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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.

Statistics for Terrified Biologists, 2nd Edition

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 ? 2 324





The problem of low frequencies 325





Yates' correction for continuity 325





The ? 2 test for goodness of fit 326





The case of more than two classes 328





? 2 with heterogeneity 331





Heterogeneity ? 2 Analysis with 'Covariance' 333





Association (or contingency) ? 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