ORPP logo
Image from Google Jackets

Advanced Analysis of Variance.

By: Material type: TextTextSeries: Wiley Series in Probability and Statistics SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2017Copyright date: ©2017Edition: 1st edDescription: 1 online resource (435 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781119303343
Subject(s): Genre/Form: Additional physical formats: Print version:: Advanced Analysis of VarianceDDC classification:
  • 519.538
LOC classification:
  • QA279.H57 2017
Online resources:
Contents:
Intro -- Title Page -- Copyright Page -- Contents -- Preface -- Notation and Abbreviations -- Chapter 1 Introduction to Design and Analysis of Experiments -- 1.1 Why Simultaneous Experiments? -- 1.2 Interaction Effects -- 1.3 Choice of Factors and Their Levels -- 1.4 Classification of Factors -- 1.5 Fixed or Random Effects Model? -- 1.6 Fisher´s Three Principles of Experiments vs. Noise Factor -- 1.7 Generalized Interaction -- 1.8 Immanent Problems in the Analysis of Interaction Effects -- 1.9 Classification of Factors in the Analysis of Interaction Effects -- 1.10 Pseudo Interaction Effects (Simpson´s Paradox) in Categorical Data -- 1.11 Upper Bias by Statistical Optimization -- 1.12 Stage of Experiments: Exploratory, Explanatory or Confirmatory? -- References -- Chapter 2 Basic Estimation Theory -- 2.1 Best Linear Unbiased Estimator -- 2.2 General Minimum Variance Unbiased Estimator -- 2.3 Efficiency of Unbiased Estimator -- 2.4 Linear Model -- 2.5 Least Squares Method -- 2.5.1 LS method and BLUE -- 2.5.2 Estimation space and error space -- 2.5.3 Linear constraints on parameters for solving the normal equation -- 2.5.4 Generalized inverse of a matrix -- 2.5.5 Distribution theory of the LS estimator -- 2.6 Maximum Likelihood Estimator -- 2.7 Sufficient Statistics -- References -- Chapter 3 Basic Test Theory -- 3.1 Normal Mean -- 3.1.1 Setting a null hypothesis and a rejection region -- 3.1.2 Power function -- 3.1.3 Sample size determination -- 3.1.4 Nuisance parameter -- 3.1.5 Non-parametric test for median -- 3.2 Normal Variance -- 3.2.1 Setting a null hypothesis and a rejection region -- 3.2.2 Power function -- 3.3 Confidence Interval -- 3.3.1 Normal mean -- 3.3.2 Normal variance -- 3.4 Test Theory in the Linear Model -- 3.4.1 Construction of F-test -- 3.4.2 Optimality of F-test -- 3.5 Likelihood Ratio Test and Efficient Score Test.
3.5.1 Likelihood ratio test -- 3.5.2 Test based on the efficient score -- 3.5.3 Composite hypothesis -- References -- Chapter 4 Multiple Decision Processes and an Accompanying Confidence Region -- 4.1 Introduction -- 4.2 Determining the Sign of a Normal Mean - Unification of One- and Two-Sided Tests -- 4.3 An Improved Confidence Region -- Reference -- Chapter 5 Two-Sample Problem -- 5.1 Normal Theory -- 5.1.1 Comparison of normal means assuming equal variances -- 5.1.2 Remark on the unequal variances -- 5.1.3 Paired sample -- 5.1.4 Comparison of normal variances -- 5.2 Non-parametric Tests -- 5.2.1 Permutation test -- 5.2.2 Rank sum test -- 5.2.3 Methods for ordered categorical data -- 5.3 Unifying Approach to Non-inferiority, Equivalence and Superiority Tests -- 5.3.1 Introduction -- 5.3.2 Unifying approach via multiple decision processes -- 5.3.3 Extension to the binomial distribution model -- 5.3.4 Extension to the stratified data analysis -- 5.3.5 Meaning of non-inferiority test and a rationale of switching to superiority test -- 5.3.6 Bio-equivalence -- 5.3.7 Concluding remarks -- References -- Chapter 6 One-Way Layout, Normal Model -- 6.1 Analysis of Variance (Overall F-Test) -- 6.2 Testing the Equality of Variances -- 6.2.1 Likelihood ratio test (Bartlett´s test) -- 6.2.2 Hartley´s test -- 6.2.3 Cochran´s test -- 6.3 Linear Score Test (Non-parametric Test) -- 6.4 Multiple Comparisons -- 6.4.1 Introduction -- 6.4.2 Multiple comparison procedures for some given structures of sub-hypotheses -- 6.4.3 General approach without any particular structure of sub-hypotheses -- 6.4.4 Closed test procedure -- 6.5 Directional Tests -- 6.5.1 Introduction -- 6.5.2 General theory for unifying approach to shape and change-point hypotheses -- 6.5.3 Monotone and step change-point hypotheses -- 6.5.4 Convexity and slope change-point hypotheses.
