Statistical Design And Analysis Of Biological Experiments

✍ Scribed by Hans-Michael Kaltenbach

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 281
• Series: Statistics For Biology And Health
• Edition: 1st Edition
• Category: Library

✦ Synopsis

This richly illustrated book provides an overview of the design and analysis of experiments with a focus on non-clinical experiments in the life sciences, including animal research. It covers the most common aspects of experimental design such as handling multiple treatment factors and improving precision. In addition, it addresses experiments with large numbers of treatment factors and response surface methods for optimizing experimental conditions or biotechnological yields. The book emphasizes the estimation of effect sizes and the principled use of statistical arguments in the broader scientific context. It gradually transitions from classical analysis of variance to modern linear mixed models, and provides detailed information on power analysis and sample size determination, including ‘portable power’ formulas for making quick approximate calculations. In turn, detailed discussions of several real-life examples illustrate the complexities and aberrations that can arise in practice. Chiefly intended for students, teachers and researchers in the fields of experimental biology and biomedicine, the book is largely self-contained and starts with the necessary background on basic statistical concepts. The underlying ideas and necessary mathematics are gradually introduced in increasingly complex variants of a single example. Hasse diagrams serve as a powerful method for visualizing and comparing experimental designs and deriving appropriate models for their analysis. Manual calculations are provided for early examples, allowing the reader to follow the analyses in detail. More complex calculations rely on the statistical software R, but are easily transferable to other software. Though there are few prerequisites for effectively using the book, previous exposure to basic statistical ideas and the software R would be advisable.

