Experimental Design Techniques in Statistical Practice : A Practical Software-Based Approach

by Gardiner, William P.; Gettinby, George

• ISBN13: 9781898563358
• ISBN10: 1898563357
• Format: Paperback
• Copyright: 1998-03-01
• Publisher: Woodhead Pub Ltd

Summary

Provides an introduction to the diverse subject area of experimental design, with many practical and applicable exercises to help the reader understand, present and analyze the data. The pragmatic approach offers technical training for use of designs and teaches statistical and non-statistical skills in design and analysis of project studies throughout science and industry.

Author Biography

Dr Bill Gardiner lectures at Glasgow Caledonian University George Gettinby is Professor and Chairman in the Department of Statistics and Modelling Science at the University of Strathclyde, Glasgow

Table of Contents

Authors' Preface	xiii
Glossary	xv
Introduction
Introduction	1	(1)
Information on the Statistical Software	2	(4)
SAS	3	(1)
Minitab	4	(2)
Summarising Experimental Data	6	(5)
Graphical Presentations	6	(2)
Numerical Summaries	8	(3)
The Normal Distribution Within Data Analysis	11	(1)
Outliers in Data	12	(2)
Appendix: Introductory Software Information	14	(5)
Inferential Data Analysis for Simple Experiments
Introduction	19	(1)
Basic Concepts of Inferential Data Analysis	19	(4)
Inference Methods for Two Sample Studies	23	(7)
Hypothesis Test for Difference in Mean Responses	24	(3)
Confidence Interval for Difference in Mean Responses	27	(1)
Hypothesis Test for Variability	28	(1)
Confidence Interval for the Ratio of Two Variances	29	(1)
Non-parametric Methods	30	(1)
Inference Methods for Paired Sample Studies	30	(6)
Hypothesis Test for Mean Difference in Responses	31	(2)
Confidence Interval for Mean Difference	33	(1)
Hypothesis Test for Variability	34	(2)
Non-parametric Methods	36	(1)
Sample Size Estimation in Design Planning	36	(3)
Sample Size Estimation for Two Sample Studies	36	(2)
Sample Size Estimation for Paired Sample Studies	38	(1)
Validity and Good Statistical Practice	39	(1)
Protocols	40	(1)
Commonly Occurring Design Mistakes	41	(10)
Problems	42	(2)
Appendix: Software Information for Two Sample Studies	44	(3)
Appendix: Software Information for Paired Sample Studies	47	(4)
One Factor Designs
Introduction	51	(2)
Completely Randomised Design	53	(4)
Design Structure	53	(1)
Model for the Measured Response	54	(1)
Assumptions	55	(1)
Exploratory Data Analysis	56	(1)
ANOVA Principle for the Completely Randomised Design	57	(2)
Hypotheses	57	(1)
ANOVA Table	57	(1)
Treatment Test Statistic	58	(1)
Follow-up Analysis Procedures	59	(10)
Main Effects Plot	60	(1)
Standard Error Plot	60	(1)
Multiple Comparisons	61	(3)
Linear Contrasts	64	(3)
Orthogonal Polynomials	67	(1)
Treatment Effect Estimation	67	(2)
Model Fit	69	(1)
Diagnostic Checking of Model Assumptions	69	(5)
Graphical Checks	70	(3)
Statistical Checks	73	(1)
Power Analysis in Design Planning	74	(3)
Power Estimation	75	(1)
Sample Size Estimation	76	(1)
Non-parametric Alternative to the ANOVA Based Treatment Tests	77	(3)
The Kruskal-Wallis Test of Treatment Differences	77	(1)
Multiple Comparison Associated with the Kruskal-Wallis Test	78	(1)
Linear Contrasts	79	(1)
Data Transformations	80	(9)
Problems	82	(2)
Appendix: Software Information for Completely Randomised Design	84	(5)
One Factor Blocking Designs
Introduction	89	(1)
Randomised Block Design	89	(3)
Design Structure	90	(1)
Model for the Measured Response	90	(1)
Assumptions	91	(1)
Exploratory Data Analysis	91	(1)
ANOVA Principle for the Randomised Block Design	92	(3)
Hypotheses	92	(1)
ANOVA Table	92	(1)
Test Statistics	93	(2)
Follow-up Analysis Procedures for Randomised Block Designs	95	(2)
Additional Aspects of Blocking Designs	97	(1)
Power Analysis	97	(1)
Missing Observations	98	(1)
Efficiency	98	(1)
Non-parametric Alternative to ANOVA Based Treatment Tests	98	(2)
Friedman Test of Treatment Differences	99	(1)
Multiple Comparison Associated with Friedman's Test	99	(1)
