Nigel Walford is Professor of Applied Geographical Information Systems at Kingston University in the United Kingdom.

• Preface to the Second Edition xiiiAcknowledgements xvAbout the Companion Website xviiSection I First Principles 11 What’s in a Number? 31.1 Introduction to Quantitative Analysis 31.2 Nature of Numerical Data 71.3 Simplifying Mathematical Notation 121.4 Introduction to Case Studies and Structure of the Book 16References 17Further Reading 172 Geographical Data: Quantity and Content 192.1 Geographical Data 192.2 Populations and Samples 202.2.1 Probability Sampling Techniques 232.2.2 Subjective Sampling Techniques 352.2.3 Closing Comments on Sampling 382.3 Specifying Attributes and Variables 392.3.1 Geographical Phenomena as Points 422.3.2 Geographical Phenomena as Lines 442.3.3 Geographical Phenomena as Areas 472.3.4 Closing Comments on Attributes and Variables 49References 50Further Reading 503 Geographical Data: Collection and Acquisition 513.1 Originating Data 513.2 Collection Methods 533.2.1 Field Observation, Measurement and Survey 533.2.2 Questionnaire Surveys 573.2.2.1 Questionnaire Delivery 573.2.2.2 Question Wording 593.2.2.3 Questionnaire Structure 603.2.2.4 Questionnaire Design 613.2.3 Administrative Records and Documents 653.2.4 Interviewing, Focus Groups and Audio Recording 683.2.5 Crowdsourced Data 723.2.6 Remotely Sensed Collection Methods 743.2.6.1 Satellite Imagery 763.2.6.2 Aerial Photography 783.3 Locating Phenomena in Geographical Space 79References 83Further Reading 84Section II Exploring Geographical Data 874 Statistical Measures (or Quantities) 894.1 Descriptive Statistics 894.2 Spatial Descriptive Statistics 914.3 Central Tendency 944.3.1 Measures for Non-spatial Data 944.3.2 Measures for Spatial Data 974.3.3 Distance Measures for Spatial Data 1064.4 Dispersion 1104.4.1 Measures for Non-spatial Data 1104.4.2 Measures for Spatial Data 1124.5 Measures of Skewness and Kurtosis for Non-spatial Data 1164.6 Closing Comments 120References 121Further Reading 1215 Frequency Distributions, Probability and Hypotheses 1235.1 Frequency Distributions 1235.2 Bivariate and Multivariate Frequency Distributions 1295.3 Estimation of Statistics from Frequency Distributions 1365.4 Probability 1395.4.1 Binomial Distribution 1425.4.2 Poisson Distribution 1455.4.3 Normal Distribution 1475.5 Inference and Hypotheses 1535.6 Connecting Summary Measures, Frequency Distributions and Probability 157References 158Further Reading 159Section III Testing Times 1616 Parametric Tests 1636.1 Introduction to Parametric Tests 1636.2 One Variable and One Sample 1656.2.1 Comparing a Sample Mean with a Population Mean 1666.2.2 Comparing Differences Between Pairs of Measurements for a Sample Divided into Two Parts 1766.3 Two Samples and One Variable 1786.3.1 Comparing Two Sample Means with Population Means 1796.3.2 Comparing Two-Sample Variances with Population Variances 1836.4 Three or More Samples and One Variable 1876.4.1 Comparing Three or More Sample Means with Population Means 1876.5 Confidence Intervals 1926.6 Closing Comments 194Further Reading 1947 Non-parametric Tests 1977.1 Introduction to Non-parametric Tests 1977.2 One Variable and One Sample 1997.2.1 Comparing a Sample Mean with a Population Mean 2007.2.2 Comparing a Sample’s Nominal Counts with a Population 2037.2.3 Comparing a Sample’s Ordinal Counts with a Population 2077.2.4 Comparing the Ordinal Sequence of Dichotomous Outcomes for a Sample with a Population 2107.3 Two Samples and One (or More) Variable(s) 2147.3.1 Comparing Two Attributes for One Sample (or One Attribute for Two or More Samples) 2157.3.2 Comparing the Medians of an Ordinal Variable for One or Two Samples 2197.4 