Statistics for terrified biologists

著者

• Van Emden, Helmut Fritz

書誌事項

Statistics for terrified biologists

Helmut F. van Emden

Wiley Blackwell, 2019

2nd ed

• : pbk

注記

Includes bibliographical references (p. [393]-395) and index

内容説明・目次

内容説明

Makes mathematical and statistical analysis understandable to even the least math-minded biology student This unique textbook aims to demystify statistical formulae for the average biology student. Written in a lively and engaging style, Statistics for Terrified Biologists, 2nd Edition draws on the author's 30 years of lecturing experience to teach statistical methods to even the most guarded of biology students. It presents basic methods using straightforward, jargon-free language. Students are taught to use simple formulae and how to interpret what is being measured with each test and statistic, while at the same time learning to recognize overall patterns and guiding principles. Complemented by simple examples and useful case studies, this is an ideal statistics resource tool for undergraduate biology and environmental science students who lack confidence in their mathematical abilities. Statistics for Terrified Biologists presents readers with the basic foundations of parametric statistics, the t-test, analysis of variance, linear regression and chi-square, and guides them to important extensions of these techniques. It introduces them to non-parametric tests, and includes a checklist of non-parametric methods linked to their parametric counterparts. The book also provides many end-of-chapter summaries and additional exercises to help readers understand and practice what they've learned. Presented in a clear and easy-to-understand style Makes statistics tangible and enjoyable for even the most hesitant student Features multiple formulas to facilitate comprehension Written by of the foremost entomologists of his generation This second edition of Statistics for Terrified Biologists is an invaluable guide that will be of great benefit to pre-health and biology undergraduate students.

