1st Edition

Practical Data Analysis for Designed Experiments

By Brian S. Yandell Copyright 1997
    452 Pages
    by Chapman & Hall

    Placing data in the context of the scientific discovery of knowledge through experimentation, Practical Data Analysis for Designed Experiments examines issues of comparing groups and sorting out factor effects and the consequences of imbalance and nesting, then works through more practical applications of the theory. Written in a modern and accessible manner, this book is a useful blend of theory and methods. Exercises included in the text are based on real experiments and real data.

    Part A: Placing Data in Context
    Practical Data Analysis
    Effect of Factors
    Nature of Data
    Summary Tables
    Plots for Statistics
    Collaboration in Science
    Asking Questions
    Learning from Plots
    Mechanics of a Consulting Session
    Philosophy and Ethics
    Intelligence, Culture and Learning
    Experimental Design
    Types of Studies
    Designed Experiments
    Design Structure
    Treatment Structure
    Designs in This Book
    Part B: Working with Groups of Data
    Group Summaries
    Graphical Summaries
    Estimates of Means and Variance
    Assumptions and Pivot Statistics
    Interval Estimates of Means
    Testing Hypotheses about Means
    Formal Inference on the Variance
    Comparing Several Means
    Linear Contrasts of Means
    Overall Test of Difference
    Partitioning Sums of Squares
    Expected Mean Squares
    Power and Sample Size
    Multiple Comparisons of Means
    Experiment- and Comparison-Wise Error Rates
    Comparisons Based on F-Tests
    Comparisons Based on Range of Means
    Comparisons of Comparisons
    Part C: Sorting Out Effects with Data
    Factorial Designs
    Cell Means Models
    Effects Models
    Estimable Functions
    Linear Constraints
    General Form of Estimable Functions
    Balanced Experiments
    Additive Models
    Full Models with Two Factors
    Interaction Plots
    Higher Orders Models
    Model Selection
    Pooling Interactions
    Selected the "Best" Model
    Model Selection Criteria
    One Observation per Cell
    Tukey's Test for Interaction
    Part D: Dealing with Imbalance
    Unbalanced Experiments
    Unequal Samples
    Additive Model
    Types I, II, III and IV
    Missing Cells
    What Are Missing Cells?
    Connected Cells and Incomplete Designs
    Type IV Comparisons
    Latin Square Designs
    Fractional Factorial Designs
    Linear Models Inference
    Matrix Preliminaries
    Ordinary Least Squares
    Weighted Least Squares
    Maximum Likelihood
    Restricted Maximum Likelihood
    Inference for Fixed Effect Models
    Anova and Regression Models
    Part E: Questioning Assumptions
    Residual Plots
    Departures from Assumptions
    Incorrect Model
    Correlated Responses
    Unequal Variance
    Non-Normal Data
    Comparisons with Unequal Variance
    Comparing Means When Variances Are Unequal
    Weighted Analysis of Variances
    Satterthwaite Approximation
    Generalized Inference
    Testing for Unequal Variances
    Getting Free from Assumptions
    Transforming Data
    Comparisons Using Ranks
    Monte Carlo Methods
    Part F: Regressing with Factors
    Ordered Groups
    Groups in a Line
    Testing for Linearity
    Path Analysis Diagrams
    Regression Calibration
    Classical Error in Variables
    Parallel Lines
    Parallel Lines Model
    Adjusted Estimates
    Plots with Symbols
    Sequential Tests with Multiple Responses
    Sequential Tests with Driving Covariate
    Adjusted (Type III) Tests of Hypotheses
    Different Slopes for Different Groups
    Multiple Responses
    Overall Tests for Group Differences
    Matrix Analog to F Test
    How Do Groups Differ?
    Causal Models
    Part G: Deciding on Fixed or Random Effects
    Models with Random Effects
    Single Factor Random Model
    Test for Class Variation
    Distribution of Sums of Squares
    Variance Components
    Grand Menu
    General Random Models
    Two Factor Random Models
    Unbalanced Two-Factor Random Model
    General Random Model
    Quadratic Forms in Random Effects
    Application to Two Factor Random Model
    Mixed Effect Models
    Two Factor Mixed Models
    General Mixed Models
    Part H: Nesting Experimental Units
    Nested Designs
    Nested and Crossed Factors
    Nesting of Fixed Effects
    Nesting of Random Effects
    Split Plot Design
    Several Views of Split Plot
    Split Plot Model
    Contrasts in a Split Plot
    General Nested Designs
    Extensions of Split Plot
    Split Plot
    Imbalance in Nested Designs
    Covariates in Nested Designs
    Explained Variation in Nested Designs
    Part I: Repeating Measures on Subjects
    Repeated Measures as Split Plot
    Repeated Measures Designs
    Repeated Measures Model
    Split Plot More or Less
    Expected Mean Squares under Sphericity
    Contrasts under Sphericity
    Adjustments for Correlation
    Adjustments to Split Plot
    Contrasts over Time
    Multivariate Repeated Measures
    Cross-Over Design
    Cross-Over Model
    Confounding in Cross-Over Designs
    Partition of Sum of Squares
    Replicated Latin Square Design
    General Cross-Over Designs


    BrianS. Yandell

    "…the book should be useful for statisticians who are starting out as consultants…also contains much good practical advice based on the writer's experience as a teacher and statistical advisor."
    -M. Talbot, Biometrics, December 1998
    "…gives a generally lucid and well thought out introduction to the use of data driven approaches for statistical data analysis…the explanations are clear, without being obscured by too much mathematical detail…an excellent basis for a statistics course with an applied orientation, and most institutions that teach statistics or analyse data will probably want a library copy."
    -S.N. Wood,Biometrics,December 1998