## Randomization, Bootstrap and Monte Carlo Methods in Biology, Third EditionModern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific disciplines. This new edition of the bestselling Randomization, Bootstrap and Monte Carlo Methods in Biology illustrates the value of a number of these methods with an emphasis on biological applications. This textbook focuses on three related areas in computational statistics: randomization, bootstrapping, and Monte Carlo methods of inference. The author emphasizes the sampling approach within randomization testing and confidence intervals. Similar to randomization, the book shows how bootstrapping, or resampling, can be used for confidence intervals and tests of significance. It also explores how to use Monte Carlo methods to test hypotheses and construct confidence intervals. New to the Third Edition Providing comprehensive coverage of computer-intensive applications while also offering data sets online, Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition supplies a solid foundation for the ever-expanding field of statistics and quantitative analysis in biology. |

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### Contents

Randomization | 1 |

12 Examples of Randomization Tests | 4 |

13 Aspects of Randomization Testing Raised by the Examples | 14 |

14 Confidence Limits by Randomization | 18 |

15 Applications of Randomization in Biology and Related Areas | 21 |

16 Randomization and Observational Studies | 25 |

17 Chapter Summary | 26 |

The Jackknife | 29 |

92 The Mantel Test | 205 |

93 Sampling the Randomization Distribution | 207 |

94 Confidence Limits for Regression Coefficients | 210 |

95 The Multiple Mantel Test | 212 |

96 Other Approaches with More Than Two Matrices | 213 |

97 Further Reading | 230 |

98 Chapter Summary | 232 |

Other Analyses on Spatial Data | 239 |

22 Applications of Jackknifing in Biology | 35 |

23 Chapter Summary | 40 |

The Bootstrap | 41 |

32 Standard Bootstrap Confidence Limits | 42 |

33 Simple Percentile Confidence Limits | 46 |

34 BiasCorrected Percentile Confidence Limits | 52 |

35 Accelerated BiasCorrected Percentile Limits | 57 |

36 Other Methods for Constructing Confidence Intervals | 65 |

37 Transformations to Improve Bootstrapt Intervals | 68 |

38 Parametric Confidence Intervals | 70 |

310 Bootstrap Tests of Significance | 71 |

311 Balanced Bootstrap Sampling | 74 |

313 Further Reading | 78 |

314 Chapter Summary | 79 |

Monte Carlo Methods | 81 |

42 Generalized Monte Carlo Tests | 84 |

43 Implicit Statistical Models | 86 |

44 Applications of Monte Carlo Methods in Biology | 88 |

45 Chapter Summary | 90 |

Some General Considerations | 93 |

52 Power | 94 |

54 Determining a Randomization Distribution Exactly | 99 |

55 The Number of Replications for Confidence Intervals | 101 |

56 More Efficient Bootstrap Sampling Methods | 103 |

58 The Generation of Random Permutations | 104 |

59 Chapter Summary | 105 |

One and TwoSample Tests | 107 |

62 The OneSample Randomization Test | 112 |

63 The TwoSample Randomization Test | 113 |

64 Bootstrap Tests | 116 |

65 Randomizing Residuals | 117 |

66 Comparing the Variation in Two Samples | 119 |

67 A Simulation Study | 122 |

68 The Comparison of Two Samples on Multiple Measurements | 124 |

69 Further Reading | 129 |

610 Chapter Summary | 130 |

Analysis of Variance | 135 |

72 Tests for Constant Variance | 137 |

73 Testing for Mean Differences Using Residuals | 138 |

74 Examples of More Complicated Types of Analysis of Variance | 143 |

75 Procedures for Handling Unequal Variances | 161 |

76 Other Aspects of Analysis of Variance | 162 |

77 Further Reading | 163 |

78 Chapter Summary | 165 |

Regression Analysis | 169 |

82 Randomizing Residuals | 171 |

83 Testing for a Nonzero 𝛽 Value | 175 |

85 Multiple Linear Regression | 176 |

86 Alternative Randomization Methods with Multiple Regression | 180 |

87 Bootstrapping and Jackknifing with Regression | 196 |

88 Further Reading | 197 |

89 Chapter Summary | 200 |

Distance Matrices and Spatial Data | 203 |

103 Meads Randomization Test | 240 |

104 Tests for Randomness Based on Distances | 245 |

105 Testing for an Association between Two Point Patterns | 247 |

106 The BesagDiggle Test | 248 |

107 Tests Using Distances between Points | 250 |

108 Testing for Random Marking | 252 |

109 Further Reading | 255 |

1010 Chapter Summary | 256 |

Time Series | 261 |

112 Randomization Tests for Serial Correlation | 262 |

113 Randomization Tests for Trend | 267 |

114 Randomization Tests for Periodicity | 274 |

115 Irregularly Spaced Series | 281 |

116 Tests on Times of Occurrence | 283 |

117 Discussion on Procedures for Irregular Series | 285 |

118 Bootstrap Methods | 290 |

1110 ModelBased vs MovingBlock Resampling | 292 |

1111 Further Reading | 294 |

1112 Chapter Summary | 297 |

Multivariate Data | 301 |

123 Comparison of Sample Mean Vectors | 302 |

124 ChiSquared Analyses for Count Data | 312 |

125 Comparison of Variations for Several Samples | 314 |

127 Discriminant Function Analysis | 317 |

128 Further Reading | 320 |

129 Chapter Summary | 321 |

Survival and Growth Data | 325 |

132 Bootstrapping for Variable Selection | 327 |

133 Bootstrapping for Model Selection | 329 |

134 Group Comparisons | 330 |

135 Growth Data | 331 |

136 Further Reading | 336 |

137 Chapter Summary | 337 |

Nonstandard Situations | 341 |

143 Alternative Switching Algorithms | 351 |

144 Examining Time Changes in Niche Overlap | 354 |

145 Probing Multivariate Data with Random Skewers | 360 |

146 Ant Species Sizes in Europe | 365 |

147 Chapter Summary | 370 |

Bayesian Methods | 371 |

152 The Gibbs Sampler and Related Methods | 372 |

153 Biological Applications | 377 |

154 Further Reading | 378 |

155 Chapter Summary | 379 |

Final Comments | 381 |

162 Bootstrapping | 382 |

164 Classical vs Bayesian Inference | 383 |

References | 385 |

Software for ComputerIntensive Statistics | 435 |

439 | |

449 | |

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### Common terms and phrases

algorithm alternative analysis of variance approach approximately assess bias-corrected bootstrap distribution bootstrap samples bootstrap test calculated CM CM CM colonies comparing comparison computer-intensive confidence interval confidence limits data values determined differences between months discussed domization effects Efron environmental estimated evidence example F value F-distribution F-statistic genetic give groups habitat involves islands jackknife jackknife estimate Levene's test linear lizards Manly Mantel test matrix mean difference Monte Carlo methods Monte Carlo test multivariate normal distribution null hypothesis o o o o o o o o o observed data observed value Ol Ol parameter percentage percentile method permutations population possible probability procedure random allocation random sample randomiza randomization distribution randomization test randomizing observations randomizing residuals regression coefficient resampling rH rH sample mean sets of data shown in Table significance level significant results similar simulation situation spatial species standard deviation sum of squares test statistic tion variables variation zero

### Popular passages

Page 397 - Faith, DP (1991). Cladistic permutation tests for monophyly and nonmonophyly. Systematic Zoology 40: 366-75.