Preface to the Second Edition xiii Acknowledgements xv About the Companion Website xvii Section I First Principles 1 1 What''s in a Number? 3 1.1 Introduction to Quantitative Analysis 3 1.2 Nature of Numerical Data 7 1.3 Simplifying Mathematical Notation 12 1.4 Introduction to Case Studies and Structure of the Book 16 References 17 Further Reading 17 2 Geographical Data: Quantity and Content 19 2.1 Geographical Data 19 2.2 Populations and Samples 20 2.2.

1 Probability Sampling Techniques 23 2.2.2 Subjective Sampling Techniques 35 2.2.3 Closing Comments on Sampling 38 2.3 Specifying Attributes and Variables 39 2.3.1 Geographical Phenomena as Points 42 2.

3.2 Geographical Phenomena as Lines 44 2.3.3 Geographical Phenomena as Areas 47 2.3.4 Closing Comments on Attributes and Variables 49 References 50 Further Reading 50 3 Geographical Data: Collection and Acquisition 51 3.1 Originating Data 51 3.2 Collection Methods 53 3.

2.1 Field Observation, Measurement and Survey 53 3.2.2 Questionnaire Surveys 57 3.2.2.1 Questionnaire Delivery 57 3.2.

2.2 Question Wording 59 3.2.2.3 Questionnaire Structure 60 3.2.2.4 Questionnaire Design 61 3.

2.3 Administrative Records and Documents 65 3.2.4 Interviewing, Focus Groups and Audio Recording 68 3.2.5 Crowdsourced Data 72 3.2.6 Remotely Sensed Collection Methods 74 3.

2.6.1 Satellite Imagery 76 3.2.6.2 Aerial Photography 78 3.3 Locating Phenomena in Geographical Space 79 References 83 Further Reading 84 Section II Exploring Geographical Data 87 4 Statistical Measures (or Quantities) 89 4.1 Descriptive Statistics 89 4.

2 Spatial Descriptive Statistics 91 4.3 Central Tendency 94 4.3.1 Measures for Non-spatial Data 94 4.3.2 Measures for Spatial Data 97 4.3.3 Distance Measures for Spatial Data 106 4.

4 Dispersion 110 4.4.1 Measures for Non-spatial Data 110 4.4.2 Measures for Spatial Data 112 4.5 Measures of Skewness and Kurtosis for Non-spatial Data 116 4.6 Closing Comments 120 References 121 Further Reading 121 5 Frequency Distributions, Probability and Hypotheses 123 5.1 Frequency Distributions 123 5.

2 Bivariate and Multivariate Frequency Distributions 129 5.3 Estimation of Statistics from Frequency Distributions 136 5.4 Probability 139 5.4.1 Binomial Distribution 142 5.4.2 Poisson Distribution 145 5.4.

3 Normal Distribution 147 5.5 Inference and Hypotheses 153 5.6 Connecting Summary Measures, Frequency Distributions and Probability 157 References 158 Further Reading 159 Section III Testing Times 161 6 Parametric Tests 163 6.1 Introduction to Parametric Tests 163 6.2 One Variable and One Sample 165 6.2.1 Comparing a Sample Mean with a Population Mean 166 6.2.

2 Comparing Differences Between Pairs of Measurements for a Sample Divided into Two Parts 176 6.3 Two Samples and One Variable 178 6.3.1 Comparing Two Sample Means with Population Means 179 6.3.2 Comparing Two-Sample Variances with Population Variances 183 6.4 Three or More Samples and One Variable 187 6.4.

1 Comparing Three or More Sample Means with Population Means 187 6.5 Confidence Intervals 192 6.6 Closing Comments 194 Further Reading 194 7 Non-parametric Tests 197 7.1 Introduction to Non-parametric Tests 197 7.2 One Variable and One Sample 199 7.2.1 Comparing a Sample Mean with a Population Mean 200 7.2.

2 Comparing a Sample''s Nominal Counts with a Population 203 7.2.3 Comparing a Sample''s Ordinal Counts with a Population 207 7.2.4 Comparing the Ordinal Sequence of Dichotomous Outcomes for a Sample with a Population 210 7.3 Two Samples and One (or More) Variable(s) 214 7.3.1 Comparing Two Attributes for One Sample (or One Attribute for Two or More Samples) 215 7.

3.2 Comparing the Medians of an Ordinal Variable for One or Two Samples 219 7.4 Multiple Samples and/or Multiple Variables 223 7.4.1 Comparing Three or More Attributes for One Sample (or Two or More Attributes for Three or More Samples) 224 7.4.2 Comparing the Medians of an Ordinal Variable for Three or More Samples (or One Sample Separated Into Three or More Groups) 224 7.5 Closing Comments 231 Further Reading 231 Section IV Forming an Association or Relationship 233 8 Correlation 235 8.

1 Nature of Relationships Between Variables 235 8.2 Correlation of Normally Distributed Scalar Variables 241 8.2.1 Pearson''s Product Moment Correlation Coefficient 244 8.2.2 Correlating Ordinal Variables 251 8.3 Correlation of Non-normally Distributed or Ordinal Variables 251 8.3.