Incomplete Block Designs	100	(4)
Balanced Incomplete Block Design	101	(1)
ANOVA Principle	102	(1)
Follow-up Analysis Procedures	103	(1)
Other Incomplete Designs	104	(1)
Latin Square Design	104	(15)
Design Structure	104	(1)
Model for the Measured Response	105	(1)
ANOVA Principle	106	(2)
Follow-up Analysis Procedures	108	(2)
Missing Observations	110	(1)
Efficiency	111	(1)
Problems	111	(3)
Appendix: Software Information for Randomised Block Design	114	(2)
Appendix: Software Information for Balanced Incomplete Block Design	116	(1)
Appendix: Software Information for Latin Square Design	117	(2)
Factorial Experimental Designs
Introduction	119	(1)
Two Factor Factorial Design with n Replications per Cell	120	(4)
Design Structure	121	(2)
Model for the Measured Response	123	(1)
Exploratory Data Analysis	124	(1)
ANOVA Principle for the Two Factor Factorial Design	124	(3)
Hypotheses	125	(1)
ANOVA Table	125	(1)
Test Statistics	125	(2)
Follow-up Analysis Procedures for Factorial Designs of Model I Type	127	(7)
Significant Interaction	128	(2)
Non-significant Interaction but Significant Factor Effect	130	(1)
Linear Contrasts	130	(1)
Orthogonal Polynomials	130	(1)
Estimation	131	(1)
Diagnostic Checking	132	(2)
Overview of Data Analysis for Two Factor Factorial Designs	134	(1)
Power Analysis in Two Factor Factorial Designs	134	(1)
Non-parametric Inference for a Two Factor Factorial Design	135	(1)
Random Effects - Model II/Mixed Model Experiments	136	(5)
Additional Effect Assumptions	137	(1)
EMS Expressions and Test Statistic Derivation	138	(2)
Analysis Components for Models with Random Effects	140	(1)
Power Analysis for Random Effects	140	(1)
Unbalanced Two Factor Factorial Design	141	(6)
Type I to IV Sums of Squares	142	(2)
Type I to III Hypotheses	144	(3)
Three Factor Factorial Design with n Replications per Cell	147	(9)
Model for the Measured Response	148	(1)
ANOVA Principle and Test Statistics	148	(4)
Overview of Data Analysis for Three Factor Factorial Designs	152	(3)
Pooling of Factor Effects	155	(1)
Unbalanced Approaches	156	(1)
Analysis of Covariance	156	(10)
Problems	156	(6)
Appendix: Software Information for Two Factor Factorial Designs	162	(2)
Appendix: Software Information for Three Factor Factorial Designs	164	(2)
Hierarchical Designs
Introduction	166	(1)
Two Factor Nested Design	166	(3)
Design Structure	166	(2)
Model for the Measured Response	168	(1)
Exploratory Data Analysis	169	(1)
ANOVA Principle for the Two Factor Nested Design	169	(3)
Hypotheses	169	(1)
ANOVA Table	170	(1)
Test Statistics	170	(2)
Follow-up Analysis	172
Analysis of Factor Effects	172	(1)
Mixed Model - Significant Nested Factor	173	(1)
Mixed Model and Model II Variability Analysis	174	(1)
Diagnostic Checking	175
Other Features Associated with Two Factor Nested Designs	171	(7)
Relative Efficiency	177	(1)
Power Analysis	177	(1)
Unequal Replicates	178	(1)
Three Factor Nested Design	178	(1)
Model for the Measured Response	178	(1)
ANOVA Table and Test Statistics	179	(1)
Repeated Measures Design	179	(11)
Design Structure	179	(1)
Model for the Measured Response	180	(2)
ANOVA Table and Test Statistics	182	(4)
Follow-up Procedures	186	(2)
Diagnostic Checking	188	(1)
Unbalanced Designs	189	(1)
CrossOver Design	190	(6)
Design Structure	191	(1)
Model for the Measured Response	192	(1)
ANOVA Table and Test Statistics	193	(3)
Split-Plot Designs	196	(11)
Design Structure	196	(1)
Model for the Measured Response	196	(1)
ANOVA Table and Test Statistics	197	(1)
Problems	198	(4)
Appendix: Software Information for Nested Designs	202	(2)
Appendix: Software Information for Repeated Measures Designs	204	(1)
Appendix: Software Information for CrossOver Designs	205	(2)
Two-level Factorial Designs
Introduction	207	(2)
Contrasts and Effect Estimation	209	(5)
Contrasts	209	(3)
Effect Estimation	212	(2)
Missing Values	214	(1)
Initial Analysis Components	214	(6)
Exploratory Analysis	214	(1)
Effect Estimate Plots	214	(4)
