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Analysis of Variance and Design of Experiments

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Analysis of Variance and Design of Experiments

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.

Advanced StatisticsStatistics
Author
The Pennsylvania State University
Publisher
LibreTexts
Source
LibreTexts
License
CC BY-NC
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 100 sections
  1. 01: Overview of ANOVA
  2. 1.01: The Working Hypothesis
  3. 1.02: The 7-Step Process of Statistical Hypothesis Testing
  4. 1.03: Chapter 1 Summary
  5. 02: ANOVA Foundations
  6. 2.01: Building the ANOVA Table - Notation
  7. 2.02: Computing Quantities for the ANOVA Table
  8. 2.03: Tukey Test for Pairwise Mean Comparisons
  9. 2.04: Other Pairwise Mean Comparison Methods
  10. 2.05: Contrast Analysis
  11. 2.06: Try It
  12. 2.07: Chapter 2 Summary
  13. 03: ANOVA Models Part I
  14. 3.01: The Model
  15. 3.02: Assumptions and Diagnostics
  16. 3.03: Anatomy of SAS Programming for ANOVA
  17. 3.04: Greenhouse Example in SAS
  18. 3.05: SAS Output for ANOVA
  19. 3.06: One-Way ANOVA Greenhouse Example in Minitab
  20. 3.07: One-Way ANOVA Greenhouse Example in R
  21. 3.08: Power Analysis
  22. 3.09: Try It
  23. 3.10: Chapter 3 Summary
  24. 04: ANOVA Models Part II
  25. 4.01: How is ANOVA Calculated
  26. 4.02: The Overall Mean Model
  27. 4.03: Cell Means Model
  28. 4.04: Dummy Variable Regression
  29. 4.05: Computational Aspects of the Effects Model
  30. 4.06: The Study Diagram
  31. 4.07: Try It
  32. 4.08: Chapter 4 Summary
  33. 05: Multi-Factor ANOVA
  34. 5.01: Factorial or Crossed Treatment Designs
  35. 5.1.01: Two-Factor Factorial - Greenhouse Example (SAS)
  36. 5.1.1a: The Additive Model (No Interaction)
  37. 5.1.02: Two-Factor Factorial - Greenhouse Example (Minitab)
  38. 5.1.03: Two-Factor Factorial - Greenhouse Example (R)
  39. 5.1.3a: The Additive Model
  40. 5.02: Nested Treatment Design
  41. 5.2.01: Nested Model in SAS
  42. 5.2.02: Nested Model in Minitab
  43. 5.2.03: Nested Model in R
  44. 5.03: Crossed-Nested Designs
  45. 5.04: Try It
  46. 5.05: Chapter 5 Summary
  47. 5.06: Treatment Design Summary (Optional Enrichment Material)
  48. 06: Random Effects and Introduction to Mixed Models
  49. 6.01: Random Effects
  50. 6.02: Battery Life Example
  51. 6.03: Random Effects in Factorial and Nested Designs
  52. 6.04: Special Case - Fully Nested Random Effects Design
  53. 6.05: Quality Control Example
  54. 6.5.01: Using Minitab
  55. 6.5.02: Using R
  56. 6.06: Introduction to Mixed Models
  57. 6.07: Mixed Model Example
  58. 6.7.01: Using Minitab
  59. 6.7.02: Using SAS
  60. 6.7.03: Using R
  61. 6.08: Complexity Happens
  62. 6.09: Try It
  63. 6.10: Chapter 6 Summary
  64. 07: Randomization Design Part I
  65. 7.01: Experimental Unit and Replication
  66. 7.02: Completely Randomized Design
  67. 7.03: Restriction on Randomization - RCBD
  68. 7.04: Blocking in 2 Dimensions - Latin Square
  69. 7.05: Try It
  70. 7.06: Chapter 7 Summary
  71. 08: Randomization Design Part II
  72. 8.01: Split-Plot Design in RCBD
  73. 8.02: Split-Plot Design in CRD
  74. 8.03: Split-Split-Plot Design
  75. 8.04: Try It
  76. 8.05: Chapter 8 Summary
  77. 09: ANCOVA Part I
  78. 9.01: Role of the Covariate
  79. 9.02: ANCOVA in the GLM Setting - The Covariate as a Regression Variable
  80. 9.03: Steps in ANCOVA
  81. 9.04: Using Technology - Equal Slopes Model
  82. 9.05: Using Technology - Unequal Slopes Model
  83. 9.06: Chapter 9 Summary
  84. 10: ANCOVA Part II
  85. 10.01: ANCOVA with Quantitative Factor Levels
  86. 10.02: Quantitative Predictors - Orthogonal Polynomials
  87. 10.03: Chapter 10 Summary
  88. 11: Introduction to Repeated Measures
  89. 11.01: Historical Methods
  90. 11.02: Correlated Residuals
  91. 11.03: More on Covariance Structures
  92. 11.04: Worked Example
  93. 11.05: Chapter 11 Summary
  94. 12: Cross-over Repeated Measure Designs
  95. 12.01: Introduction to Cross-Over Designs
  96. 12.02: Coding for Carry-Over Covariates
  97. 12.03: Programming for Steer Example
  98. 12.04: Testing the Significance of the Carry-Over Effect
  99. 12.05: Try It
  100. 12.06: Chapter 12 Summary