Enhanced descriptions from Syndetics:

Practical Statistics for Field Biology, 2nd Edition

Provides an excellent introductory text for students on the principles and methods of statistical analysis in the life sciences, helping them choose and analyse statistical tests for their own problems and present their findings.

An understanding of statistical principles and methods is essential for any scientist but is particularly important for those in the life sciences. The field biologist faces very particular problems and challenges with statistics as "real-life" situations such as collecting insects with a sweep net or counting seagulls on a cliff face can hardly be expected to be as reliable or controllable as a laboratory-based experiment. Acknowledging the peculiarites of field-based data and its interpretation, this book provides a superb introduction to statistical analysis helping students relate to their particular and often diverse data with confidence and ease.

To enhance the usefulness of this book, the new edition incorporates the more advanced method of multivariate analysis, introducing the nature of multivariate problems and describing the the techniques of principal components analysis, cluster analysis and discriminant analysis which are all applied to biological examples. An appendix detailing the statistical computing packages available has also been included.

It will be extremely useful to undergraduates studying ecology, biology, and earth and environmental sciences and of interest to postgraduates who are not familiar with the application of multiavirate techniques and practising field biologists working in these areas.

Table of contents provided by Syndetics

• Preface (p. xi)
• 1 Introduction (p. 1)
• 1.1 What do we mean by statistics? (p. 1)
• 1.2 Why is statistics necessary? (p. 1)
• 1.3 Statistics in field biology (p. 2)
• 1.4 The limitations of statistics (p. 2)
• 1.5 The purpose of this text (p. 2)
• 2 Measurement and Sampling Concepts (p. 3)
• 2.1 Populations, samples and observations (p. 3)
• 2.2 Counting things--the sampling unit (p. 3)
• 2.3 Random sampling (p. 5)
• 2.4 Random numbers (p. 5)
• 2.5 Independence (p. 6)
• 2.6 Statistics and parameters (p. 6)
• 2.7 Descriptive and inferential statistics (p. 7)
• 2.8 Parametric and non-parametric statistics (p. 7)
• 3 Processing Data (p. 8)
• 3.1 Scales of measurement (p. 8)
• 3.2 The nominal scale (p. 8)
• 3.3 The ordinal scale (p. 8)
• 3.4 The interval scale (p. 9)
• 3.5 The ratio scale (p. 9)
• 3.6 Conversion of interval observations to an ordinal scale (p. 10)
• 3.7 Derived variables (p. 10)
• 3.8 The precision of observations (p. 12)
• 3.9 How precise should we be? (p. 13)
• 3.10 The frequency table (p. 13)
• 3.11 Aggregating frequency classes (p. 14)
• 3.12 Frequency distribution of count observations (p. 16)
• 3.13 Dispersion (p. 17)
• 3.14 Bivariate data (p. 17)
• 4 Presenting Data (p. 18)
• 4.1 Introduction (p. 18)
• 4.2 Dot plot or line plot (p. 18)
• 4.3 Bar graph (p. 19)
• 4.4 Histogram (p. 20)
• 4.5 Frequency polygon and frequency curve (p. 22)
• 4.6 Scattergram (scatter plot) (p. 23)
• 4.7 Circle or pie graph (p. 24)
• 5 Measuring the Average (p. 26)
• 5.1 What is an average? (p. 26)
• 5.2 The mean (p. 26)
• 5.3 The median--a resistant statistic (p. 28)
• 5.4 The mode (p. 32)
• 5.5 Relationship between the mean, median and mode (p. 33)
• 6 Measuring Variability (p. 35)
• 6.1 Variability (p. 35)
• 6.2 The range (p. 35)
• 6.3 The standard deviation (p. 36)
• 6.4 Calculating the standard deviation (p. 37)
• 6.5 Calculating the standard deviation from grouped data (p. 38)
• 6.6 Variance (p. 39)
• 6.7 An alternative formula for calculating the variance and standard deviation (p. 39)
• 6.8 Obtaining the standard deviation, variance and the sum of squares from a calculator (p. 40)