Multiple Samples and/or Multiple Variables 2237.4.1 Comparing Three or More Attributes for One Sample (or Two or More Attributes for Three or More Samples) 2247.4.2 Comparing the Medians of an Ordinal Variable for Three or More Samples (or One Sample Separated Into Three or More Groups) 2247.5 Closing Comments 231Further Reading 231Section IV Forming an Association or Relationship 2338 Correlation 2358.1 Nature of Relationships Between Variables 2358.2 Correlation of Normally Distributed Scalar Variables 2418.2.1 Pearson’s Product Moment Correlation Coefficient 2448.2.2 Correlating Ordinal Variables 2518.3 Correlation of Non-normally Distributed or Ordinal Variables 2518.3.1 Spearman’s Rank Correlation 2518.3.2 Kendall’s Tau Correlation Coefficient 2568.4 Correlation of Nominal Scale Attributes 2618.4.1 Phi Correlation Coefficient 2618.4.2 Cramer’s V Correlation Coefficient and the Kappa Index of Agreement 2648.5 Closing Comments 264Further Reading 2659 Regression 2679.1 Specification of Linear Relationships 2679.2 Bivariate Regression 2709.2.1 Simple Linear (Ordinary Least Squares) Regression 2719.2.2 Testing the Significance of Simple Linear Regression 2799.2.2.1 Testing the Whole OLS Regression Model 2799.2.2.2 Testing the Constants and Predicted Y Values in OLS Regression 2809.2.3 Explanatory Power of OLS Regression and Effect of Limits in Range of X Values 2859.3 Non-linear Bivariate Relationships 2879.3.1 Forms of Non-linear and Curvilinear Bivariate Relationship 2889.3.2 Testing the Significance of Bivariate Polynomial Regression 2909.4 Complex Relationships 2959.4.1 Multivariate (Multiple) Regression 2959.4.2 Testing the Significance of Multivariate Regression 3009.5 Closing Comments 304Reference 305Further Reading 305Section V Explicitly Spatial 30710 Exploring Spatial Aspects of Geographical Data 30910.1 Location of Spatial Entities 30910.2 Introduction to Spatial Autocorrelation 31110.3 Analysis of Spatial Patterns of Points 31510.3.1 Statistics Based on Distance 31510.3.1.1 Nearest Neighbour Analysis 31510.3.1.2 Ripley’s K Function 31910.3.2 Statistics Based on Quadrats 32310.3.2.1 Variance–Mean Ratio 32310.3.2.2 Pearson’s Chi-square Test 32710.4 Analysis of Spatial Patterns of Lines 32810.5 Analysis of Spatial Patterns of Polygons 33110.6 Closing Comments 334References 335Further Reading 33511 Analysis and Modelling of Spatial Data 33711.1 Introduction 33711.2 More About Spatial Autocorrelation 33811.3 Global Spatial Autocorrelation 34511.3.1 Join Counts Statistics 34511.3.2 Moran’s I Index with Polygon Features 35511.3.3 Significance Testing and the Moran’s I Index 37211.3.4 Moran’s I Index with Point Features 37211.3.5 Geary C and Getis-Ord G Statistics 37411.4 Local Measures of Spatial Association (LISA) 37911.5 Trend Surface Analysis 38711.5.1 Fitting a Global Surface 38811.5.2 Dealing with Local Variation in a Surface 39311.6 Geographically Weighted Regression (GWR) 39611.7 Closing Comments 399References 403Further Reading 404Section VI Practical Application 40712 Practicalities of Applying, Interpreting and Visualising Quantitative Analysis in Geographical Projects 40912.1 Introduction 40912.2 Summary of Results from Quantitative Analysis of Previously Used Datasets 41012.2.1 Isle of Wight Residents’ Survey Dataset 41012.2.2 Les Bossons Glacier Meltwater Stream Dataset 41112.2.3 Mid-Wales Village Residents’ Shopping Survey 41212.2.4 Parked Cars and Other Vehicles along One Side of a Road 41412.2.5 Pittsburgh Fast Food Restaurants 41512.2.6 Sample of Farms in South-east England During the Early Years of World War II 41512.2.7 Moraine Debris on Les Bossons Glacier Outwash (Sandur) Plain 41812.2.8 Slit Trenches Dug for Defensive