Efnisyfirlit

• CONTENTS
• Preface
• 1 Introduction
  • 1.1 What do we mean by statistics?
  • 1.2 Why is statistics necessary?
  • 1.3 Statistics in field biology
  • 1.4 The limitations of statistics
  • 1.5 The purpose of this text
• 2 Measurement and Sampling Concepts
  • 2.1 Populations, samples and observations
  • 2.2 Counting things – the sampling unit
  • 2.3 Random sampling
  • 2.4 Random numbers
  • 2.5 Independence
  • 2.6 Statistics and parameters
  • 2.7 Descriptive and inferential statistics
  • 2.8 Parametric and non-parametric statistics
• 3 Processing Data
  • 3.1 Scales of measurement
  • 3.2 The nominal scale
  • 3.3 The ordinal scale
  • 3.4 The interval scale
  • 3.5 The ratio scale
  • 3.6 Conversion of interval observations to an ordinal scale
  • 3.7 Derived variables
  • 3.8 The precision of observations
  • 3.9 How precise should we be?
  • 3.10 The frequency table
  • 3.11 Aggregating frequency classes
  • 3.12 Frequency distribution of count observations
  • 3.13 Dispersion
  • 3.14 Bivariate data
• 4 Presenting Data
  • 4.1 Introduction
  • 4.2 Dot plot or line plot
  • 4.3 Bar graph
  • 4.4 Histogram
  • 4.5 Frequency polygon and frequency curve
  • 4.6 Scattergram (scatter plot)
  • 4.7 Circle or pie graph
• 5 Measuring the Average
  • 5.1 What is an average?
  • 5.2 The mean
  • 5.3 The median – a resistant statistic
  • 5.4 The mode
  • 5.5 Relationship between the mean, median and mode
• 6 Measuring Variability
  • 6.1 Variability
  • 6.2 The range
  • 6.3 The standard deviation
  • 6.4 Calculating the standard deviation
  • 6.5 Calculating the standard deviation from grouped data
  • 6.6 Variance
  • 6.7 An alternative formula for calculating the variance and standard deviation
  • 6.8 Obtaining the standard deviation, variance and the sum of squares from a calculator
  • 6.9 Degrees of freedom
  • 6.10 The coefficient of variation
• 7 Probability
  • 7.1 The meaning of probability
  • 7.2 Compound probabilities
  • 7.3 Probability distribution
  • 7.4 Models of probability distribution
  • 7.5 The binomial probability distribution
  • 7.6 The Poisson probability distribution
  • 7.7 The negative binomial probability distribution
  • 7.8 Critical probability
• 8 Probability Distributions as Models of Dispersion
  • 8.1 Dispersion
  • 8.2 An Index of Dispersion
  • 8.3 Choosing a model of dispersion
  • 8.4 The binomial model
  • 8.5 Poisson model
  • 8.6 The negative binomial model
  • 8.7 Deciding the goodness of fit
• 9 The Normal Distribution
  • 9.1 The normal curve
  • 9.2 Some mathematical properties of the normal curve
  • 9.3 Standardizing the normal curve
  • 9.4 Two-tailed or one-tailed?
  • 9.5 Small samples: the t-distribution
  • 9.6 Are our data 'normal'?
• 10 Data Transformation
  • 10.1 The need for transformation
  • 10.2 The logarithmic transformation
  • 10.3 When there are zero counts – the arcsinh transformation
  • 10.4 The square root transformation
  • 10.5 The arcsine transformation
  • 10.6 Back-transforming transformed numbers
  • 10.7 Is data transformation really necessary?
• 11 How Good are our Estimates?
