Practical Data Analysis for Designed Experiments
Preview
Book Description
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.
Table of Contents
Preface
Part A: Placing Data in Context
Practical Data Analysis
Effect of Factors
Nature of Data
Summary Tables
Plots for Statistics
Computing
Interpretation
Problems
Collaboration in Science
Asking Questions
Learning from Plots
Mechanics of a Consulting Session
Philosophy and Ethics
Intelligence, Culture and Learning
Writing
Problems
Experimental Design
Types of Studies
Designed Experiments
Design Structure
Treatment Structure
Designs in This Book
Problems
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
Problems
Comparing Several Means
Linear Contrasts of Means
Overall Test of Difference
Partitioning Sums of Squares
Expected Mean Squares
Power and Sample Size
Problems
Multiple Comparisons of Means
Experiment- and Comparison-Wise Error Rates
Comparisons Based on F-Tests
Comparisons Based on Range of Means
Comparisons of Comparisons
Problems
Part C: Sorting Out Effects with Data
Factorial Designs
Cell Means Models
Effects Models
Estimable Functions
Linear Constraints
General Form of Estimable Functions
Problems
Balanced Experiments
Additive Models
Full Models with Two Factors
Interaction Plots
Higher Orders Models
Problems
Model Selection
Pooling Interactions
Selected the "Best" Model
Model Selection Criteria
One Observation per Cell
Tukey's Test for Interaction
Problems
Part D: Dealing with Imbalance
Unbalanced Experiments
Unequal Samples
Additive Model
Types I, II, III and IV
Problems
Missing Cells
What Are Missing Cells?
Connected Cells and Incomplete Designs
Type IV Comparisons
Latin Square Designs
Fractional Factorial Designs
Problems
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
Problems
Part E: Questioning Assumptions
Residual Plots
Departures from Assumptions
Incorrect Model
Correlated Responses
Unequal Variance
Non-Normal Data
Problems
Comparisons with Unequal Variance
Comparing Means When Variances Are Unequal
Weighted Analysis of Variances
Satterthwaite Approximation
Generalized Inference
Testing for Unequal Variances
Problems
Getting Free from Assumptions
Transforming Data
Comparisons Using Ranks
Randomization
Monte Carlo Methods
Problems
Part F: Regressing with Factors
Ordered Groups
Groups in a Line
Testing for Linearity
Path Analysis Diagrams
Regression Calibration
Classical Error in Variables
Problems
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
Problems
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
Problems
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
Problems
Mixed Effect Models
Two Factor Mixed Models
General Mixed Models
Problems
Part H: Nesting Experimental Units
Nested Designs
Sub-Sampling
Blocking
Nested and Crossed Factors
Nesting of Fixed Effects
Nesting of Random Effects
Problems
Split Plot Design
Several Views of Split Plot
Split Plot Model
Contrasts in a Split Plot
Problems
General Nested Designs
Extensions of Split Plot
Split Plot
Imbalance in Nested Designs
Covariates in Nested Designs
Explained Variation in Nested Designs
Problems
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
Problems
Adjustments for Correlation
Adjustments to Split Plot
Contrasts over Time
Multivariate Repeated Measures
Problems
Cross-Over Design
Cross-Over Model
Confounding in Cross-Over Designs
Partition of Sum of Squares
Replicated Latin Square Design
General Cross-Over Designs
Problems
References
Index
Reviews
"…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