• 6.9 Degrees of freedom (p. 40)
• 6.10 The coefficient of variation (p. 41)
• 7 Probability (p. 42)
• 7.1 The meaning of probability (p. 42)
• 7.2 Compound probabilities (p. 43)
• 7.3 Probability distribution (p. 44)
• 7.4 Models of probability distribution (p. 45)
• 7.5 The binomial probability distribution (p. 46)
• 7.6 The Poisson probability distribution (p. 54)
• 7.7 The negative binomial probability distribution (p. 56)
• 7.8 Critical probability (p. 59)
• 8 Probability Distributions as Models of Dispersion (p. 62)
• 8.1 Dispersion (p. 62)
• 8.2 An Index of Dispersion (p. 63)
• 8.3 Choosing a model of dispersion (p. 66)
• 8.4 The binomial model (p. 67)
• 8.5 Poisson model (p. 68)
• 8.6 The negative binomial model (p. 70)
• 8.7 Deciding the goodness of fit (p. 73)
• 9 The Normal Distribution (p. 74)
• 9.1 The normal curve (p. 74)
• 9.2 Some mathematical properties of the normal curve (p. 75)
• 9.3 Standardizing the normal curve (p. 76)
• 9.4 Two-tailed or one-tailed? (p. 77)
• 9.5 Small samples: the t-distribution (p. 79)
• 9.6 Are our data 'normal'? (p. 81)
• 10 Data Transformation (p. 83)
• 10.1 The need for transformation (p. 83)
• 10.2 The logarithmic transformation (p. 84)
• 10.3 When there are zero counts--the arcsinh transformation (p. 86)
• 10.4 The square root transformation (p. 87)
• 10.5 The arcsine transformation (p. 87)
• 10.6 Back-transforming transformed numbers (p. 88)
• 10.7 Is data transformation really necessary? (p. 89)
• 11 How Good are our Estimates? (p. 90)
• 11.1 Sampling error (p. 90)
• 11.2 The distribution of a sample mean (p. 90)
• 11.3 The confidence interval of the mean of a large sample (p. 92)
• 11.4 The confidence interval of the mean of a small sample (p. 93)
• 11.5 The confidence interval of the mean of a sample of count data (p. 94)
• 11.6 The difference between the means of two large samples (p. 96)
• 11.7 The difference between the means of two small samples (p. 98)
• 11.8 Estimating a proportion (p. 99)
• 11.9 Estimating a Lincoln Index (p. 100)
• 11.10 Estimating a diversity index (p. 101)
• 11.11 The distribution of a variance--chi-square distribution (p. 102)
• 12 The Basis of Statistical Testing (p. 104)
• 12.1 Introduction (p. 104)
• 12.2 The experimental hypothesis (p. 104)
• 12.3 The statistical hypothesis (p. 105)
• 12.4 Test statistics (p. 106)
• 12.5 One-tailed tests and two-tailed tests (p. 107)
• 12.6 Hypothesis testing and the normal curve (p. 108)
• 12.7 Type 1 and type 2 errors (p. 108)
• 12.8 Parametric and non-parametric statistics: some further observations (p. 109)
• 12.9 The power of a test (p. 110)
• 13 Analysing Frequencies (p. 111)
• 13.1 The chi-square test (p. 111)
• 13.2 Calculating the x[superscript 2] test statistic (p. 112)
• 13.3 A practical example of a test for homogeneous frequencies (p. 114)
• 13.4 The problem of independence (p. 115)
• 13.5 One degree of freedom--Yates' correction (p. 116)
• 13.6 Goodness of fit tests (p. 116)
• 13.7 Tests for association--the contingency table (p. 117)
• 13.8 The r [times] c contingency table (p. 120)
• 13.9 The G-test (p. 122)
• 13.10 Applying the G-test to a one-way classification of frequencies (p. 122)
• 13.11 Applying the G-test to a 2 [times] 2 contingency table (p. 124)
• 13.12 Applying the G-test to an r [times] c contingency table (p. 126)
• 13.13 Advice on analysing frequencies (p. 128)
• 14 Measuring Correlations (p. 130)
• 14.1 The meaning of correlation (p. 130)
• 14.2 Investigating correlation (p. 130)
• 14.3 The strength and significance of a correlation (p. 132)
• 14.4 Covariance (p. 133)
• 14.5 The Product Moment Correlation Coefficient (p. 135)
• 14.6 The coefficient of determination r[superscript 2] (p. 137)
• 14.7 The Spearman Rank Correlation Coefficient r[subscript s] (p. 138)
