for the fixed sample and the sequential case. Chapter 1 deals with some subset selection procedures for binomial populations in terms of the entropy functions, which is different from the usual selection problem in terms of the success probabilities. In Chapter 2, some fixed sample optimal subset selection procedures are discussed for model I and II problems in the analysis of variance in treatments versus control, and a method for constructing some subset selection procedures is derived. Chapter 3 discusses a method for constructing some sequential subset selection procedures and some optimal sequential subset selection procedure in treatments versus control. An upper bound on the expected sample size for Bechhofer-Kiefer-Sobel sequential selection procedure with indifference zone approach is also derived. (Author).

Author: S. Panchapakesan
Publisher: Springer Science & Business Media
ISBN: 1461223083
Category : Mathematics
Languages : en
Pages : 478

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Book Description
Shanti S. Gupta has made pioneering contributions to ranking and selection theory; in particular, to subset selection theory. His list of publications and the numerous citations his publications have received over the last forty years will amply testify to this fact. Besides ranking and selection, his interests include order statistics and reliability theory. The first editor's association with Shanti Gupta goes back to 1965 when he came to Purdue to do his Ph.D. He has the good fortune of being a student, a colleague and a long-standing collaborator of Shanti Gupta. The second editor's association with Shanti Gupta began in 1978 when he started his research in the area of order statistics. During the past twenty years, he has collaborated with Shanti Gupta on several publications. We both feel that our lives have been enriched by our association with him. He has indeed been a friend, philosopher and guide to us.

Author: Patricia F. Moodie
Publisher: CRC Press
ISBN: 0429527039
Category : Mathematics
Languages : en
Pages : 490

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Book Description
Applied Regression and ANOVA Using SAS® has been written specifically for non-statisticians and applied statisticians who are primarily interested in what their data are revealing. Interpretation of results are key throughout this intermediate-level applied statistics book. The authors introduce each method by discussing its characteristic features, reasons for its use, and its underlying assumptions. They then guide readers in applying each method by suggesting a step-by-step approach while providing annotated SAS programs to implement these steps. Those unfamiliar with SAS software will find this book helpful as SAS programming basics are covered in the first chapter. Subsequent chapters give programming details on a need-to-know basis. Experienced as well as entry-level SAS users will find the book useful in applying linear regression and ANOVA methods, as explanations of SAS statements and options chosen for specific methods are provided. Features: •Statistical concepts presented in words without matrix algebra and calculus •Numerous SAS programs, including examples which require minimum programming effort to produce high resolution publication-ready graphics •Practical advice on interpreting results in light of relatively recent views on threshold p-values, multiple testing, simultaneous confidence intervals, confounding adjustment, bootstrapping, and predictor variable selection •Suggestions of alternative approaches when a method’s ideal inference conditions are unreasonable for one’s data This book is invaluable for non-statisticians and applied statisticians who analyze and interpret real-world data. It could be used in a graduate level course for non-statistical disciplines as well as in an applied undergraduate course in statistics or biostatistics.