Purposes on the South Downs, England, During World War II 41912.2.9 Fields Identified for Ploughing Up on Farms on the South Downs, England, During World War II 42012.2.10 Distribution of Dianthus gratianopolitanus on Mont Cantal in the Auvergne, France 42112.2.11 Index of Multiple Deprivation in the 33 London Boroughs, 2007 42212.3 Describing and Presenting Quantitative Results in Geographical Journal Articles 42312.4 Software for Quantitative Analysis 42512.4.1 Data Input and Storage 42612.4.2 Data Processing and Statistical Software 43012.5 Introduction to Human and Physical Geography Projects 43712.5.1 Crime and Deprivation 43712.5.1.1 Research Context 43712.5.1.2 Data and Methods 43812.5.1.3 Results 43912.5.1.4 Discussion and Limitations 44212.5.2 Pick Your Own Farm Enterprises 44412.5.2.1 Research Context 44412.5.2.2 Data and Methods 44512.5.2.3 Results 45012.5.2.4 Discussion and Limitations 45312.5.3 Trees and Greenspaces in Urban Environments 45412.5.3.1 Research Context 45412.5.3.2 Data and Methods 45412.5.3.3 Results 45612.5.3.4 Discussion and Limitations 46112.6 Closing Comments 464References 465Glossary 467Index 477Plate section: Statistical Analysis Planner and Checklist falls between pages 159 and 161

Nigel Walford is Professor of Applied Geographical Information Systems at Kingston University in the United Kingdom.

• Preface to the Second Edition xiiiAcknowledgements xvAbout the Companion Website xviiSection I First Principles 11 What’s in a Number? 31.1 Introduction to Quantitative Analysis 31.2 Nature of Numerical Data 71.3 Simplifying Mathematical Notation 121.4 Introduction to Case Studies and Structure of the Book 16References 17Further Reading 172 Geographical Data: Quantity and Content 192.1 Geographical Data 192.2 Populations and Samples 202.2.1 Probability Sampling Techniques 232.2.2 Subjective Sampling Techniques 352.2.3 Closing Comments on Sampling 382.3 Specifying Attributes and Variables 392.3.1 Geographical Phenomena as Points 422.3.2 Geographical Phenomena as Lines 442.3.3 Geographical Phenomena as Areas 472.3.4 Closing Comments on Attributes and Variables 49References 50Further Reading 503 Geographical Data: Collection and Acquisition 513.1 Originating Data 513.2 Collection Methods 533.2.1 Field Observation, Measurement and Survey 533.2.2 Questionnaire Surveys 573.2.2.1 Questionnaire Delivery 573.2.2.2 Question Wording 593.2.2.3 Questionnaire Structure 603.2.2.4 Questionnaire Design 613.2.3 Administrative Records and Documents 653.2.4 Interviewing, Focus Groups and Audio Recording 683.2.5 Crowdsourced Data 723.2.6 Remotely Sensed Collection Methods 743.2.6.1 Satellite Imagery 763.2.6.2 Aerial Photography 783.3 Locating Phenomena in Geographical Space 79References 83Further Reading 84Section II Exploring Geographical Data 874 Statistical Measures (or Quantities) 894.1 Descriptive Statistics 894.2 Spatial Descriptive Statistics 914.3 Central Tendency 944.3.1 Measures for Non-spatial Data 944.3.2 Measures for Spatial Data 974.3.3 Distance Measures for Spatial Data 1064.4 Dispersion 1104.4.1 Measures for Non-spatial Data 1104.4.2 Measures for Spatial Data 1124.5 Measures of Skewness and Kurtosis for Non-spatial Data 1164.6 Closing Comments 120References 121Further Reading 1215 Frequency Distributions, Probability and Hypotheses 1235.1 Frequency Distributions 1235.2 Bivariate and Multivariate Frequency Distributions 1295.3 Estimation of Statistics from Frequency Distributions 1365.4 Probability 1395.4.1 Binomial Distribution 1425.4.2 Poisson Distribution 1455.4.3 Normal Distribution 1475.5 Inference and Hypotheses 1535.6 Connecting Summary Measures, Frequency Distributions and Probability 157References 158Further