• 14.8 Advice on measuring correlations (p. 141)
• 15 Regression Analysis (p. 142)
• 15.1 Introduction (p. 142)
• 15.2 Gradients and triangles (p. 142)
• 15.3 Dependent and independent variables (p. 144)
• 15.4 A perfect rectilinear relationship (p. 145)
• 15.5 The line of least squares (p. 146)
• 15.6 Simple linear regression (p. 147)
• 15.7 Fitting the regression line to the scattergram (p. 150)
• 15.8 The error of a regression line (p. 150)
• 15.9 Confidence limits of an individual estimate (p. 152)
• 15.10 The significance of the regression line (p. 154)
• 15.11 The difference between two regression lines (p. 154)
• 15.12 Dealing with curved relationships (p. 156)
• 15.13 Transformation of both axes (p. 158)
• 15.14 Regression through the origin (p. 160)
• 15.15 An alternative line of best fit (p. 161)
• 15.16 Advice on using regression analysis (p. 163)
• 16 Comparing Averages (p. 165)
• 16.1 Introduction (p. 165)
• 16.2 Matched and unmatched observations (p. 165)
• 16.3 The Mann--Whitney U-test for unmatched samples (p. 166)
• 16.4 Advice on using the Mann--Whitney U-test (p. 167)
• 16.5 More than two samples--the Kruskal--Wallis test (p. 168)
• 16.6 Advice on using the Kruskal--Wallis test (p. 169)
• 16.7 The Wilcoxon test for matched pairs (p. 170)
• 16.8 Advice on using the Wilcoxon test for matched pairs (p. 172)
• 16.9 Comparing means--parametric tests (p. 172)
• 16.10 The F-test (two-tailed) (p. 173)
• 16.11 The z-test for comparing the means of two large samples (p. 174)
• 16.12 The t-test for comparing the means of two small samples (p. 175)
• 16.13 The t-test for matched pairs (p. 176)
• 16.14 Advice on comparing means (p. 178)
• 17 Analysis of Variance--ANOVA (p. 179)
• 17.1 Why do we need ANOVA? (p. 179)
• 17.2 How ANOVA works (p. 180)
• 17.3 Procedure for computing one-way ANOVA (p. 181)
• 17.4 Procedure for computing the Tukey test (p. 184)
• 17.5 Two-way ANOVA (p. 187)
• 17.6 Procedure for computing two-way ANOVA (p. 190)
• 17.7 Procedure for computing the Tukey test in two-way ANOVA (p. 194)
• 17.8 Two-way ANOVA with single observations (p. 195)
• 17.9 The randomized block design (p. 198)
• 17.10 The Latin square (p. 202)
• 17.11 Analysis of variance in regression (p. 207)
• 17.12 Advice on using ANOVA (p. 208)
• 18 Multivariate Analysis (p. 210)
• 18.1 Introduction (p. 210)
• 18.2 What is information? (p. 211)
• 18.3 Making large problems manageable (p. 211)
• 18.4 Are there three groups or four? (p. 220)
• 18.5 Learning from experience? (p. 225)
• 18.6 Variations on a theme (p. 233)
• 18.7 Summary (p. 233)
• Appendices
• Appendix 1 Table of random numbers (p. 235)
• Appendix 2 t-distribution (p. 236)
• Appendix 3 X[superscript 2]-distribution (p. 237)
• Appendix 4 Critical values of Spearman's Rank Correlation Coefficient (p. 238)
• Appendix 5 Product moment correlation values at the 0.05 and 0.01 levels of significance (p. 239)
• Appendix 6 Mann--Whitney U-test values (two-tailed test) P = 0.05 (p. 240)
• Appendix 7 Critical values of T in the Wilcoxon test for two matched samples (p. 241)
• Appendix 8 F-distribution, 0.05 level of significance, two-tailed test (p. 242)
• Appendix 9 Critical values of F[subscript max] 0.05 level of significance (p. 243)
• Appendix 10 F-distribution (p. 244)
• Appendix 11 Tukey test (p. 248)
• Appendix 12 Symbols (p. 250)
• Appendix 13 Matrices and vectors (p. 251)
• Appendix 14 Computer packages (p. 255)
• Bibliography and further reading (p. 256)
• Index (p. 257)

Author notes provided by Syndetics

Jim Fowler, Principal Lecturer, Department of Biological Sciences, De Montfort University, Leicester, UK.

Lou Cohen, Emeritus Professor of Education, Loughborough University of Technology, Loughborough, UK.

Phil Jarvis, Senior Statistician, Safety of Medicines, Zeneca Pharmaceuticals, Macclesfield, UK.