目次

Preface to the second edition xv Preface to the first edition xvii 1 How to use this book 1 Introduction 1 The text of the chapters 1 What should you do if you run into trouble? 2 Elephants 3 The numerical examples in the text 3 Boxes 4 Spare-time activities 4 Executive summaries 5 Why go to all that bother? 5 The bibliography 7 2 Introduction 9 What are statistics? 9 Notation 10 Notation for calculating the mean 12 3 Summarising variation 13 Introduction 13 Different summaries of variation 14 Range 14 Total deviation 14 Mean deviation 15 Variance 16 Why n 1? 17 Why are the deviations squared? 18 The standard deviation 19 The next chapter 21 Spare-time activities 21 4 When are sums of squares NOT sums of squares? 23 Introduction 23 Calculating machines offer a quicker method of calculating the sum of squares 24 Added squares 24 The correction factor 24 Avoid being confused by the term sum of squares 24 Summary of the calculator method for calculations as far as the standard deviation 25 Spare-time activities 26 5 The normal distribution 27 Introduction 27 Frequency distributions 27 The normal distribution 28 What percentage is a standard deviation worth? 30 Are the percentages always the same as these? 30 Other similar scales in everyday life 33 The standard deviation as an estimate of the frequency of a number occurring in a sample 33 From percentage to probability 34 Executive Summary 1 - The standard deviation 36 6 The relevance of the normal distribution to biological data 39 To recap 39 Is our observed distribution normal? 41 Checking for normality 42 What can we do about a distribution that clearly is not normal? 42 Transformation 42 Grouping samples 47 Doing nothing! 47 How many samples are needed? 47 Type 1 and Type 2 errors 48 Calculating how many samples are needed 49 7 Further calculations from the normal distribution 51 Introduction 51 Is A bigger than B? 52 The yardstick for deciding 52 The standard error of a difference between two means of three eggs 53 Derivation of the standard error of a difference between two means 53 Step 1: from variance of single data to variance of means 55 Step 2: From variance of single data to variance of differences 57 Step 3: The combination of Steps 1 and 2: the standard error of difference between means (s.e.d.m.) 58 Recap of the calculation of s.e.d.m. from the variance calculated from the individual values 61 The importance of the standard error of differences between means 61 Summary of this chapter 62 Executive Summary 2 - Standard error of a difference between two means 66 Spare-time activities 67 8 Thet-test 69 Introduction 69 The principle of the t-test 70 The t-test in statistical terms 71 Why t? 71 Tables of the t-distribution 72 The standard t-test 75 The procedure 76 The actual t-test 81 t-test for means associated with unequal variances 81 The s.e.d.m. when variances are unequal 82 A worked example of the t-test for means associated with unequal variances 85 The paired t-test 87 Pair when possible 90 Executive Summary 3 - The t-test 92 Spare-time activities 94 9 One tail or two? 95 Introduction 95 Why is the analysis of variance F-test one-tailed? 95 The two-tailed F-test 96 Howmany tails has the t-test? 98 The final conclusion on number of tails 99 10 Analysis of variance (ANOVA): what is it? How does it work? 101 Introduction 101 Sums of squares in ANOVA 102 Some 'made-up' variation to analyse by ANOVA 102 The sum of squares table 104 Using ANOVA to sort out the variation in Table C 104 Phase 1 104 Phase 2 105 SqADS: an important acronym 107 Back to the sum of squares table 108 How well does the analysis reflect the input? 109 End phase 109 Degrees of freedom in ANOVA 110 The completion of the end phase 112 The variance ratio 113 The relationship between t and F 114 Constraints on ANOVA 115 Adequate size of experiment 115 Equality of variance between treatments 117 Testing the homogeneity of variance 117 The element of chance: randomisation 118 Comparison between treatment means in ANOVA 119 The least significant difference 121 A caveat about using the LSD 123 Executive Summary 4 - The principle of ANOVA 124 11 Experimental designs for analysis of variance (ANOVA) 129 Introduction 129 Fully randomised 130 Data for analysis of a fully randomised experiment 131 Prelims 132 Phase 1 132 Phase 2 133 End phase 133 Randomised blocks 135 Data for analysis of a randomised block experiment 137 Prelims 138 Phase 1 139 Phase 2 140 End phase 141 Incomplete blocks 142 Latin square 145 Data for the analysis of a Latin square 145 Prelims 146 Phase 1 150 Phase 2 150 End phase 151 Further comments on the Latin square design 152 Split plot 154 Types of analysis of variance 154 One- and two-way analysis of variance 155 Fixed-, random-, and mixed-effects analysis of variance 156 Executive Summary 5 - Analysis of a one-way randomised block experiment 158 Spare-time activities 159 12 Introduction to factorial experiments 163 What is a factorial experiment? 163 Interaction: what does it mean biologically? 165 If there is no interaction 167 What if there IS interaction? 167 How about a biological example? 168 Measuring any interaction between factors is often the main/only purpose of an experiment 170 How does a factorial experiment change the form of the analysis of variance? 