Reading 159Section III Testing Times 1616 Parametric Tests 1636.1 Introduction to Parametric Tests 1636.2 One Variable and One Sample 1656.2.1 Comparing a Sample Mean with a Population Mean 1666.2.2 Comparing Differences Between Pairs of Measurements for a Sample Divided into Two Parts 1766.3 Two Samples and One Variable 1786.3.1 Comparing Two Sample Means with Population Means 1796.3.2 Comparing Two-Sample Variances with Population Variances 1836.4 Three or More Samples and One Variable 1876.4.1 Comparing Three or More Sample Means with Population Means 1876.5 Confidence Intervals 1926.6 Closing Comments 194Further Reading 1947 Non-parametric Tests 1977.1 Introduction to Non-parametric Tests 1977.2 One Variable and One Sample 1997.2.1 Comparing a Sample Mean with a Population Mean 2007.2.2 Comparing a Sample’s Nominal Counts with a Population 2037.2.3 Comparing a Sample’s Ordinal Counts with a Population 2077.2.4 Comparing the Ordinal Sequence of Dichotomous Outcomes for a Sample with a Population 2107.3 Two Samples and One (or More) Variable(s) 2147.3.1 Comparing Two Attributes for One Sample (or One Attribute for Two or More Samples) 2157.3.2 Comparing the Medians of an Ordinal Variable for One or Two Samples 2197.4 Multiple Samples and/or Multiple Variables 2237.4.1 Comparing Three or More Attributes for One Sample (or Two or More Attributes for Three or More Samples) 2247.4.2 Comparing the Medians of an Ordinal Variable for Three or More Samples (or One Sample Separated Into Three or More Groups) 2247.5 Closing Comments 231Further Reading 231Section IV Forming an Association or Relationship 2338 Correlation 2358.1 Nature of Relationships Between Variables 2358.2 Correlation of Normally Distributed Scalar Variables 2418.2.1 Pearson’s Product Moment Correlation Coefficient 2448.2.2 Correlating Ordinal Variables 2518.3 Correlation of Non-normally Distributed or Ordinal Variables 2518.3.1 Spearman’s Rank Correlation 2518.3.2 Kendall’s Tau Correlation Coefficient 2568.4 Correlation of Nominal Scale Attributes 2618.4.1 Phi Correlation Coefficient 2618.4.2 Cramer’s V Correlation Coefficient and the Kappa Index of Agreement 2648.5 Closing Comments 264Further Reading 2659 Regression 2679.1 Specification of Linear Relationships 2679.2 Bivariate Regression 2709.2.1 Simple Linear (Ordinary Least Squares) Regression 2719.2.2 Testing the Significance of Simple Linear Regression 2799.2.2.1 Testing the Whole OLS Regression Model 2799.2.2.2 Testing the Constants and Predicted Y Values in OLS Regression 2809.2.3 Explanatory Power of OLS Regression and Effect of Limits in Range of X Values 2859.3 Non-linear Bivariate Relationships 2879.3.1 Forms of Non-linear and Curvilinear Bivariate Relationship 2889.3.2 Testing the Significance of Bivariate Polynomial Regression 2909.4 Complex Relationships 2959.4.1 Multivariate (Multiple) Regression 2959.4.2 Testing the Significance of Multivariate Regression 3009.5 Closing Comments 304Reference 305Further Reading 305Section V Explicitly Spatial 30710 Exploring Spatial Aspects of Geographical Data 30910.1 Location of Spatial Entities 30910.2 Introduction to Spatial Autocorrelation 31110.3 Analysis of Spatial Patterns of Points 31510.3.1 Statistics Based on Distance 31510.3.1.1 Nearest Neighbour Analysis 31510.3.1.2 Ripley’s K Function 31910.3.2 Statistics Based on Quadrats 32310.3.2.1 Variance–Mean Ratio 32310.3.2.2 Pearson’s Chi-square Test 32710.4 Analysis of Spatial Patterns of Lines 32810.5 Analysis of Spatial Patterns of Polygons 33110.6 Closing Comments 334References 335Further Reading 33511 Analysis and Modelling of Spatial Data 33711.1 Introduction 33711.2 More About Spatial Autocorrelation 33811.3 Global Spatial