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| Preface | |
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| Introduction | |
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| What do we mean by statistics? | |
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| Why is statistics necessary? | |
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| Statistics in field biology | |
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| The limitations of statistics | |
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| The purpose of this text | |
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| Measurement and Sampling Concepts | |
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| Populations, samples and observations | |
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| Counting things--the sampling unit | |
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| Random sampling | |
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| Random numbers | |
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| Independence | |
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| Statistics and parameters | |
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| Descriptive and inferential statistics | |
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| Parametric and non-parametric statistics | |
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| Processing Data | |
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| Scales of measurement | |
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| The nominal scale | |
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| The ordinal scale | |
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| The interval scale | |
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| The ratio scale | |
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| Conversion of interval observations to an ordinal scale | |
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| Derived variables | |
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| The precision of observations | |
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| How precise should we be? | |
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| The frequency table | |
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| Aggregating frequency classes | |
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| Frequency distribution of count observations | |
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| Dispersion | |
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| Bivariate data | |
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| Presenting Data | |
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| Introduction | |
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| Dot plot or line plot | |
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| Bar graph | |
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| Histogram | |
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| Frequency polygon and frequency curve | |
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| Scattergram (scatter plot) | |
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| Circle or pie graph | |
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| Measuring the Average | |
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| What is an average? | |
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| The mean | |
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| The median--a resistant statistic | |
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| The mode | |
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| Relationship between the mean, median and mode | |
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| Measuring Variability | |
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| Variability | |
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| The range | |
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| The standard deviation | |
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| Calculating the standard deviation | |
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| Calculating the standard deviation from grouped data | |
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| Variance | |
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| An alternative formula for calculating the variance and standard deviation | |
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| Obtaining the standard deviation, variance and the sum of squares from a calculator | |
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| Degrees of freedom | |
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| The coefficient of variation | |
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| Probability | |
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| The meaning of probability | |
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| Compound probabilities | |
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| Probability distribution | |
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| Models of probability distribution | |
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| The binomial probability distribution | |
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| The Poisson probability distribution | |
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| The negative binomial probability distribution | |
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| Critical probability | |
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| Probability Distributions as Models of Dispersion | |
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| Dispersion | |
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| An Index of Dispersion | |
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| Choosing a model of dispersion | |
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| The binomial model | |
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| Poisson model | |
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| The negative binomial model | |
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| Deciding the goodness of fit | |
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| The Normal Distribution | |
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| The normal curve | |
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| Some mathematical properties of the normal curve | |
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| Standardizing the normal curve | |
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| Two-tailed or one-tailed? | |
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| Small samples: the t-distribution | |
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| Are our data 'normal'? | |
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| Data Transformation | |
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| The need for transformation | |
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| The logarithmic transformation | |
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| When there are zero counts--the arcsinh transformation | |
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| The square root transformation | |
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| The arcsine transformation | |
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| Back-transforming transformed numbers | |
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| Is data transformation really necessary? | |
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| How Good are our Estimates? | |
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| Sampling error | |
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| The distribution of a sample mean | |
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| The confidence interval of the mean of a large sample | |
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| The confidence interval of the mean of a small sample | |
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| The confidence interval of the mean of a sample of count data | |
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| The difference between the means of two large samples | |
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| The difference between the means of two small samples | |
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| Estimating a proportion | |
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| Estimating a Lincoln Index | |
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| Estimating a diversity index | |
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| The distribution of a variance--chi-square distribution | |
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| The Basis of Statistical Testing | |
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| Introduction | |
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| The experimental hypothesis | |
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| The statistical hypothesis | |
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| Test statistics | |
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| One-tailed tests and two-tailed tests | |
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| Hypothesis testing and the normal curve | |
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| Type 1 and type 2 errors | |
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| Parametric and non-parametric statistics: some further observations | |
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| The power of a test | |
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| Analysing Frequencies | |
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| The chi-square test | |
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| Calculating the x[superscript 2] test statistic | |
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| A practical example of a test for homogeneous frequencies | |
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| The problem of independence | |
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| One degree of freedom--Yates' correction | |
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| Goodness of fit tests | |
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| Tests for association--the contingency table | |
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| The r [times] c contingency table | |
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| The G-test | |
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| Applying the G-test to a one-way classification of frequencies | |
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| Applying the G-test to a 2 [times] 2 contingency table | |
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| Applying the G-test to an r [times] c contingency table | |
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| Advice on analysing frequencies | |
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| Measuring Correlations | |
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| The meaning of correlation | |
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| Investigating correlation | |
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| The strength and significance of a correlation | |
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| Covariance | |
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| The Product Moment Correlation Coefficient | |
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| The coefficient of determination r[superscript 2] | |
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| The Spearman Rank Correlation Coefficient r[subscript s] | |
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| Advice on measuring correlations | |
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| Regression Analysis | |
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| Introduction | |
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| Gradients and triangles | |
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| Dependent and independent variables | |
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| A perfect rectilinear relationship | |
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| The line of least squares | |
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| Simple linear regression | |
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| Fitting the regression line to the scattergram | |
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| The error of a regression line | |
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| Confidence limits of an individual estimate | |
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| The significance of the regression line | |
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| The difference between two regression lines | |
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| Dealing with curved relationships | |
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| Transformation of both axes | |
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| Regression through the origin | |
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| An alternative line of best fit | |
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| Advice on using regression analysis | |
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| Comparing Averages | |
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| Introduction | |
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| Matched and unmatched observations | |
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| The Mann--Whitney U-test for unmatched samples | |
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| Advice on using the Mann--Whitney U-test | |
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| More than two samples--the Kruskal--Wallis test | |
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| Advice on using the Kruskal--Wallis test | |
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| The Wilcoxon test for matched pairs | |
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| Advice on using the Wilcoxon test for matched pairs | |
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| Comparing means--parametric tests | |
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| The F-test (two-tailed) | |
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| The z-test for comparing the means of two large samples | |
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| The t-test for comparing the means of two small samples | |
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| The t-test for matched pairs | |
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| Advice on comparing means | |
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| Analysis of Variance--ANOVA | |
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| Why do we need ANOVA? | |
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| How ANOVA works | |
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| Procedure for computing one-way ANOVA | |
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| Procedure for computing the Tukey test | |
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| Two-way ANOVA | |
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| Procedure for computing two-way ANOVA | |
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| Procedure for computing the Tukey test in two-way ANOVA | |
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| Two-way ANOVA with single observations | |
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| The randomized block design | |
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| The Latin square | |
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| Analysis of variance in regression | |
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| Advice on using ANOVA | |
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| Multivariate Analysis | |
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| Introduction | |
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| What is information? | |
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| Making large problems manageable | |
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| Are there three groups or four? | |
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| Learning from experience? | |
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| Variations on a theme | |
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| Summary | |
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| Appendices | |
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| Table of random numbers | |
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| t-distribution | |
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| X[superscript 2]-distribution | |
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| Critical values of Spearman's Rank Correlation Coefficient | |
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| Product moment correlation values at the 0.05 and 0.01 levels of significance | |
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| Mann--Whitney U-test values (two-tailed test) P = 0.05 | |
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| Critical values of T in the Wilcoxon test for two matched samples | |
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| F-distribution, 0.05 level of significance, two-tailed test | |
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| Critical values of F[subscript max] 0.05 level of significance | |
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| F-distribution | |
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| Tukey test | |
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| Symbols | |
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| Matrices and vectors | |
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| Computer packages | |
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| Bibliography and further reading | |
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| Index | |