6.5.5 Sigmoid and inflection point hypotheses -- 6.5.6 Discussion -- References -- Chapter 7 One-Way Layout, Binomial Populations -- 7.1 Introduction -- 7.2 Multiple Comparisons -- 7.3 Directional Tests -- 7.3.1 Monotone and step change-point hypotheses -- 7.3.2 Maximal contrast test for convexity and slope change-point hypotheses -- 7.3.3 Cumulative chi-squared test for convexity hypothesis -- 7.3.4 Power comparisons -- 7.3.5 Maximal contrast test for sigmoid and inflection point hypotheses -- References -- Chapter 8 Poisson Process -- 8.1 Max acc. t1 for the Monotone and Step Change-Point Hypotheses -- 8.1.1 Max acc. t1 statistic in the Poisson sequence -- 8.1.2 Distribution function of max acc. t1 under the null model -- 8.1.3 Max acc. t1 under step change-point model -- 8.2 Max acc. t2 for the Convex and Slope Change-Point Hypotheses -- 8.2.1 Max acc. t2 statistic in the Poisson sequence -- 8.2.2 Max acc. t2 under slope change-point model -- References -- Chapter 9 Block Experiments -- 9.1 Complete Randomized Blocks -- 9.2 Balanced Incomplete Blocks -- 9.3 Non-parametric Method in Block Experiments -- 9.3.1 Complete randomized blocks -- 9.3.2 Incomplete randomized blocks with block size two -- References -- Chapter 10 Two-Way Layout, Normal Model -- 10.1 Introduction -- 10.2 Overall ANOVA of Two-Way Data -- 10.3 Row-wise Multiple Comparisons -- 10.3.1 Introduction -- 10.3.2 Interaction elements -- 10.3.3 Simultaneous test procedure for obtaining a block interaction model -- 10.3.4 Constructing a block interaction model -- 10.3.5 Applications -- 10.3.6 Discussion on testing the interaction effects under no replicated observation -- 10.4 Directional Inference -- 10.4.1 Ordered rows or columns -- 10.4.2 Ordered rows and columns -- 10.5 Easy Method for Unbalanced Data -- 10.5.1 Introduction -- 10.5.2 Sum of squares based on cell means.
10.5.3 Testing the null hypothesis of interaction -- 10.5.4 Testing the null hypothesis of main effects under Hαβ -- 10.5.5 Accuracy of approximation by easy method -- 10.5.6 Simulation -- 10.5.7 Comparison with the LS method on real data -- 10.5.8 Estimation of the mean μij -- References -- Chapter 11 Analysis of Two-Way Categorical Data -- 11.1 Introduction -- 11.2 Overall Goodness-of-Fit Chi-Square -- 11.3 Row-wise Multiple Comparisons -- 11.3.1 Chi-squared distances among rows -- 11.3.2 Reference distribution for simultaneous inference in clustering rows -- 11.3.3 Clustering algorithm and a stopping rule -- 11.4 Directional Inference in the Case of Natural Ordering Only in Columns -- 11.4.1 Overall analysis -- 11.4.2 Row-wise multiple comparisons -- 11.4.3 Multiple comparisons of ordered columns -- 11.4.4 Re-analysis of Table taking natural ordering into consideration -- 11.5 Analysis of Ordered Rows and Columns -- 11.5.1 Overall analysis -- 11.5.2 Comparing rows -- References -- Chapter 12 Mixed and Random Effects Model -- 12.1 One-Way Random Effects Model -- 12.1.1 Model and parameters -- 12.1.2 Standard form for test and estimation -- 12.1.3 Problems of negative estimators of variance components -- 12.1.4 Testing homogeneity of treatment effects -- 12.1.5 Between and within variance ratio (SN ratio) -- 12.2 Two-Way Random Effects Model -- 12.2.1 Model and parameters -- 12.2.2 Standard form for test and estimation -- 12.2.3 Testing homogeneity of treatment effects -- 12.2.4 Easy method for unbalanced two-way random effects model -- 12.3 Two-Way Mixed Effects Model -- 12.3.1 Model and parameters -- 12.3.2 Standard form for test and estimation -- 12.3.3 Null hypothesis Hαβ of interaction and the test statistic -- 12.3.4 Testing main effects under the null hypothesis Hαβ -- 12.3.5 Testing main effects Hβ when the null hypothesis Hαβ fails.