Autocorrelation 34511.3.1 Join Counts Statistics 34511.3.2 Moran’s I Index with Polygon Features 35511.3.3 Significance Testing and the Moran’s I Index 37211.3.4 Moran’s I Index with Point Features 37211.3.5 Geary C and Getis-Ord G Statistics 37411.4 Local Measures of Spatial Association (LISA) 37911.5 Trend Surface Analysis 38711.5.1 Fitting a Global Surface 38811.5.2 Dealing with Local Variation in a Surface 39311.6 Geographically Weighted Regression (GWR) 39611.7 Closing Comments 399References 403Further Reading 404Section VI Practical Application 40712 Practicalities of Applying, Interpreting and Visualising Quantitative Analysis in Geographical Projects 40912.1 Introduction 40912.2 Summary of Results from Quantitative Analysis of Previously Used Datasets 41012.2.1 Isle of Wight Residents’ Survey Dataset 41012.2.2 Les Bossons Glacier Meltwater Stream Dataset 41112.2.3 Mid-Wales Village Residents’ Shopping Survey 41212.2.4 Parked Cars and Other Vehicles along One Side of a Road 41412.2.5 Pittsburgh Fast Food Restaurants 41512.2.6 Sample of Farms in South-east England During the Early Years of World War II 41512.2.7 Moraine Debris on Les Bossons Glacier Outwash (Sandur) Plain 41812.2.8 Slit Trenches Dug for Defensive Purposes on the South Downs, England, During World War II 41912.2.9 Fields Identified for Ploughing Up on Farms on the South Downs, England, During World War II 42012.2.10 Distribution of Dianthus gratianopolitanus on Mont Cantal in the Auvergne, France 42112.2.11 Index of Multiple Deprivation in the 33 London Boroughs, 2007 42212.3 Describing and Presenting Quantitative Results in Geographical Journal Articles 42312.4 Software for Quantitative Analysis 42512.4.1 Data Input and Storage 42612.4.2 Data Processing and Statistical Software 43012.5 Introduction to Human and Physical Geography Projects 43712.5.1 Crime and Deprivation 43712.5.1.1 Research Context 43712.5.1.2 Data and Methods 43812.5.1.3 Results 43912.5.1.4 Discussion and Limitations 44212.5.2 Pick Your Own Farm Enterprises 44412.5.2.1 Research Context 44412.5.2.2 Data and Methods 44512.5.2.3 Results 45012.5.2.4 Discussion and Limitations 45312.5.3 Trees and Greenspaces in Urban Environments 45412.5.3.1 Research Context 45412.5.3.2 Data and Methods 45412.5.3.3 Results 45612.5.3.4 Discussion and Limitations 46112.6 Closing Comments 464References 465Glossary 467Index 477Plate section: Statistical Analysis Planner and Checklist falls between pages 159 and 161

Nigel Walford is Professor of Applied Geographical Information Systems at Kingston University in the United Kingdom.

• Preface to the Second Edition xiiiAcknowledgements xvAbout the Companion Website xviiSection I First Principles 11 What’s in a Number? 31.1 Introduction to Quantitative Analysis 31.2 Nature of Numerical Data 71.3 Simplifying Mathematical Notation 121.4 Introduction to Case Studies and Structure of the Book 16References 17Further Reading 172 Geographical Data: Quantity and Content 192.1 Geographical Data 192.2 Populations and Samples 202.2.1 Probability Sampling Techniques 232.2.2 Subjective Sampling Techniques 352.2.3 Closing Comments on Sampling 382.3 Specifying Attributes and Variables 392.3.1 Geographical Phenomena as Points 422.3.2 Geographical Phenomena as Lines 442.3.3 Geographical Phenomena as Areas 472.3.4 Closing Comments on Attributes and Variables 49References 50Further Reading 503 Geographical Data: Collection and Acquisition 513.1 Originating Data 513.2 Collection Methods 533.2.1 Field Observation, Measurement and Survey 533.2.2 Questionnaire Surveys 573.2.2.1 Questionnaire Delivery 573.2.2.2 Question Wording 593.2.2.3 Questionnaire Structure 603.2.2.4 Questionnaire Design 613.2.3 