Data Plots and Summaries	218	(2)
Statistical Components of Analysis	220	(4)
Statistical Assessment of Proposed Model	220	(1)
Prediction	221	(1)
Diagnostic Checking	222	(2)
General Unreplicated 2k Designs	224	(2)
Use of Replication	226	(1)
Three-level Designs	227	(7)
Problems	227	(2)
Appendix: Software Information for Two-level Factorial Designs	229	(5)
Two-level Fractional Factorial Designs
Introduction	234	(1)
Confounding	234	(2)
Block Construction Procedures	236	(3)
Even/Odd Method	236	(2)
Linear Combination Method	238	(1)
Fractional Factorial Designs	239	(9)
Alias Structure	242	(3)
Design Resolution	245	(3)
Analysis Components for Fractional Factorial Designs	248	(10)
Exploratory Analysis	249	(1)
Effect Estimates Analysis	249	(1)
Data Plots and Summaries	250	(1)
Statistical Components	251	(7)
Three-level Fractional Factorial Designs	258	(9)
Problems	259	(3)
Appendix: Software Information for Two-level Fractional Factorial Designs	262	(5)
Two-level Orthogonal Arrays
Introduction	267	(1)
Array Structures	267	(3)
Experimental Plans	270	(7)
Plans Based on the OA82(27) Structure	270	(2)
Plans Based on the OA16(215) Structure	272	(2)
Aliasing and Resolution in Orthogonal Arrays	274	(2)
Saturated Designs	276	(1)
Analysis Components for Two-Level Orthogonal Arrays	277	(4)
Three-level Orthogonal Arrays	281	(1)
Plackett-Burman Designs	282	(7)
Problems	283	(3)
Appendix: Software Information for Two-Level Orthogonal Array Designs	286	(3)
Taguchi Methods
Introduction	289	(2)
Design Structures	291	(6)
Performance Statistics	297	(3)
Data Analysis Components for Two-level Taguchi Parameter Designs	300	(7)
Estimation of Factor Effects	300	(1)
Factor Effect Plots	301	(1)
Data Plots	302	(2)
ANOVA Modelling	304	(3)
Data Analysis Components for Three-level Taguchi Parameter Designs	307	(5)
Data Plots	309	(3)
ANOVA Modelling	312	(1)
Other Data Analysis Components	312	(1)
Exponential/Weibull Plots	312	(1)
Test of Homogeneity of the Factor Mean Squares	313	(1)
Final Comments	313	(9)
Problems	314	(3)
Appendix: Software Information for Two-level Taguchi Designs	317	(3)
Appendix: Software Information for Three-level Taguchi Designs	320	(2)
Response Surface Methods
Introduction	322	(1)
First-order Design Structures	323	(1)
Two-level Desing	323	(1)
Simplex Design	324	(1)
Response Surface Analysis for First-order Designs	324	(8)
First-order Response Model	324	(2)
Parameter Estimation	326	(1)
ANOVA Table	327	(1)
Adequacy of Fit	328	(3)
Statistical Validity of Fitted Model	331	(1)
Additional Aspects of Analysis	331	(1)
Contour Plot	332	(1)
Method of Steepest Ascent	332	(3)
Second-order Design Structures	335	(5)
Central Composite Design	335	(3)
Three-level Design	338	(1)
Box-Behnken Design	338	(1)
Face-Centred Design	338	(1)
Blocking Design	339	(1)
Response Surface Analysis for Second-order Designs	340	(8)
Second-order Response Model	340	(1)
Parameter Estimation	341	(2)
Adequacy of Fit	343	(1)
Statistical Validity of Fitted Model	343	(1)
Additional Analysis	344	(1)
Contour Plot	345	(1)
Exploration of Response Surface	346	(2)
Mixture Designs	348	(1)
Further Aspects of Response Surface Methods	349	(6)
Multiple Responses and Non-parametric Methods	349	(1)
Optimal Design Theory	349	(1)
Problems	349	(3)
Appendix: Software Information for Response Surface Designs	352	(3)
Bibliography	355	(4)
Appendix A Statistical Tables	359	(15)
Critical Values of the Student's t Distribution	360	(1)
Critical Values of the X2 Distribution	361	(1)
Critical Values of the F Distribution	362	(4)
Table of z Scores for the Standard Normal Distribution	366	(1)
5% Critical Values for the Studentised Range Statistic	367	(1)
1% Critical Values for the Studentised Range Statistic	368	(1)
Orthogonal Polynomials	369	(1)
Critical Values for the Ryan-Joiner Correlation Test of Normality	370	(1)
Power Values for Treatment F Test Based on the Non-central F(f1, f2, λ) Distribution for 5% Significance Testing	371	(3)
Appendix B Answers to Selected Problems	374	(10)
Subject Index	384