12.3.6 Exact test of Hβ when the null hypothesis Hαβ fails -- 12.4 General Linear Mixed Effects Model -- 12.4.1 Gaussian linear mixed effects model -- 12.4.2 Estimation of parameters -- 12.4.3 Estimation of random effects (BLUP) -- References -- Chapter 13 Profile Analysis of Repeated Measurements -- 13.1 Comparing Treatments Based on Upward or Downward Profiles -- 13.1.1 Introduction -- 13.1.2 Popular approaches -- 13.1.3 Statistical model and approach -- 13.2 Profile Analysis of 24-Hour Measurements of Blood Pressure -- 13.2.1 Introduction -- 13.2.2 Data set and classical approach -- 13.2.3 Statistical model and new approach -- References -- Chapter 14 Analysis of Three-Way Categorical Data -- 14.1 Analysis of Three-Way Response Data -- 14.1.1 General theory -- 14.1.2 Cumulative chi-squared statistics for the ordered categorical responses -- 14.2 One-Way Experiment with Two-Way Categorical Responses -- 14.2.1 General theory -- 14.2.2 Applications -- 14.3 Two-Way Experiment with One-Way Categorical Responses -- 14.3.1 General theory -- 14.3.2 Applications -- References -- Chapter 15 Design and Analysis of Experiments by Orthogonal Arrays -- 15.1 Experiments by Orthogonal Array -- 15.1.1 Orthogonal array -- 15.1.2 Planning experiments by interaction diagram -- 15.1.3 Analysis of experiments from an orthogonal array -- 15.2 Ordered Categorical Responses in a Highly Fractional Experiment -- 15.3 Optimality of an Orthogonal Array -- References -- Appendix -- Index -- EULA.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
No physical items for this record

Intro -- Title Page -- Copyright Page -- Contents -- Preface -- Notation and Abbreviations -- Chapter 1 Introduction to Design and Analysis of Experiments -- 1.1 Why Simultaneous Experiments? -- 1.2 Interaction Effects -- 1.3 Choice of Factors and Their Levels -- 1.4 Classification of Factors -- 1.5 Fixed or Random Effects Model? -- 1.6 Fisher´s Three Principles of Experiments vs. Noise Factor -- 1.7 Generalized Interaction -- 1.8 Immanent Problems in the Analysis of Interaction Effects -- 1.9 Classification of Factors in the Analysis of Interaction Effects -- 1.10 Pseudo Interaction Effects (Simpson´s Paradox) in Categorical Data -- 1.11 Upper Bias by Statistical Optimization -- 1.12 Stage of Experiments: Exploratory, Explanatory or Confirmatory? -- References -- Chapter 2 Basic Estimation Theory -- 2.1 Best Linear Unbiased Estimator -- 2.2 General Minimum Variance Unbiased Estimator -- 2.3 Efficiency of Unbiased Estimator -- 2.4 Linear Model -- 2.5 Least Squares Method -- 2.5.1 LS method and BLUE -- 2.5.2 Estimation space and error space -- 2.5.3 Linear constraints on parameters for solving the normal equation -- 2.5.4 Generalized inverse of a matrix -- 2.5.5 Distribution theory of the LS estimator -- 2.6 Maximum Likelihood Estimator -- 2.7 Sufficient Statistics -- References -- Chapter 3 Basic Test Theory -- 3.1 Normal Mean -- 3.1.1 Setting a null hypothesis and a rejection region -- 3.1.2 Power function -- 3.1.3 Sample size determination -- 3.1.4 Nuisance parameter -- 3.1.5 Non-parametric test for median -- 3.2 Normal Variance -- 3.2.1 Setting a null hypothesis and a rejection region -- 3.2.2 Power function -- 3.3 Confidence Interval -- 3.3.1 Normal mean -- 3.3.2 Normal variance -- 3.4 Test Theory in the Linear Model -- 3.4.1 Construction of F-test -- 3.4.2 Optimality of F-test -- 3.5 Likelihood Ratio Test and Efficient Score Test.

