Statistical Analysis of Geographical Data

Preface xi

1 Dealing with data 1

1.1 The role of statistics in geography 1

1.2 About this book 3

1.3 Data and measurement error 3

2 Collecting and summarizing data 13

2.1 Sampling methods 13

2.2 Graphicalsummaries 17

2.3 Summarizing data numerically 24

3 Probability and sampling distributions 37

3.1 Probability 37

3.2 Probability and the normal distribution: z]scores 39

3.3 Sampling distributions and the central limit theorem 43

4 Estimating parameters with confidence intervals 49

4.1 Confidence intervals on the mean of a normal distribution: the basics 49

4.2 Confidence intervals in practice: the t]distribution 50

4.3 Sample size 53

4.4 Confidence intervals for a proportion 53

5 Comparing datasets 55

5.1 Hypothesis testing with one sample: general principles 55

5.2 Comparing means from small samples: one]sample t]test 61

5.3 Comparing proportions for one sample 63

5.4 Comparing two samples 64

5.5 Non]parametric hypothesis testing 75

6 Comparing distributions: the Chi]squared test 81

6.1 Chi]squared test with one sample 81

6.2 Chi]squared test for two samples 84

7 Analysis of variance 89

7.1 Oneway analysis of variance 90

7.2 Assumptions and diagnostics 99

7.3 Multiple comparison tests after analysis of variance 101

7.4 Non]parametric methods in the analysis of variance 105

7.5 Summary and further applications 106

8 Correlation 109

8.1 Correlation analysis 109

8.2 Pearsonâs product]moment correlation coefficient 110

8.3 Significance tests of correlation coefficient 112

8.4 Spearmanâs rank correlation coefficient 114

8.5 Correlation and causality 116

9 Linear regression 121

9.1 Least]squares linear regression 121

9.2 Scatter plots 122

9.3 Choosing the line of best fit: the âleast]squaresâprocedure 124

9.4 Analysis of residuals 128

9.5 Assumptions and caveats with regression 130

9.6 Is the regression significant? 131

9.7 Coefficient of determination 135

9.8 Confidence intervals and hypothesis tests concerning regression parameters 137

9.9 Reduced major axis regression 140

10 Spatial statistics 145

10.1 Spatial data 145

10.2 Summarizing spatial data 157

10.3 Identifying clusters 159

10.4 Interpolation and plotting contour maps 162

10.5 Spatial relationships 163

11 Time series analysis 173

11.1 Time series in geographical research 173

11.2 Analysing time series 174

Appendix A: Introduction to the R package 193

Appendix B: Statistical tables 205

References 241

Index 243