Analysis of Variance and Design of Experiments

by The Pennsylvania State University

Read here Read at LibreTextsPDF

This is a graduate-level course that provides a thorough introduction to statistical methods used to analyze data resulting from a wide range of experimental designs. The concepts of comparative experiments, randomization, replication, repeated measures, blocking, and factorial designs will be discussed. The main goal of the course will be to develop problem-solving skills for identifying a variety of designs and making inferences on associated parameters.

Description from LibreTexts.

Subjects
Statistics, Advanced Statistics
Licence
CC BY-NC 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Overview of ANOVA
  7. 1.1: The Working Hypothesis
  8. 1.2: The 7-Step Process of Statistical Hypothesis Testing
  9. 1.3: Chapter 1 Summary
  10. 2: ANOVA Foundations
  11. 2.1: Building the ANOVA Table - Notation
  12. 2.2: Computing Quantities for the ANOVA Table
  13. 2.3: Tukey Test for Pairwise Mean Comparisons
  14. 2.4: Other Pairwise Mean Comparison Methods
  15. 2.5: Contrast Analysis
  16. 2.6: Try It!
  17. 2.7: Chapter 2 Summary
  18. 3: ANOVA Models Part I
  19. 3.1: The Model
  20. 3.2: Assumptions and Diagnostics
  21. 3.3: Anatomy of SAS Programming for ANOVA
  22. 3.4: Greenhouse Example in SAS
  23. 3.5: SAS Output for ANOVA
  24. 3.6: One-Way ANOVA Greenhouse Example in Minitab
  25. 3.7: One-Way ANOVA Greenhouse Example in R
  26. 3.8: Power Analysis
  27. 3.9: Try It!
  28. 3.10: Chapter 3 Summary
  29. 4: ANOVA Models Part II
  30. 4.1: How is ANOVA Calculated?
  31. 4.2: The Overall Mean Model
  32. 4.3: Cell Means Model
  33. 4.4: Dummy Variable Regression
  34. 4.5: Computational Aspects of the Effects Model
  35. 4.6: The Study Diagram
  36. 4.7: Try It!
  37. 4.8: Chapter 4 Summary
  38. 5: Multi-Factor ANOVA
  39. 5.1: Factorial or Crossed Treatment Designs
  40. 5.1.1: Two-Factor Factorial - Greenhouse Example (SAS)
  41. 5.1.1a: The Additive Model (No Interaction)
  42. 5.1.2: Two-Factor Factorial - Greenhouse Example (Minitab)
  43. 5.1.3: Two-Factor Factorial - Greenhouse Example (R)
  44. 5.1.3a: The Additive Model
  45. 5.2: Nested Treatment Design
  46. 5.2.1: Nested Model in SAS
  47. 5.2.2: Nested Model in Minitab
  48. 5.2.3: Nested Model in R
  49. 5.3: Crossed-Nested Designs
  50. 5.4: Try It!
  51. 5.5: Chapter 5 Summary
  52. 5.6: Treatment Design Summary (Optional Enrichment Material)
  53. 6: Random Effects and Introduction to Mixed Models
  54. 6.1: Random Effects
  55. 6.2: Battery Life Example
  56. 6.3: Random Effects in Factorial and Nested Designs
  57. 6.4: Special Case - Fully Nested Random Effects Design
  58. 6.5: Quality Control Example
  59. 6.5.1: Using Minitab
  60. 6.5.2: Using R
  61. 6.6: Introduction to Mixed Models
  62. 6.7: Mixed Model Example
  63. 6.7.1: Using Minitab
  64. 6.7.2: Using SAS
  65. 6.7.3: Using R
  66. 6.8: Complexity Happens
  67. 6.9: Try It!
  68. 6.10: Chapter 6 Summary
  69. 7: Randomization Design Part I
  70. 7.1: Experimental Unit and Replication
  71. 7.2: Completely Randomized Design
  72. 7.3: Restriction on Randomization - RCBD
  73. 7.4: Blocking in 2 Dimensions - Latin Square
  74. 7.5: Try It!
  75. 7.6: Chapter 7 Summary
  76. 8: Randomization Design Part II
  77. 8.1: Split-Plot Design in RCBD
  78. 8.2: Split-Plot Design in CRD
  79. 8.3: Split-Split-Plot Design
  80. 8.4: Try It!
  81. 8.5: Chapter 8 Summary
  82. 9: ANCOVA Part I
  83. 9.1: Role of the Covariate
  84. 9.2: ANCOVA in the GLM Setting - The Covariate as a Regression Variable
  85. 9.3: Steps in ANCOVA
  86. 9.4: Using Technology - Equal Slopes Model
  87. 9.5: Using Technology - Unequal Slopes Model
  88. 9.6: Chapter 9 Summary
  89. 10: ANCOVA Part II
  90. 10.1: ANCOVA with Quantitative Factor Levels
  91. 10.2: Quantitative Predictors - Orthogonal Polynomials
  92. 10.3: Chapter 10 Summary
  93. 11: Introduction to Repeated Measures
  94. 11.1: Historical Methods
  95. 11.2: Correlated Residuals
  96. 11.3: More on Covariance Structures
  97. 11.4: Worked Example
  98. 11.5: Chapter 11 Summary
  99. 12: Cross-over Repeated Measure Designs
  100. 12.1: Introduction to Cross-Over Designs
  101. 12.2: Coding for Carry-Over Covariates
  102. 12.3: Programming for Steer Example
  103. 12.4: Testing the Significance of the Carry-Over Effect
  104. 12.5: Try It!
  105. 12.6: Chapter 12 Summary
  106. Back Matter
  107. Index
  108. Glossary
  109. Detailed Licensing
  110. Detailed Licensing