  • 11.1 Sampling error
  • 11.2 The distribution of a sample mean
  • 11.3 The confidence interval of the mean of a large sample
  • 11.4 The confidence interval of the mean of a small sample
  • 11.5 The confidence interval of the mean of a sample of count data
  • 11.6 The difference between the means of two large samples
  • 11.7 The difference between the means of two small samples
  • 11.8 Estimating a proportion
  • 11.9 Estimating a Lincoln Index
  • 11.10 Estimating a diversity index
  • 11.11 The distribution of a variance – chi-square distribution
• 12 The Basis of Statistical Testing
  • 12.1 Introduction
  • 12.2 The experimental hypothesis
  • 12.3 The statistical hypothesis
  • 12.4 Test statistics
  • 12.5 One-tailed tests and two-tailed tests
  • 12.6 Hypothesis testing and the normal curve
  • 12.7 Type 1 and type 2 errors
  • 12.8 Parametric and non-parametric statistics: some further observations
  • 12.9 The power of a test
• 13 Analysing Frequencies
  • 13.1 The chi-square test
  • 13.2 Calculating the x2 test statistic
  • 13.3 A practical example of a test for homogeneous frequencies
  • 13.4 The problem of independence
  • 13.5 One degree of freedom – Yates' correction
  • 13.6 Goodness of fit tests
  • 13.7 Tests for association – the contingency table
  • 13.8 The r x c contingency table
  • 13.9 The G-test
  • 13.10 Applying the G-test to a one-way classification of frequencies
  • 13.11 Applying the G-test to a 2 x 2 contingency table
  • 13.12 Applying the G-test to an r x c contingency table
  • 13.13 Advice on analysing frequencies
• 14 Measuring Correlations
  • 14.1 The meaning of correlation
  • 14.2 Investigating correlation
  • 14.3 The strength and significance of a correlation
  • 14.4 Covariance
  • 14.5 The Product Moment Correlation Coefficient
  • 14.6 The coefficient of determination r2
  • 14.7 The Spearman Rank Correlation Coefficient rs
  • 14.8 Advice on measuring correlations
• 15 Regression Analysis
  • 15.1 Introduction
  • 15.2 Gradients and triangles
  • 15.3 Dependent and independent variables
  • 15.4 A perfect rectilinear relationship
  • 15.5 The line of least squares
  • 15.6 Simple linear regression
  • 15.7 Fitting the regression line to the scattergram
  • 15.8 The error of a regression line
  • 15.9 Confidence limits of an individual estimate
  • 15.10 The significance of the regression line
  • 15.11 The difference between two regression lines
  • 15.12 Dealing with curved relationships
  • 15.13 Transformation of both axes
  • 15.14 Regression through the origin
  • 15.15 An alternative line of best fit
  • 15.16 Advice on using regression analysis
• 16 Comparing Averages
  • 16.1 Introduction
  • 16.2 Matched and unmatched observations
  • 16.3 The Mann–Whitney U-test for unmatched samples
  • 16.4 Advice on using the Mann–Whitney U-test
  • 16.5 More than two samples – the Kruskal–Wallis test
  • 16.6 Advice on using the Kruskal-Wallis test
  • 16.7 The Wilcoxon test for matched pairs
  • 16.8 Advice on using the Wilcoxon test for matched pairs
  • 16.9 Comparing means – parametric tests
  • 16.10 The F-test (two-tailed)
  • 16.11 The z-test for comparing the means of two large samples
  • 16.12 The t-test for comparing the means of two small samples
  • 16.13 The t-test for matched pairs
  • 16.14 Advice on comparing means
• 17 Analysis of Variance – ANOVA
  • 17.1 Why do we need ANOVA?
  • 17.2 How ANOVA works
  • 17.3 Procedure for computing one-way ANOVA
  • 17.4 Procedure for computing the Tukey test
  • 17.5 Two-way ANOVA
  • 17.6 Procedure for computing two-way ANOVA
  • 17.7 Procedure for computing the Tukey test in two-way ANOVA
  • 17.8 Two-way ANOVA with single observations
  • 17.9 The randomized block design
  • 17.10 The Latin square
  • 17.11 Analysis of variance in regression
  • 17.12 Advice on using ANOVA
• 18 Multivariate Analysis
  • 18.1 Introduction
  • 18.2 What is information?
  • 18.3 Making large problems manageable
  • 18.4 Are there three groups or four?
  • 18.5 Learning from experience?
  • 18.6 Variations on a theme
  • 18.7 Summary
• Appendices
  • Appendix 1: Table of random numbers
  • Appendix 2: t-distribution
  • Appendix 3: x2-distribution
  • Appendix 4: Critical values of Spearman's Rank Correlation Coefficient
  • Appendix 5: Product moment correlation values at the 0.05 and 0.01 levels of significance
  • Appendix 6: Mann–Whitney U-test values (two-tailed test) P = 0.05
  • Appendix 7: Critical values of T in the Wilcoxon test for two matched samples
  • Appendix 8: F-distribution, 0.05 level of significance, two-tailed test
  • Appendix 9: Critical values of Fmax 0.05 level of significance
  • Appendix 10: F-distribution
  • Appendix 11: Tukey test
  • Appendix 12: Symbols
  • Appendix 13: Matrices and vectors
  • Appendix 14: Computer packages
• Bibliography and further reading
• Index

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