ANALYSIS oF MESSY DATA VOLUME

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ANALYSIS oF MESSY DATA VOLUME 1 DESIGNED EXPERIMENTS
Chapman & Hall/CRC
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2009 by Taylor & Francis Group, LLC
Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business
Milliken, George A., 1943-
Analysis of messy data / by George A. Milliken, Dallas E. Johnson. -- 2nd ed.
p. cm.
Includes bibliographical references and index.
Contents: v. 1. Designed experiments
ISBN-13: 978-1-58488-334-0 (v. 1)
ISBN-10: 1-58488-334-0 (v. 1)
1. Analysis of variance. 2. Experimental design. 3. Sampling (Statistics) I. Johnson, Dallas E.,
1938- II. Title.

1. The Simplest Case: One-Way Treatment Structure in a Completely
Randomized Design Structure with Homogeneous Errors ....................................... 1
1.1 Model Defi nitions and Assumptions ....................................................................... 1
1.2 Parameter Estimation ................................................................................................. 2
1.3 Inferences on Linear Combinations—Tests and Confi dence Intervals ............... 4
1.4 Example—Tasks and Pulse Rate ............................................................................... 5
1.5 Simultaneous Tests on Several Linear Combinations ............................................ 7
1.6 Example—Tasks and Pulse Rate (Continued) ......................................................... 9
1.7 Testing the Equality of All Means .......................................................................... 11
1.8 Example—Tasks and Pulse Rate (Continued) ....................................................... 12
1.9 General Method for Comparing Two Models—The Principle of
Conditional Error ...................................................................................................... 13
1.10 Example—Tasks and Pulse Rate (Continued) ....................................................... 15
1.11 Computer Analyses ................................................................................................... 15
1.12 Concluding Remarks ................................................................................................ 16
1.13 Exercises ...................................................................................................................... 17
2. One-Way Treatment Structure in a Completely Randomized Design
Structure with Heterogeneous Errors .......................................................................... 21
2.1 Model Defi nitions and Assumptions ..................................................................... 22
2.2 Parameter Estimation ............................................................................................... 22
2.3 Tests for Homogeneity of Variances ....................................................................... 23
2.3.1 Hartley’s F-Max Test ..................................................................................... 23
2.3.2 Bartlett’s Test .................................................................................................. 24
2.3.3 Levene’s Test ................................................................................................... 24
2.3.4 Brown and Forsythe’s Test ........................................................................... 24
2.3.5 O’Brien’s Test .................................................................................................. 25
2.3.6 Some Recommendations .............................................................................. 25
2.4 Example—Drugs and Errors ................................................................................... 25
2.5 Inferences on Linear Combinations ....................................................................... 29
2.6 Example—Drugs and Errors (Continued) ............................................................. 31
vi  Contents
2.7 General Satterthwaite Approximation for Degrees of Freedom ........................ 33
2.8 Comparing All Means .............................................................................................. 34
2.9 Concluding Remarks ................................................................................................ 38
2.10 Exercises ...................................................................................................................... 39
3. Simultaneous Inference Procedures and Multiple Comparisons .......................... 43
3.1 Error Rates .................................................................................................................. 44
3.2 Recommendations ..................................................................................................... 45
3.3 Least Signifi cant Difference ..................................................................................... 46
3.4 Fisher’s LSD Procedure ............................................................................................. 47
3.5 Bonferroni’s Method ................................................................................................. 48
3.6 Scheffé’s Procedure ................................................................................................... 48
3.7 Tukey–Kramer Method ............................................................................................. 49
3.8 Simulation Methods .................................................................................................. 50
3.9 Šidák Procedure ......................................................................................................... 51
3.10 Example—Pairwise Comparisons .......................................................................... 51
3.11 Dunnett’s Procedure ................................................................................................. 53
3.12 Example—Comparing with a Control ................................................................... 54
3.13 Multivariate t .............................................................................................................. 55
3.14 Example—Linearly Independent Comparisons ................................................... 56
3.15 Sequential Rejective Methods .................................................................................. 57
3.15.1 Bonferroni–Holm Method ........................................................................... 58
3.15.2 Šidák–Holm Method ..................................................................................... 58
3.15.3 Benjamini and Hochberg Method to Control FDR .................................. 58
3.16 Example—Linearly Dependent Comparisons ...................................................... 59
3.17 Multiple Range Tests ................................................................................................. 61
......
30.3.1 Example 30.1: Continuation ........................................................................ 634
30.4 Analysis Using JMP ................................................................................................ 636
30.5 Concluding Remarks .............................................................................................. 640
30.6 Exercises .................................................................................................................... 640
Appendix .................................................................................................................................. 643
References ................................................................................................................................ 651
Index ......................................................................................................................................... 655

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