Analysis of Messy Data : Analysis of Covariance (Analysis of Messy Data) 〈3〉

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Analysis of Messy Data : Analysis of Covariance (Analysis of Messy Data) 〈3〉

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  • 製本 Hardcover:ハードカバー版/ページ数 584 p.
  • 言語 ENG,ENG
  • 商品コード 9781584880837
  • DDC分類 519.5352

基本説明

For Statisticians in biometry, medicine, pharmaceutical applications, quality control, etc.

Full Description


Analysis of covariance is a very useful but often misunderstood methodology for analyzing data where important characteristics of the experimental units are measured but not included as factors in the design. Analysis of Messy Data, Volume 3: Analysis of Covariance takes the unique approach of treating the analysis of covariance problem by looking at a set of regression models, one for each of the treatments or treatment combinations. Using this strategy, analysts can use their knowledge of regression analysis and analysis of variance to help attack the problem. The authors describe the strategy for one- and two-way treatment structures with one and multiple covariates in a completely randomized design structure. They present new methods for comparing models and sets of parameters, including beta-hat models. They carefully investigate the effect of blocking, explore mixed models, and present a new methodology for using covariates to analyze data from nonreplicated experiments.Analysis of covariance provides an invaluable set of strategies for analyzing data. With its careful balance of theory and examples, Analysis of Messy Data: Volume 3 provides a unique and outstanding guide to the strategy's techniques, theory, and application.