Administrative Records and Documents 653.2.4 Interviewing, Focus Groups and Audio Recording 683.2.5 Crowdsourced Data 723.2.6 Remotely Sensed Collection Methods 743.2.6.1 Satellite Imagery 763.2.6.2 Aerial Photography 783.3 Locating Phenomena in Geographical Space 79References 83Further Reading 84Section II Exploring Geographical Data 874 Statistical Measures (or Quantities) 894.1 Descriptive Statistics 894.2 Spatial Descriptive Statistics 914.3 Central Tendency 944.3.1 Measures for Non-spatial Data 944.3.2 Measures for Spatial Data 974.3.3 Distance Measures for Spatial Data 1064.4 Dispersion 1104.4.1 Measures for Non-spatial Data 1104.4.2 Measures for Spatial Data 1124.5 Measures of Skewness and Kurtosis for Non-spatial Data 1164.6 Closing Comments 120References 121Further Reading 1215 Frequency Distributions, Probability and Hypotheses 1235.1 Frequency Distributions 1235.2 Bivariate and Multivariate Frequency Distributions 1295.3 Estimation of Statistics from Frequency Distributions 1365.4 Probability 1395.4.1 Binomial Distribution 1425.4.2 Poisson Distribution 1455.4.3 Normal Distribution 1475.5 Inference and Hypotheses 1535.6 Connecting Summary Measures, Frequency Distributions and Probability 157References 158Further Reading 159Section III Testing Times 1616 Parametric Tests 1636.1 Introduction to Parametric Tests 1636.2 One Variable and One Sample 1656.2.1 Comparing a Sample Mean with a Population Mean 1666.2.2 Comparing Differences Between Pairs of Measurements for a Sample Divided into Two Parts 1766.3 Two Samples and One Variable 1786.3.1 Comparing Two Sample Means with Population Means 1796.3.2 Comparing Two-Sample Variances with Population Variances 1836.4 Three or More Samples and One Variable 1876.4.1 Comparing Three or More Sample Means with Population Means 1876.5 Confidence Intervals 1926.6 Closing Comments 194Further Reading 1947 Non-parametric Tests 1977.1 Introduction to Non-parametric Tests 1977.2 One Variable and One Sample 1997.2.1 Comparing a Sample Mean with a Population Mean 2007.2.2 Comparing a Sample’s Nominal Counts with a Population 2037.2.3 Comparing a Sample’s Ordinal Counts with a Population 2077.2.4 Comparing the Ordinal Sequence of Dichotomous Outcomes for a Sample with a Population 2107.3 Two Samples and One (or More) Variable(s) 2147.3.1 Comparing Two Attributes for One Sample (or One Attribute for Two or More Samples) 2157.3.2 Comparing the Medians of an Ordinal Variable for One or Two Samples 2197.4 Multiple Samples and/or Multiple Variables 2237.4.1 Comparing Three or More Attributes for One Sample (or Two or More Attributes for Three or More Samples) 2247.4.2 Comparing the Medians of an Ordinal Variable for Three or More Samples (or One Sample Separated Into Three or More Groups) 2247.5 Closing Comments 231Further Reading 231Section IV Forming an Association or Relationship 2338 Correlation 2358.1 Nature of Relationships Between Variables 2358.2 Correlation of Normally Distributed Scalar Variables 2418.2.1 Pearson’s Product Moment Correlation Coefficient 2448.2.2 Correlating Ordinal Variables 2518.3 Correlation of Non-normally Distributed or Ordinal Variables 2518.3.1 Spearman’s Rank Correlation 2518.3.2 Kendall’s Tau Correlation Coefficient 2568.4 Correlation of Nominal Scale Attributes 2618.4.1 Phi Correlation Coefficient 2618.4.2 Cramer’s V Correlation Coefficient and the Kappa Index of Agreement 2648.5 Closing Comments 264Further Reading 2659 Regression 2679.1 Specification of Linear Relationships 2679.2 Bivariate Regression 2709.2.1 Simple Linear (Ordinary Least Squares) Regression 2719.2.2 Testing the Significance of Simple Linear Regression 2799.2.2.1 Testing the Whole OLS Regression Model 2799.2.2.2 