3.5.1 Likelihood ratio test -- 3.5.2 Test based on the efficient score -- 3.5.3 Composite hypothesis -- References -- Chapter 4 Multiple Decision Processes and an Accompanying Confidence Region -- 4.1 Introduction -- 4.2 Determining the Sign of a Normal Mean - Unification of One- and Two-Sided Tests -- 4.3 An Improved Confidence Region -- Reference -- Chapter 5 Two-Sample Problem -- 5.1 Normal Theory -- 5.1.1 Comparison of normal means assuming equal variances -- 5.1.2 Remark on the unequal variances -- 5.1.3 Paired sample -- 5.1.4 Comparison of normal variances -- 5.2 Non-parametric Tests -- 5.2.1 Permutation test -- 5.2.2 Rank sum test -- 5.2.3 Methods for ordered categorical data -- 5.3 Unifying Approach to Non-inferiority, Equivalence and Superiority Tests -- 5.3.1 Introduction -- 5.3.2 Unifying approach via multiple decision processes -- 5.3.3 Extension to the binomial distribution model -- 5.3.4 Extension to the stratified data analysis -- 5.3.5 Meaning of non-inferiority test and a rationale of switching to superiority test -- 5.3.6 Bio-equivalence -- 5.3.7 Concluding remarks -- References -- Chapter 6 One-Way Layout, Normal Model -- 6.1 Analysis of Variance (Overall F-Test) -- 6.2 Testing the Equality of Variances -- 6.2.1 Likelihood ratio test (Bartlett´s test) -- 6.2.2 Hartley´s test -- 6.2.3 Cochran´s test -- 6.3 Linear Score Test (Non-parametric Test) -- 6.4 Multiple Comparisons -- 6.4.1 Introduction -- 6.4.2 Multiple comparison procedures for some given structures of sub-hypotheses -- 6.4.3 General approach without any particular structure of sub-hypotheses -- 6.4.4 Closed test procedure -- 6.5 Directional Tests -- 6.5.1 Introduction -- 6.5.2 General theory for unifying approach to shape and change-point hypotheses -- 6.5.3 Monotone and step change-point hypotheses -- 6.5.4 Convexity and slope change-point hypotheses.

6.5.5 Sigmoid and inflection point hypotheses -- 6.5.6 Discussion -- References -- Chapter 7 One-Way Layout, Binomial Populations -- 7.1 Introduction -- 7.2 Multiple Comparisons -- 7.3 Directional Tests -- 7.3.1 Monotone and step change-point hypotheses -- 7.3.2 Maximal contrast test for convexity and slope change-point hypotheses -- 7.3.3 Cumulative chi-squared test for convexity hypothesis -- 7.3.4 Power comparisons -- 7.3.5 Maximal contrast test for sigmoid and inflection point hypotheses -- References -- Chapter 8 Poisson Process -- 8.1 Max acc. t1 for the Monotone and Step Change-Point Hypotheses -- 8.1.1 Max acc. t1 statistic in the Poisson sequence -- 8.1.2 Distribution function of max acc. t1 under the null model -- 8.1.3 Max acc. t1 under step change-point model -- 8.2 Max acc. t2 for the Convex and Slope Change-Point Hypotheses -- 8.2.1 Max acc. t2 statistic in the Poisson sequence -- 8.2.2 Max acc. t2 under slope change-point model -- References -- Chapter 9 Block Experiments -- 9.1 Complete Randomized Blocks -- 9.2 Balanced Incomplete Blocks -- 9.3 Non-parametric Method in Block Experiments -- 9.3.1 Complete randomized blocks -- 9.3.2 Incomplete randomized blocks with block size two -- References -- Chapter 10 Two-Way Layout, Normal Model -- 10.1 Introduction -- 10.2 Overall ANOVA of Two-Way Data -- 10.3 Row-wise Multiple Comparisons -- 10.3.1 Introduction -- 10.3.2 Interaction elements -- 10.3.3 Simultaneous test procedure for obtaining a block interaction model -- 10.3.4 Constructing a block interaction model -- 10.3.5 Applications -- 10.3.6 Discussion on testing the interaction effects under no replicated observation -- 10.4 Directional Inference -- 10.4.1 Ordered rows or columns -- 10.4.2 Ordered rows and columns -- 10.5 Easy Method for Unbalanced Data -- 10.5.1 Introduction -- 10.5.2 Sum of squares based on cell means.