Table of Contents

  Introduction to the Analysis of Covariance       1  (10)
Introduction 1 (1)
The Covariate Adjustment Process 1 (6)
A General AOC Model and the Basic Philosophy 7 (4)
References 10 (1)
One-Way Analysis of Covariance---One 11 (30)
Covariate in a Completely Randomized Design
Structure
The Model 11 (1)
Estimation 12 (2)
Strategy for Determining the Form of the 14 (3)
Model
Comparing the Treatments or Regression Lines 17 (8)
Equal Slopes Model 18 (3)
Unequal Slopes Model-Covariate by 21 (4)
Treatment Interaction
Confidence Bands about the Difference of 25 (1)
Two Treatments
Summary of Strategies 25 (1)
Analysis of Covariance Computations via the 26 (12)
SAS® System
Using PROC GLM and PROC MIXED 26 (5)
Using JMP® 31 (7)
Conclusions 38 (3)
References 39 (1)
Exercise 39 (2)
Examples: One-Way Analysis of 41 (52)
Covariance---One Covariate in a Completely
Randomized Design Structure
Introduction 41 (1)
Chocolate Candy---Equal Slopes 41 (13)
Analysis Using PROC GLM 42 (5)
Analysis Using PROC MIXED 47 (3)
Analysis Using JMP® 50 (4)
Exercise Programs and Initial Resting Heart 54 (12)
Rate---Unequal Slopes
Effect of Diet on Cholesterol Level: An 66 (4)
Exception to the Basic Analysis of
Covariance Strategy
Change from Base Line Analysis Using Effect 70 (4)
of Diet on Cholesterol Level Data
Shoe Tread Design Data for Exception to the 74 (4)
Basic Strategy
Equal Slopes within Groups of Treatments 78 (5)
and Unequal Slopes between Groups
Unequal Slopes and Equal Intercepts---Part 1 83 (2)
Unequal Slopes and Equal Intercepts---Part 2 85 (8)
References 90 (1)
Exercises 90 (3)
Multiple Covariates in a One-Way Treatment 93 (30)
Structure in a Completely Randomized Design
Structure
Introduction 93 (1)
The Model 93 (2)
Estimation 95 (1)
Example: Driving A Golf Ball with Different 95 (4)
Shafts
Example: Effect of Herbicides on the Yield 99 (6)
of Soybeans---Three Covariates
Example: Models That Are Quadratic 105(7)
Functions of the Covariate
Example: Comparing Response Surface Models 112(11)
Reference 121(1)
Exercises 121(2)
Two-Way Treatment Structure and Analysis of 123(40)
Covariance in a Completely Randomized Design
Structure
Introduction 123(1)
The Model 123(4)
Using the SAS® System 127(3)
Using PROC GLM and PROC MIXED 128(1)
Using JMP® 129(1)
Example: Average Daily Gains and Birth 130(6)
Weight---Common Slope
Example: Energy from Wood of Different 136(8)
Types of Trees---Some Unequal Slopes
Missing Treatment Combinations 144(3)
Example: Two-Way Treatment Structure with 147(11)
Missing Cells
Extensions 158(5)
Reference 160(1)
Exercises 160(3)
Beta-Hat Models 163(12)
Introduction 163(1)
The Beta-Hat Model and Analysis 163(2)
Testing Equality of Parameters 165(1)
Complex Treatment Structures 166(1)
Example: One-Way Treatment Structure 167(4)
Example: Two-Way Treatment Structure 171(3)
Summary 174(1)
Exercises 174(1)
Variable Selection in the Analysis of 175(14)
Covariance Model
Introduction 175(1)
Procedure for Equal Slopes 175(2)
Example: One-Way Treatment Structure with 177(7)
Equal Slopes Model
Some Theory 184(1)
When Slopes are Possibly Unequal 185(4)
References 186(1)
Exercises 186(3)
Comparing Models for Several Treatments 189(14)
Introduction 189(1)
Testing Equality of Models for a One-Way 190(1)
Treatment Structure
Comparing Models for a Two-Way Treatment 191(2)
Structure
Example: One-Way Treatment Structure with 193(2)
One Covariate
Example: One-Way Treatment Structure with 195(2)
Three Covariates
Example: Two-Way Treatment Structure with 197(3)
One Covariate
Discussion 200(3)
References 201(1)
Exercises 201(2)
Two Treatments in a Randomized Complete Block 203(30)
Design Structure
Introduction 203(1)
Complete Block Designs 203(1)
Within Block Analysis 204(2)
Between Block Analysis 206(1)
Combining Within Block and Between Block 207(2)
Information
Determining the Form of the Model 209(2)
Common Slope Model 211(3)
Comparing the Treatments 214(1)
Equal Slopes Models 215(1)
Unequal Slopes Model 215(1)
Confidence Intervals about Differences of 215(2)
Two Regression Lines
Within Block Analysis 216(1)
Combined Within Block and Between Block 216(1)
Analysis
Computations for Model 9.1 Using the 217(4)
SAS® System
Example: Effect of Drugs on Heart Rate 221(5)
Summary 226(7)
References 231(1)
Exercises 231(2)
More Than Two Treatments in a Blocked Design 233(26)
Structure
Introduction 233(1)
RCB Design Structure---Within and Between 233(1)
Block Information
Incomplete Block Design Structure---Within 234(2)
and Between Block Information
Combining Between Block and Within Block 236(4)
Information
Example: Five Treatments in RCB Design 240(7)
Structure
Example: Balanced Incomplete Block Design 247(4)
Structure with Four Treatments
Example: Balanced Incomplete Block Design 251(3)
Structure with Four Treatments Using
JMP®
Summary 254(5)
References 256(1)
Exercises 256(3)
Covariate Measured on the Block in RCB and 259(28)
Incomplete Block Design Structures
Introduction 259(1)
The Within Block Model 260(1)
The Between Block Model 261(1)