Testing the Constants and Predicted Y Values in OLS Regression 2809.2.3 Explanatory Power of OLS Regression and Effect of Limits in Range of X Values 2859.3 Non-linear Bivariate Relationships 2879.3.1 Forms of Non-linear and Curvilinear Bivariate Relationship 2889.3.2 Testing the Significance of Bivariate Polynomial Regression 2909.4 Complex Relationships 2959.4.1 Multivariate (Multiple) Regression 2959.4.2 Testing the Significance of Multivariate Regression 3009.5 Closing Comments 304Reference 305Further Reading 305Section V Explicitly Spatial 30710 Exploring Spatial Aspects of Geographical Data 30910.1 Location of Spatial Entities 30910.2 Introduction to Spatial Autocorrelation 31110.3 Analysis of Spatial Patterns of Points 31510.3.1 Statistics Based on Distance 31510.3.1.1 Nearest Neighbour Analysis 31510.3.1.2 Ripley’s K Function 31910.3.2 Statistics Based on Quadrats 32310.3.2.1 Variance–Mean Ratio 32310.3.2.2 Pearson’s Chi-square Test 32710.4 Analysis of Spatial Patterns of Lines 32810.5 Analysis of Spatial Patterns of Polygons 33110.6 Closing Comments 334References 335Further Reading 33511 Analysis and Modelling of Spatial Data 33711.1 Introduction 33711.2 More About Spatial Autocorrelation 33811.3 Global Spatial Autocorrelation 34511.3.1 Join Counts Statistics 34511.3.2 Moran’s I Index with Polygon Features 35511.3.3 Significance Testing and the Moran’s I Index 37211.3.4 Moran’s I Index with Point Features 37211.3.5 Geary C and Getis-Ord G Statistics 37411.4 Local Measures of Spatial Association (LISA) 37911.5 Trend Surface Analysis 38711.5.1 Fitting a Global Surface 38811.5.2 Dealing with Local Variation in a Surface 39311.6 Geographically Weighted Regression (GWR) 39611.7 Closing Comments 399References 403Further Reading 404Section VI Practical Application 40712 Practicalities of Applying, Interpreting and Visualising Quantitative Analysis in Geographical Projects 40912.1 Introduction 40912.2 Summary of Results from Quantitative Analysis of Previously Used Datasets 41012.2.1 Isle of Wight Residents’ Survey Dataset 41012.2.2 Les Bossons Glacier Meltwater Stream Dataset 41112.2.3 Mid-Wales Village Residents’ Shopping Survey 41212.2.4 Parked Cars and Other Vehicles along One Side of a Road 41412.2.5 Pittsburgh Fast Food Restaurants 41512.2.6 Sample of Farms in South-east England During the Early Years of World War II 41512.2.7 Moraine Debris on Les Bossons Glacier Outwash (Sandur) Plain 41812.2.8 Slit Trenches Dug for Defensive Purposes on the South Downs, England, During World War II 41912.2.9 Fields Identified for Ploughing Up on Farms on the South Downs, England, During World War II 42012.2.10 Distribution of Dianthus gratianopolitanus on Mont Cantal in the Auvergne, France 42112.2.11 Index of Multiple Deprivation in the 33 London Boroughs, 2007 42212.3 Describing and Presenting Quantitative Results in Geographical Journal Articles 42312.4 Software for Quantitative Analysis 42512.4.1 Data Input and Storage 42612.4.2 Data Processing and Statistical Software 43012.5 Introduction to Human and Physical Geography Projects 43712.5.1 Crime and Deprivation 43712.5.1.1 Research Context 43712.5.1.2 Data and Methods 43812.5.1.3 Results 43912.5.1.4 Discussion and Limitations 44212.5.2 Pick Your Own Farm Enterprises 44412.5.2.1 Research Context 44412.5.2.2 Data and Methods 44512.5.2.3 Results 45012.5.2.4 Discussion and Limitations 45312.5.3 Trees and Greenspaces in Urban Environments 45412.5.3.1 Research Context 45412.5.3.2 Data and Methods 45412.5.3.3 Results 45612.5.3.4 Discussion and Limitations 46112.6 Closing Comments 464References 465Glossary 467Index 477Plate section: Statistical Analysis Planner and Checklist falls between pages 159 and 161