Statistical Analysis of Geographic

Statistical Analysis and Modeling of Geographic Information with ArcView GIS is an update to Lee and Wong's Statistical Analysis with ArcView GIS, featuring expanded coverage of classical statistical methods, probability and statistical testing, new student exercises to facilitate classroom use, new exercises featuring interactive ArcView Avenue scripts, and a new overview of compatible spatial analytical functions in ArcGIS 9.0.

David W. S. Wong, PhD, is Professor and Chair of the Earth Systems and GeoInformation Sciences Program at George Mason University in Fairfax, Virginia.

Jay Lee, PhD, is Professor and Chair of the Department of Geography at Kent State University in Kent, Ohio.

Preface

xiii

Acknowledgments

xvii

Introduction

1

(44)

Why Statistics and Sampling?

1

(5)

What Are Special about Spatial Data?

6

(5)

MAUP---The Modifiable Areal Unit Problem

7

(2)

Spatial Autocorrelation

9

(2)

Spatial Data and the Need for Spatial Analysis/Statistics

11

(2)

Fundamentals of Spatial Analysis and Statistics

13

(15)

Scales of Measurement

13

(9)

Mathematical Notations

22

(3)

Scale, Extent, and Projection

25

(3)

ArcView Notes---Data Model and Examples

28

(17)

Data Model Used in ArcView GIS

30

(1)

Random Sampling---the Generic Way

30

(5)

Random and Systematic Point Sampling---an Extended Function

35

(6)

References

41

(1)

Exercises

42

(3)

PART I CLASSICAL STATISTICS

45

(138)

Distribution Descriptors: One Variable (Univariate)

47

(46)

Measures of Central Tendency

47

(9)

Mode

48

(2)

Median

50

(2)

Mean

52

(3)

Grouped or Weighted Mean

55

(1)

Measures of Dispersion

56

(9)

Range, Minimum, Maximum, and Percentiles

57

(1)

Mean Deviation

58

(2)

Variance and Standard Deviation

60

(3)

Weighted Variance and Weighted Standard Deviation

63

(2)

Coefficient of Variation

65

(1)

ArcView Examples

65

(4)

Descriptive Statistics

66

(3)

Higher Moment Statistics

69

(5)

Skewness and Kurtosis

69

(5)

ArcView Examples

74

(10)

Additional Statistics

81

(3)

Application Example

84

(7)

Summary

91

(2)

References

91

(1)

Exercises

91

(2)

Relationship Descriptors: Two Variables (Bivariate)

93

(34)

Correlation Analysis

94

(3)

Correlation: Nominal Scale

97

(6)

Nominal Scale and Binary: Phi Coefficient

97

(3)

Nominal Scale and Polychotomous: Chi-Square Statistic

100

(3)

Correlation: Ordinal Scale

103

(2)

Correlation: Interval/Ratio Scale

105

(3)

Trend Analysis

108

(7)

Simple Linear Regression Models

108

(3)

Coefficient of Determination

111

(1)

Empirical Examples

112

(3)

ArcView Notes

115

(7)

Application Examples

122

(5)

Reference

124

(1)

Exercises

124

(3)

Hypothesis Testers

127

(56)

Probability Concepts

128

(2)

Probability Functions

130

(11)

Binomial Distribution

131

(2)

Poisson Distribution

133

(3)

Normal Distribution

136

(4)

ArcView Notes

140

(1)

Central Limit Theorem and Confidence Intervals

141

(2)

Hypothesis Testing

143

(3)

ArcView Notes

146

(1)

Types of Error

146

(1)

Parametric Test Statistics

146

(7)

Difference in Variances

147

(1)

ArcView Note

148

(5)

Difference in Means

153

(10)

Small Sample Size

153

(3)

Large Sample Size

156

(1)

ArcView Note

157

(6)

Difference Between a Mean and a Fixed Value

163

(1)

ArcView Note

164

(1)

Significance of Pearson's Correlation Coefficient

164

(4)

ArcView Note

165

(3)

Significance of Regression Parameters

168

(4)

ArcView Note

169

(3)

Testing Nonparametric Statistics

172

(6)

Chi-Square Statistic

172

(1)

ArcView Note

173

(2)

Spearman's Rank Correlation Coefficient

175

(1)

ArcView Note

176

(1)

Kolmogorov-Smirnov Test

176

(2)