171 Degrees of freedom for interactions 171 The similarity between the residual in Phase 2 and the interaction in Phase 3 172 Sums of squares for interactions 172 13 2-Factor factorial experiments 175 Introduction 175 An example of a 2-factor experiment 175 Analysis of the 2-factor experiment 176 Prelims 176 Phase 1 177 Phase 2 177 End phase (of Phase 2) 178 Phase 3 179 End phase (of Phase 3) 183 Two important things to remember about factorials before tackling the next chapter 185 Analysis of factorial experiments with unequal replication 185 Executive Summary 6 - Analysis of a 2-factor randomised block experiment 188 Spare-time activity 190 14 Factorial experiments with more than two factors - leave this out if you wish! 191 Introduction 191 Different 'orders' of interaction 191 Example of a 4-factor experiment 192 Prelims 194 Phase 1 196 Phase 2 196 Phase 3 197 To the end phase 205 Spare-time activity 214 15 Factorial experiments with split plots 217 Introduction 217 Deriving the split plot design from the randomised block design 218 Degrees of freedom in a split plot analysis 221 Main plots 221 Sub-plots 222 Numerical example of a split plot experiment and its analysis 224 Calculating the sums of squares 225 End phase 229 Comparison of split plot and randomised block experiments 229 Uses of split plot designs 233 Spare-time activity 235 16 The t-test in the analysis of variance 237 Introduction 237 Brief recap of relevant earlier sections of this book 238 Least significant difference test 239 Multiple range tests 240 Operating the multiple range test 242 Testing differences between means 246 My rules for testing differences between means 246 Presentation of the results of tests of differences between means 247 The results of the experiments analysed by analysis of variance in Chapters 11-15 249 Fully randomised design (p. 131) 250 Randomised block experiment (p. 137) 251 Latin square design (p. 146) 253 2-Factor experiment (p. 176) 255 4-Factor experiment (p. 195) 257 Split plot experiment (p. 224) 259 Some final advice 261 Spare-time activities 261 17 Linear regression and correlation 263 Introduction 263 Cause and effect 264 Other traps waiting for you to fall into 264 Extrapolating beyond the range of your data 264 Is a straight line appropriate? 265 The distribution of variability 268 Regression 268 Independent and dependent variables 272 The regression coefficient (b) 272 Calculating the regression coefficient (b) 275 The regression equation 281 A worked example on some real data 282 The data 282 Calculating the regression coefficient (b), i.e. the slope of the regression line 282 Calculating the intercept (a) 284 Drawing the regression line 285 Testing the significance of the slope (b) of the regression 286 How well do the points fit the line? The coefficient of determination (r2) 290 Correlation 291 Derivation of the correlation coefficient (r) 291 An example of correlation 292 Is there a correlation line? 293 Extensions of regression analysis 296 Nonlinear regression 297 Multiple linear regression 298 Multiple nonlinear regression 300 Executive Summary - Linear regression 301 Spare time activities 303 18 Analysis of covariance (ANCOVA) 305 Introduction 305 A worked example of ANCOVA 307 Data: cholesterol levels of subjects given different diets 307 Data: ages of subjects in experiment 308 Regression of cholesterol level on age 309 The structure of the ANCOVA table 312 Total sum of squares 313 Residual sum of squares 314 Corrected means 316 Test for significant difference between means 316 Executive Summary 8 - Analysis of covariance (ANCOVA) 319 Spare-time activity 320 19 Chi-square tests 323 Introduction 323 When not and where not to use 𝜒 2 324 The problem of low frequencies 325 Yates' correction for continuity 325 The 𝜒 2 test for goodness of fit 326 The case of more than two classes 328 𝜒 2 with heterogeneity 331 Heterogeneity 𝜒 2 Analysis with 'Covariance' 333 Association (or contingency) 𝜒 2 335 2 x 2 contingency table 336 Fisher's exact test for a 2 x 2 table 338 Larger contingency tables 340 Interpretation of contingency tables 341 Spare-time activities 343 20 Nonparametric methods (what are they?) 345 Disclaimer 345 Introduction 346 Advantages and disadvantages of parametric and nonparametric methods 347 Where nonparametric methods score 347 Where parametric methods score 349 Some ways data are organised for nonparametric tests 349 The sign test 350 The Kruskal-Wallis analysis of ranks 350 Kendall's rank correlation coefficient 352 The main nonparametric methods that are available 353 Analysis of two replicated treatments as in the t-test (Chapter 8) 353 Analysis of more than two replicated treatments as in the analysis of variance (Chapter 11) 354 Correlation of two variables (Chapter 17) 354 Appendix A How many replicates? 355 Appendix B Statistical tables 365 Appendix C Solutions to spare-time activities 373 Appendix D Bibliography 393 Index 397

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詳細情報

• NII書誌ID(NCID): BB28740649
• ISBN:
  • 9781119563679
• LCCN: 2019001708
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Hoboken, N.J.
• ページ数/冊数: xix, 402 p.
• 大きさ: 23 cm
• 分類:
  • LCC : QH323.5
  • DC22 : 570.1/5195
• 件名:
  • LCSH : Biometry -- Textbooks