✦ Table of Contents

Preface......Page 7
Contents......Page 9
1.1 Introduction......Page 15
1.2 A Cautionary Tale......Page 16
1.3 The Language of Experimental Design......Page 17
1.4 Experiment Validity......Page 18
1.4.2 Internal Validity......Page 19
1.4.3 External Validity......Page 21
1.5.1 Randomization of Treatment Allocation......Page 22
1.5.2 Blinding......Page 23
1.5.3 Analysis Plan and Registration......Page 24
1.6 Notes and Summary......Page 25
References......Page 26
2.2.1 Random Variables and Distributions......Page 28
2.2.2 Quantiles......Page 29
2.2.3 Independence and Conditional Distributions......Page 30
2.2.4 Expectation and Variance......Page 31
2.2.5 Covariance and Correlation......Page 34
2.2.6 Some Important Distributions......Page 36
2.3 Estimation......Page 40
2.3.1 Properties of Estimators......Page 41
2.3.2 Estimators of Expectation and Variance......Page 42
2.3.3 Standard Error and Precision......Page 44
2.3.4 Confidence Intervals......Page 45
2.3.5 Estimation for Comparing Two Samples......Page 48
2.4.1 The Logic of Falsification......Page 54
2.4.3 p-Values and Statistical Significance......Page 56
2.4.4 Four Additional Test Statistics......Page 60
2.5 Notes and Summary......Page 62
References......Page 64
3.2 Balancing Allocation......Page 66
3.3.1 Sub-sampling......Page 68
3.3.3 Blocking......Page 69
3.4 Sample Size and Precision......Page 70
3.4.1 Sample Size for Desired Precision......Page 71
3.5 Sample Size and Power......Page 72
3.5.1 Power Analysis for Known Variance......Page 73
3.5.2 Power Analysis for Unknown Variance......Page 75
3.5.4 `Observed Power' and Related Fallacies......Page 78
3.6 Notes and Summary......Page 80
References......Page 81
4.2 Experiment and Data......Page 82
4.3 One-Way Analysis of Variance......Page 83
4.3.1 Testing Equality of Means by Comparing Variances......Page 84
4.3.2 Analysis of Variance......Page 85
4.3.3 Effect Size Measures......Page 88
4.4 Power Analysis and Sample Size for Omnibus F-test......Page 89
4.4.1 General Idea......Page 90
4.4.2 Defining the Minimal Effect Size......Page 91
4.4.3 Calculating Power......Page 92
4.4.5 Portable Power......Page 94
4.5 Hasse Diagrams and Linear Model Specification......Page 95
4.5.1 Hasse Diagrams of Experiment Structure......Page 96
4.5.2 The Linear Model......Page 100
4.5.3 Analysis of Variance in R......Page 101
4.6.1 Analysis of Variance......Page 103
4.6.2 Estimating the Grand Mean......Page 104
4.7 Notes and Summary......Page 105
References......Page 109
5.2 Linear Contrasts......Page 110
5.2.1 Defining Contrasts......Page 111
5.2.2 Estimating Contrasts......Page 112
5.2.3 Testing Contrasts......Page 114
5.2.5 Orthogonal Contrasts and ANOVA Decomposition......Page 115
5.2.6 Contrasts for Ordered Factors......Page 117
5.2.7 Standardized Effect Size......Page 120
5.2.8 Power Analysis and Sample Size......Page 121
5.3.1 Introduction......Page 122
5.3.2 General Purpose: Bonferroni–Holm......Page 124
5.3.4 Comparisons Against a Reference: Dunnett......Page 125
5.3.5 General Purpose and Post-Hoc Contrasts: Scheffé......Page 126
5.3.6 Remarks......Page 127
5.4 A Real-Life Example—Drug Metabolization......Page 128
5.5 Notes and Summary......Page 131
References......Page 133
6.2 Experiment......Page 134
6.3.1 Linear Model......Page 137
6.3.2 Analysis of Variance......Page 139
6.3.3 Interpretation of Main Effects......Page 142
6.3.4 Interpretation of Interactions......Page 143
6.3.5 Effect Sizes......Page 145
6.3.6 Model Reduction and Marginality Principle......Page 146
6.3.7 Estimated Marginal Means......Page 147
6.3.8 A Real-Life Example—Drug Metabolization Continued......Page 148
6.4.1 Advantage of Factorial Treatment Design......Page 149
6.4.2 One Observation per Cell......Page 150
6.4.3 Higher-Order Factorials......Page 154
6.5 Unbalanced Data......Page 156
6.5.1 All-Cells-Filled Data......Page 157
6.6 Contrast Analysis......Page 161
6.6.2 Interaction Contrasts......Page 162
6.7 Power Analysis and Sample Size......Page 164
6.7.2 Interactions......Page 165
6.7.3 Contrasts......Page 166
6.8 Notes and Summary......Page 167
References......Page 169
7.1 Introduction......Page 170
7.2.2 Model and Hasse Diagram......Page 171
7.2.3 Contrasts......Page 177
7.2.4 Evaluating and Choosing a Blocking Factor......Page 178
7.2.5 Power Analysis and Sample Size......Page 180
7.2.6 Replication Within Blocks......Page 182
7.2.7 Fixed Blocking Factors......Page 183
7.2.8 Factorial Treatment Structure......Page 184
7.3.1 Introduction......Page 187
7.3.2 Defining a Balanced Incomplete Block Design......Page 188
7.3.3 Analysis......Page 189
7.3.4 Contrasts......Page 192
7.3.5 A Real-Life Example—Between-Plates Variability......Page 193
7.3.7 Reference Designs......Page 194
7.4.2 Nesting Blocks......Page 196
7.4.3 Crossing Blocks: Latin Squares......Page 197
7.5 Notes and Summary......Page 202
References......Page 204
8.1 Introduction......Page 205
8.2.1 Experiment......Page 206
8.2.2 Hasse Diagram......Page 207
8.2.3 Analysis of Variance......Page 208
8.2.5 Contrast Analysis......Page 209
8.3 A Historical Example—Oat Varieties......Page 210
8.4.1 Accommodating an Additional Factor......Page 214
8.4.3 Criss-Cross or Split-Block Designs......Page 216
8.4.4 Cross-Over Designs......Page 218
8.4.5 Pretest-Posttest Designs......Page 221
8.5 Notes and Summary......Page 222
References......Page 224
9.1 Introduction......Page 225
9.2.1 Introduction......Page 226
9.2.2 Effect Estimates......Page 227
9.2.3 Reduction to Four Treatment Combinations......Page 228
9.2.4 The Half-Replicate or Fractional Factorial......Page 230
9.3.1 Using Generators......Page 231
9.4 A Real-Life Example—Yeast Medium Composition......Page 233
9.4.1 Experimental Design......Page 234
9.4.2 Analysis......Page 235
9.5 Multiple Aliasing......Page 236
9.5.1 A Generic 2^{5-2}-Fractional Factorial......Page 237
9.5.3 A Real-Life Example—2^{7-2}-Fractional Factorial......Page 238
9.6.1 Resolution......Page 239
9.6.2 Aberration......Page 240
9.7.1 Fractional Factorials......Page 241
9.8 Blocking Factorial Experiments......Page 242
9.8.2 Half-Fraction with Alternating Replication......Page 243
9.8.4 Half-Fraction with Multiple Generators......Page 245
9.8.6 A Real-Life Example—Proteomics......Page 247
9.9 Notes and Summary......Page 249
References......Page 252
10.1 Introduction......Page 253
10.2 Response Surface Methodology......Page 254
10.3.2 Path of Steepest Ascent......Page 256
10.3.3 Experimental Design......Page 257
10.3.4 Example—Yeast Medium Optimization......Page 258
10.4.1 Model......Page 260
10.4.3 Experimental Design......Page 261
10.4.4 Sequential Experiments......Page 263
10.5 A Real-Life Example—Yeast Medium Optimization......Page 264
10.5.1 First Response Surface Exploration......Page 265
10.5.2 First Path of Steepest Ascent......Page 266
10.5.3 Second Response Surface Exploration......Page 268
10.5.4 Second Path of Steepest Ascent......Page 269
10.5.5 Conclusion......Page 270
10.6 Notes and Summary......Page 271
References......Page 272
Index......Page 273

✦ Subjects

Statistical Theory And Methods