1 Spearman''s Rank Correlation 251 8.3.2 Kendall''s Tau Correlation Coefficient 256 8.4 Correlation of Nominal Scale Attributes 261 8.4.1 Phi Correlation Coefficient 261 8.4.2 Cramer''s V Correlation Coefficient and the Kappa Index of Agreement 264 8.

5 Closing Comments 264 Further Reading 265 9 Regression 267 9.1 Specification of Linear Relationships 267 9.2 Bivariate Regression 270 9.2.1 Simple Linear (Ordinary Least Squares) Regression 271 9.2.2 Testing the Significance of Simple Linear Regression 279 9.2.

2.1 Testing the Whole OLS Regression Model 279 9.2.2.2 Testing the Constants and Predicted Y Values in OLS Regression 280 9.2.3 Explanatory Power of OLS Regression and Effect of Limits in Range of X Values 285 9.3 Non-linear Bivariate Relationships 287 9.

3.1 Forms of Non-linear and Curvilinear Bivariate Relationship 288 9.3.2 Testing the Significance of Bivariate Polynomial Regression 290 9.4 Complex Relationships 295 9.4.1 Multivariate (Multiple) Regression 295 9.4.

2 Testing the Significance of Multivariate Regression 300 9.5 Closing Comments 304 Reference 305 Further Reading 305 Section V Explicitly Spatial 307 10 Exploring Spatial Aspects of Geographical Data 309 10.1 Location of Spatial Entities 309 10.2 Introduction to Spatial Autocorrelation 311 10.3 Analysis of Spatial Patterns of Points 315 10.3.1 Statistics Based on Distance 315 10.3.

1.1 Nearest Neighbour Analysis 315 10.3.1.2 Ripley''s K Function 319 10.3.2 Statistics Based on Quadrats 323 10.3.

2.1 Variance-Mean Ratio 323 10.3.2.2 Pearson''s Chi-square Test 327 10.4 Analysis of Spatial Patterns of Lines 328 10.5 Analysis of Spatial Patterns of Polygons 331 10.6 Closing Comments 334 References 335 Further Reading 335 11 Analysis and Modelling of Spatial Data 337 11.

1 Introduction 337 11.2 More About Spatial Autocorrelation 338 11.3 Global Spatial Autocorrelation 345 11.3.1 Join Counts Statistics 345 11.3.2 Moran''s I Index with Polygon Features 355 11.3.

3 Significance Testing and the Moran''s I Index 372 11.3.4 Moran''s I Index with Point Features 372 11.3.5 Geary C and Getis-Ord G Statistics 374 11.4 Local Measures of Spatial Association (LISA) 379 11.5 Trend Surface Analysis 387 11.5.

1 Fitting a Global Surface 388 11.5.2 Dealing with Local Variation in a Surface 393 11.6 Geographically Weighted Regression (GWR) 396 11.7 Closing Comments 399 References 403 Further Reading 404 Section VI Practical Application 407 12 Practicalities of Applying, Interpreting and Visualising Quantitative Analysis in Geographical Projects 409 12.1 Introduction 409 12.2 Summary of Results from Quantitative Analysis of Previously Used Datasets 410 12.2.

1 Isle of Wight Residents'' Survey Dataset 410 12.2.2 Les Bossons Glacier Meltwater Stream Dataset 411 12.2.3 Mid-Wales Village Residents'' Shopping Survey 412 12.2.4 Parked Cars and Other Vehicles along One Side of a Road 414 12.2.

5 Pittsburgh Fast Food Restaurants 415 12.2.6 Sample of Farms in South-east England During the Early Years of World War II 415 12.2.7 Moraine Debris on Les Bossons Glacier Outwash (Sandur) Plain 418 12.2.8 Slit Trenches Dug for Defensive Purposes on the South Downs, England, During World War II 419 12.2.

9 Fields Identified for Ploughing Up on Farms on the South Downs, England, During World War II 420 12.2.10 Distribution of Dianthus gratianopolitanus on Mont Cantal in the Auvergne, France 421 12.2.11 Index of Multiple Deprivation in the 33 London Boroughs, 2007 422 12.3 Describing and Presenting Quantitative Results in Geographical Journal Articles 423 12.4 Software for Quantitative Analysis 425 12.4.

1 Data Input and Storage 426 12.4.2 Data Processing and Statistical Software 430 12.5 Introduction to Human and Physical Geography Projects 437 12.5.1 Crime and Deprivation 437 12.5.1.

1 Research Context 437 12.5.1.2 Data and Methods 438 12.5.1.3 Results 439 12.5.

1.4 Discussion and Limitations 442 12.5.2 Pick Your Own Farm Enterprises 444 12.5.2.1 Research Context 444 12.5.

2.2 Data and Methods 445 12.5.2.3 Results 450 12.5.2.4 Discussion and Limitations 453 12.

5.3 Trees and Greenspaces in Urban Environments 454 12.5.3.1 Research Context 454 12.