Combining Within Block and Between Block 261(2)
Information
Common Slope Model 263(1)
Adjusted Means and Comparing Treatments 264(1)
Common Slope Model 264(1)
Non--Parallel Lines Model 264(1)
Example: Two Treatments 265(4)
Example: Four Treatments in RCB 269(8)
Example: Four Treatments in BIB 277(5)
Summary 282(5)
References 284(1)
Exercises 284(3)
Random Effects Models with Covariates 287(38)
Introduction 287(1)
The Model 287(5)
Estimation of the Variance Components 292(5)
Changing Location of the Covariate Changes 297(2)
the Estimates of the Variance Components
Example: Balanced One--Way Treatment 299(5)
Structure
Example: Unbalanced One--Way Treatment 304(5)
Structure
Example: Two--Way Treatment Structure 309(6)
Summary 315(10)
References 320(1)
Exercises 321(4)
Mixed Models 325(28)
Introduction 325(1)
The Matrix Form of the Mixed Model 325(4)
Fixed Effects Treatment Structure 329(1)
Estimation of Fixed Effects and Some Small 329(2)
Sample Size Approximations
Fixed Treatments and Locations Random 331(1)
Example: Two--Way Mixed Effects Treatment 332(5)
Structure in a CRD
Example: Treatments are Fixed and Locations 337(16)
are Random with a RCB at Each Location
References 350(1)
Exercises 351(2)
Analysis of Covariance Models with 353(38)
Heterogeneous Errors
Introduction 353(1)
The Unequal Variance Model 353(1)
Tests for Homogeneity of Variances 354(2)
Levene's Test for Equal Variances 354(1)
Hartley's F-Max Test for Equal Variances 355(1)
Bartlett's Test for Equal Variances 355(1)
Likelihood Ratio Test for Equal Variances 356(1)
Estimating the Parameters of the Regression 356(1)
Model
Least Squares Estimation 356(1)
Maximum Likelihood Methods 357(1)
Determining the Form of the Model 357(2)
Comparing the Models 359(3)
Comparing the Nonparallel Lines Models 359(2)
Comparing the Parallel Lines Models 361(1)
Computational Issues 362(1)
Example: One--Way Treatment Structure with 362(7)
Unequal Variances
Example: Two--Way Treatment Structure with 369(12)
Unequal Variances
Example: Treatments in Multi--location Trial 381(8)
Summary 389(2)
References 389(1)
Exercises 389(2)
Analysis of Covariance for Split--Plot and 391(60)
Strip--Plot Design Structures
Introduction 391(1)
Some Concepts 392(1)
Covariate Measured on the Whole Plot or 392(3)
Large Size of Experimental Unit
Covariate is Measured on the Small Size of 395(3)
Experimental Unit
Covariate is Measured on the Large Size of 398(1)
Experimental Unit and a Covariate is
Measured on the Small Size of Experimental
Unit
General Representation of the Covariate 399(7)
Part of the Model
Covariate Measured on Large Size of 401(2)
Experimental Unit
Covariate Measured on the Small Size of 403(2)
Experimental Units
Summary of General Representation 405(1)
Example: Flour Milling 406(8)
Experiment---Covariate Measured on the
Whole Plot
Example: Cookie Baking 414(12)
Example: Teaching Methods with One 426(6)
Covariate Measured on the Large Size
Experimental Unit and One Covariate
Measured on the Small Size Experimental Unit
Example: Comfort Study in a Strip--Plot 432(12)
Design with Three Sizes of Experimental
Units and Three Covariates
Conclusions 444(7)
References 446(1)
Exercises 446(5)
Analysis of Covariance for Repeated Measures 451(42)
Designs
Introduction 451(2)
The Covariance Part of the 453(3)
Model---Selecting R
Covariance Structure of the Data 456(1)
Specifying the Random and Repeated 457(1)
Statements for PROC MIXED of the SAS®
System
Selecting an Adequate Covariance Structure 458(1)
Example: Systolic Blood Pressure Study with 459(11)
Covariate Measured on the Large Size
Experimental Unit
Example: Oxide Layer Development Experiment 470(9)
with Three Sizes of Experimental Units
Where the Repeated Measure is at the Middle
Size of Experimental Unit and the Covariate
is Measured on the Small Size Experimental
Unit
Conclusions 479(14)
References 487(1)
Exercises 487(6)
Analysis of Covariance for Nonreplicated 493(40)
Experiments
Introduction 493(2)
Experiments with A Single Covariate 495(4)
Experiments with Multiple Covariates 499(2)
Selecting Non--null and Null Partitions 501(1)
Estimating the Parameters 502(1)
Example: Milling Flour Using Three Factors 503(5)
Each at Two Levels
Example: Baking Bread Using Four Factors 508(3)
Each at Two Levels
Example: Hamburger Patties with Four 511(1)
Factors Each at Two Levels
Example: Strength of Composite Material 512(8)
Coupons with Two Covariates
Example: Effectiveness of Paint on Bricks 520(7)
with Unequal Slopes
Summary 527(6)
References 529(1)
Exercises 530(3)
Special Applications of Analysis of Covariance 533(64)
Introduction 533(1)
Blocking and Analysis of Covariance 533(10)
Treatments Have Different Ranges of the 543(9)
Covariate
Nonparametric Analysis of Covariance 552(7)
Heart Rate Data from Exercise Programs 552(3)
Average Daily Gain Data from a Two--Way 555(4)
Treatment Structure
Crossover Design with Covariates 559(5)
Nonlinear Analysis of Covariance 564(8)
Effect of Outliers 572(25)
References 590(1)
Exercises 590(7)
Index 597