Using Statistics to Understand the Environment

Evaluating and using statistics is an essential part of environmental science courses from pollution studies to environmental management and ecology. This text focuses on the needs of the researcher and provides a concise student-friendly introduction to this core area of Environmental Studies. Statistics for Environmental Investigationscovers all the basic tests required for environmental projects and points the way to the more advanced techniques.

Series editors' preface

ix

List of figures

xi

List of tables

xiv

List of boxes

xvi

List of worked examples

xviii

Acknowledgements

xx

Using this book

xxii

Project design

1

(24)

Variables

3

(1)

Populations, samples and individuals

3

(1)

Observations and manipulations

4

(1)

Sampling

5

(2)

Block designs

7

(1)

The block design in manipulative experiments

7

(1)

Sampling people

8

(5)

Questionnaire design

10

(2)

Semi-structured and unstructured interviews

12

(1)

Sample size

13

(1)

Independence of data

14

(1)

Sources of error

15

(3)

Data types

18

(3)

Data records

21

(1)

Summary

22

(1)

Questions

23

(2)

Describing data

25

(25)

Descriptive statistics

25

(14)

Frequency tables

26

(1)

Frequency histograms

26

(4)

Measures of central tendency

30

(2)

Measuring variation of normally distributed data

32

(5)

Reliability of the sample mean

37

(2)

Measuring variation of ordinal or non-normal data

39

(1)

Methods of presenting data

39

(8)

Presenting measures of central tendency

40

(3)

Presenting relationships between variables

43

(1)

Cross-tabulation of data

44

(3)

General guidelines for drawing graphs and charts

47

(1)

Summary

47

(1)

Questions

48

(2)

Using statistics to answer questions

50

(17)

Hypothesis testing

50

(5)

Statistical tests

55

(10)

Transforming data

58

(1)

Square root transformation

59

(1)

Logarithmic transformation

60

(1)

Other transformations to correct skewness

60

(1)

Arcsine transformation

61

(1)

Back-transformation of descriptive statistics

62

(1)

Choosing a statistical test

62

(3)

Summary

65

(1)

Questions

66

(1)

Differences between two samples

67

(22)

Unmatched comparisons

68

(11)

t test

69

(5)

Mann--Whitney U test

74

(5)

Matched-pair tests

79

(6)

Paired t test

80

(3)

Wilcoxon matched-pairs test

83

(2)

Summary

85

(1)

Questions

86

(3)

Relationships between variables

89

(32)

Correlations

92

(8)

Pearson's product moment correlation coefficient

94

(3)

Spearman's rank correlation coefficient

97

(3)

Regression

100

(14)

Testing the significance of the regression line

105

(5)

Using the regression equation as a predictive model

110

(1)

Assumptions of simple linear regression

110

(4)

Fitting a regression line through the origin

114

(1)

Relationships between more than two variables

114

(2)

Correlation matrix

114

(1)

Multiple correlation

115

(1)

Concordance

116

(1)

Multiple regression and logistic regression

116

(1)

Summary

116

(1)

Questions

117

(4)

Analysing frequency data

121

(14)

Associations between frequency distributions

121

(8)

The special case of 2 x 2 contingency tables

127

(2)

Goodness of fit against theoretical distributions

129

(3)

The special case of two-category goodness of fit tests

130

(1)

Goodness of fit against model distributions

131

(1)

Assumptions of chi-square frequency analysis

132

(1)

Fisher's exact test and G tests

132

(1)

Testing for associations between more than two distributions

133

(1)

Summary

133

(1)

Questions

134

(1)

Differences between more than two samples

135

(57)

Parametric one-way analysis of variance

136

(14)

Testing for equality of variances

137

(2)

Calculating the F statistic for ANOVA

139

(5)

Multiple comparison tests with equal sample sizes: the Tukey test

144

(3)

Multiple comparison tests with unequal sample sizes: the Tukey--Kramer test

147

(3)

Kruskal--Wallis one-way anlysis of variance using ranks

150

(9)

Multiple comparison tests with equal sample sizes: the Nemenyi test

154

(2)

Multiple comparison tests with unequal sample sizes: Dunn's test

156

(3)

Parametric two-way analysis of variance

159

(14)

Interpretation of significant interactions

166

(4)

Two-way ANOVA with single observations in each cell

170

(3)

Two-way analysis of variance using ranks

173

(10)

Friedman's matched group analysis of variance using ranks

178

(5)

Testing specific hypotheses

183

(1)

Other models of analysis of variance

183

(3)

More than two independent variables

184

(1)

Analysing Latin square designs

184

(1)

Nested analysis of variance

184

(1)

Analysis of covariance

185

(1)

Multivariate analysis of variance

185

(1)

Summary

186

(1)

Questions

187

(5)

Glossary

192

(13)

Definitions of statistical terms

192

(10)

Mathematical symbols

202

(3)

Appendix A Basic mathematical methods and notation

205

(2)

Appendix B Using statistical software

207

(8)

Appendix C Further reading

215

(2)

Selected texts

215

(1)

Statistical tables

216

(1)

Appendix D Statistical tables

217

(10)

Appendix E Answers to exercises

227

(14)

Chapter 1

227

(2)

Chapter 2

229

(2)

Chapter 3

231

(1)

Chapter 4

232

(1)

Chapter 5

233

(2)

Chapter 6

235

(1)

Chapter 7

236

(5)

References

241

(2)

Index

243

(3)

Key to commonly used statistical tests

246

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Using Statistics to Understand the Environment

Summary

Table of Contents

Supplemental Materials