10.5.3 Testing the null hypothesis of interaction -- 10.5.4 Testing the null hypothesis of main effects under Hαβ -- 10.5.5 Accuracy of approximation by easy method -- 10.5.6 Simulation -- 10.5.7 Comparison with the LS method on real data -- 10.5.8 Estimation of the mean μij -- References -- Chapter 11 Analysis of Two-Way Categorical Data -- 11.1 Introduction -- 11.2 Overall Goodness-of-Fit Chi-Square -- 11.3 Row-wise Multiple Comparisons -- 11.3.1 Chi-squared distances among rows -- 11.3.2 Reference distribution for simultaneous inference in clustering rows -- 11.3.3 Clustering algorithm and a stopping rule -- 11.4 Directional Inference in the Case of Natural Ordering Only in Columns -- 11.4.1 Overall analysis -- 11.4.2 Row-wise multiple comparisons -- 11.4.3 Multiple comparisons of ordered columns -- 11.4.4 Re-analysis of Table taking natural ordering into consideration -- 11.5 Analysis of Ordered Rows and Columns -- 11.5.1 Overall analysis -- 11.5.2 Comparing rows -- References -- Chapter 12 Mixed and Random Effects Model -- 12.1 One-Way Random Effects Model -- 12.1.1 Model and parameters -- 12.1.2 Standard form for test and estimation -- 12.1.3 Problems of negative estimators of variance components -- 12.1.4 Testing homogeneity of treatment effects -- 12.1.5 Between and within variance ratio (SN ratio) -- 12.2 Two-Way Random Effects Model -- 12.2.1 Model and parameters -- 12.2.2 Standard form for test and estimation -- 12.2.3 Testing homogeneity of treatment effects -- 12.2.4 Easy method for unbalanced two-way random effects model -- 12.3 Two-Way Mixed Effects Model -- 12.3.1 Model and parameters -- 12.3.2 Standard form for test and estimation -- 12.3.3 Null hypothesis Hαβ of interaction and the test statistic -- 12.3.4 Testing main effects under the null hypothesis Hαβ -- 12.3.5 Testing main effects Hβ when the null hypothesis Hαβ fails.

12.3.6 Exact test of Hβ when the null hypothesis Hαβ fails -- 12.4 General Linear Mixed Effects Model -- 12.4.1 Gaussian linear mixed effects model -- 12.4.2 Estimation of parameters -- 12.4.3 Estimation of random effects (BLUP) -- References -- Chapter 13 Profile Analysis of Repeated Measurements -- 13.1 Comparing Treatments Based on Upward or Downward Profiles -- 13.1.1 Introduction -- 13.1.2 Popular approaches -- 13.1.3 Statistical model and approach -- 13.2 Profile Analysis of 24-Hour Measurements of Blood Pressure -- 13.2.1 Introduction -- 13.2.2 Data set and classical approach -- 13.2.3 Statistical model and new approach -- References -- Chapter 14 Analysis of Three-Way Categorical Data -- 14.1 Analysis of Three-Way Response Data -- 14.1.1 General theory -- 14.1.2 Cumulative chi-squared statistics for the ordered categorical responses -- 14.2 One-Way Experiment with Two-Way Categorical Responses -- 14.2.1 General theory -- 14.2.2 Applications -- 14.3 Two-Way Experiment with One-Way Categorical Responses -- 14.3.1 General theory -- 14.3.2 Applications -- References -- Chapter 15 Design and Analysis of Experiments by Orthogonal Arrays -- 15.1 Experiments by Orthogonal Array -- 15.1.1 Orthogonal array -- 15.1.2 Planning experiments by interaction diagram -- 15.1.3 Analysis of experiments from an orthogonal array -- 15.2 Ordered Categorical Responses in a Highly Fractional Experiment -- 15.3 Optimality of an Orthogonal Array -- References -- Appendix -- Index -- EULA.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.

© 2024 Resource Centre. All rights reserved.