ArcView Note

178

(1)

Summary

178

(5)

References

179

(1)

Exercises

179

(4)

PART II SPATIAL STATISTICS

183

(236)

Point Pattern Descriptors

185

(33)

The Nature of Point Features

185

(2)

Central Tendency of Point Distributions

187

(10)

Mean Center

189

(3)

Weighted Mean Center

192

(3)

Median Center

195

(2)

Dispersion and Orientation of Point Distributions

197

(11)

Standard Distance

198

(5)

Standard Deviational Ellipses

203

(5)

ArcView Notes

208

(6)

Application Examples

214

(4)

References

215

(1)

Exercises

216

(2)

Point Pattern Analyzers

218

(62)

Scale and Extent

219

(2)

Quadrat Analysis

221

(16)

General Concepts in Quadrat Analysis

222

(4)

Comparing Observed and Expected Distributions Using the K-S test

226

(6)

Comparing Observed and Expected Patterns Using the Variance-Mean Ratio

232

(5)

Ordered Neighbor Analysis

237

(16)

Nearest Neighbor Statistic

239

(4)

Testing for Pattern Using the Nearest Neighbor Statistic

243

(3)

Higher-Order Neighbor Statistics

246

(2)

Boundary Adjustments of the Nearest Neighbor Statistics

248

(5)

K-Function

253

(7)

Spatial Autocorrelation of Points

260

(10)

Measures for Spatial Autocorrelation

261

(3)

Significance Testing of Spatial Autocorrelation Measures

264

(6)

Application Examples

270

(10)

References

275

(2)

Exercises

277

(3)

Line Pattern Analyzers

280

(47)

The Nature of Linear Features: Vectors and Networks

280

(3)

Characteristics and Attributes of Linear Features

283

(6)

Geometric Characteristics of Linear Features

283

(1)

Spatial Attributes of Linear Features: Length

284

(2)

Spatial Attributes of Linear Features: Orientation and Direction

286

(1)

ArcView Example: Linear Attributes

287

(2)

Directional Statistics

289

(15)

Exploring Statistics for Liner Features

290

(4)

Directional Mean

294

(5)

Circular Variance

299

(3)

ArcView Example: Directional Statistics

302

(2)

Network Analysis

304

(10)

Spatial Attribute of Network Features: Connectivity or Topology

304

(2)

Assessing Connectivity Level

306

(3)

Evaluating Accessibility

309

(3)

ArcView Example: Network Analysis

312

(2)

Application Examples

314

(13)

Length Attribute Analysis of Linear Features

315

(2)

Application Example for Directional Statistics

317

(2)

Application Example for Network Analysis

319

(5)

References

324

(1)

Exercises

324

(3)

Polygon Pattern Analyzers

327

(92)

Introduction

327

(1)

Spatial Relationships

328

(2)

Spatial Dependency

330

(4)

Spatial Weights Matrices

334

(15)

Neighborhood Definitions

335

(1)

Binary Connectivity Matrix

336

(3)

Stochastic or Row-Standardized Weights Matrix

339

(2)

Centroid Distances

341

(2)

Nearest Distances

343

(2)

ArcView Example: Spatial Weights Matrices

345

(4)

Spatial Autocorrelation Statistics and Notations

349

(4)

Joint Count Statistics

353

(14)

Free Sampling

355

(6)

Randomization Sampling

361

(6)

Spatial Autocorrelation Global Statistics

367

(20)

Moran's I

367

(6)

Geary's Ratio

373

(3)

General G-Statistic

376

(6)

ArcView Example: Global Statistics for Spatial Autocorrelation

382

(5)

Local Spatial Autocorrelation Statistics

387

(8)

Local Indicators of Spatial Association

388

(5)

Local G-Statistic

393

(2)

Moran Scatterplot

395

(10)

ArcView Example: Local Spatial Autocorrelation Statistics and Moran Scatterplot

399

(6)

Bivariate Spatial Autocorrelation

405

(4)

Application Examples

409

(3)

Summary

412

(7)

References

415

(1)

Exercises

416

(3)

Appendix ArcGIS Spatial Statistics Tools

419

(12)

About the CD-ROM

431

(2)

Index

433

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Statistical Analysis of Geographic Information with ArcView GIS And ArcGIS

Summary

Author Biography

Table of Contents

Supplemental Materials