Elementary Statistics for Geographers

by Burt, James E.; Barber, Gerald M.; Rigby, David L.

• ISBN13: 9781572304840
• ISBN10: 1572304847
• Edition: 3rd
• Format: Hardcover
• Copyright: 2009-03-19
• Publisher: The Guilford Press

Summary

Widely adopted, this uniquely comprehensive text introduces the techniques and concepts of statistics in human and physical geography. Unlike other texts that gloss over the conceptual foundations and focus solely on method, the book explains not only how to apply quantitative tools but also why and how they work. Students gain important skills for utilizing both conventional and spatial statistics in their own research, as well as for critically evaluating the work of others. Most chapters are self-contained in order to provide maximum flexibility in course design. Requiring no math beyond algebra, the book is well suited for undergraduate and beginning graduate-level courses. Helpful features include chapter summaries, suggestions for further reading, and practice problems at the end of each chapter.

 

New to This Edition

*Restructured and updated to reflect current developments in the field.

*Five entirely new chapters cover graphical methods, spatial relationships, analysis of variance, extending regression analysis, and spatial analysis.

*Features even more worked examples, many with accompanying graphics.

*The companion website offers datasets and solutions to selected end-of-chapter exercises.

Author Biography

James E. Burt is Professor and former chair of Geography at the University of Wisconsin-Madison. His current research focuses on development of expert system and statistical approaches for quantitative prediction of soils information.  Gerald M. Barber is Associate Professor of Geography and teaches introductory and advanced courses in statistics at Queen’s University in Kingston, Ontario, Canada. In addition, he is the director of the program in Geographic Information Science and runs the GISLAB. His principal interests are in the application of statistical and optimization models within GIS.

David L. Rigby is Professor of Geography and Statistics at the University of California, Los Angeles. His research interests include regional growth, technological change, evolutionary economic dynamics, and the impacts of globalization and trade on wage inequality.

Table of Contents

Introduction
Statistics and Geography	p. 3
Statistical Analysis and Geography	p. 8
Data	p. 16
Measurement Evaluation	p. 28
Data and Information	p. 31
Summary	p. 33
Descriptive Statistics
Displaying and Interpreting Data	p. 39
Displaying and Interpretation of the Distributions of Qualitative Variables	p. 41
Display and Interpretation of the Distributions of Quantitative Variables	p. 46
Displaying and Interpreting Time-Series Data	p. 74
Displaying and Interpreting Spatial Data	p. 79
Summary	p. 92
Describing Data with Statistics	p. 95
Measures of Central Tendency	p. 95
Measures of Dispersion	p. 109
Higher Order Moments or Other Numerical Measures of the Characteristics of Distributions	p. 117
Using Descriptive Statistics with Time-Series Data	p. 118
Descriptive Statistics for Spatial Data	p. 124
Summary	p. 147
Review of Sigma Notation	p. 148
An Iterative Algorithm for Determining the Weighted or Unweighted Euclidean Median	p. 150
Statistical Relationships	p. 156
Relationships and Dependence	p. 157
Looking for Relationships in Graphs and Tables	p. 158
Introduction to Correlation	p. 164
Introduction to Regression	p. 172
Temporal Autocorrelation	p. 188
Summary	p. 191
Review of the Elementary Geometry of a Line	p. 192
Least Squares Solution via Elementary Calculus	p. 194
Inferential Statistics
Random Variables and Probability Distributions	p. 201
Elementary Probability Theory	p. 201
Concept of a Random Variable	p. 210
Discrete Probability Distribution Models	p. 220
Continuous Probability Distribution Models	p. 233
Bivariate Random Variables	p. 238
Summary	p. 246
Counting Rules for Computing Probabilities	p. 246
Expected Value and Variance of a Continuous Random Variable	p. 250
Sampling	p. 254
Why Do We Sample?	p. 256
Steps in the Sampling Process	p. 257
Types of Samples	p. 260
Random Sampling and Related Probability Designs	p. 262
Sampling Distributions	p. 271
Geographic Sampling	p. 282
Summary	p. 289
Point and Interval Estimation	p. 293
Statistical Estimation Procedures	p. 294
Point Estimation	p. 300
Interval Estimation	p. 303
Sample Size Determination	p. 315
Summary	p. 318
One-Sample Hypothesis Testing	p. 321
Key Steps in Classical Hypothesis Testing	p. 321
prob-value Method of Hypothesis Testing	p. 333
Hypothesis Tests Concerning the Population Mean m and p<$$$>	p. 338
Relationship between Hypothesis Testing and Confidence Interval Estimation	p. 345
Statistical Significance versus Practical Significance	p. 345
Summary	p. 349
Two-Sample Hypothesis Testing	p. 353
Difference of Means	p. 354
Difference of Means for Paired Observations	p. 363
Difference of Proportions	p. 367
The Equality of Variances	p. 369
Summary	p. 373
Nonparametric Methods	p. 376
Comparison of Parametric and Nonparametric Tests	p. 377
One- and Two-Sample Tests	p. 380
Multisample Kruskal-Wallis Test	p. 393
Goodness-of-Fit Tests	p. 395
Contingency Tables	p. 405
Estimating a Probability Distribution: Kernel Estimates	p. 408
Bootstrapping	p. 418
Summary	p. 427
Analysis of Variance	p. 432
The One-Factor, Completely Randomized Design	p. 434
The Two-Factor, Completely Randomized Design	p. 446
Multiple Comparisons Using the Scheffe Contrast	p. 453
Assumptions of the Analysis of Variance	p. 455
Summary	p. 457
Derivation of Equation 11-11 from Equation 11-10	p. 457
Inferential Aspects of Linear Regression	p. 461
Overview of the Steps in a Regression Analysis	p. 461
Assumptions of the Simple Linear Regression Model	p. 465
Inferences in Regression Analysis	p. 476
Graphical Diagnostics for the Linear Regression Model	p. 488
Summary	p. 495
Extending Regression Analysis	p. 498
Multiple Regression Analysis	p. 498
Variable Transformations and the Shape of the Regression Function	p. 514
Validating a Regression Model	p. 525
Summary	p. 528
Patterns in Space and Time
Spatial Patterns and Relationships	p. 533
Point Pattern Analysis	p. 533
Spatial Autocorrelation	p. 544
Local Indicators of Spatial Association	p. 559
Regression Models with Spatially Autocorrelated Data	p. 566
Geographically Weighted Regression	p. 570
Summary	p. 571
Time Series Analysis	p. 577
Time Series Processes	p. 578
Properties of Stochastic Processes	p. 579
Types of Stochastic Processes	p. 584
Removing Trends: Transformations to Stationarity	p. 588
Model Identification	p. 590
Model Fitting	p. 595
Times Series Models, Running Means, and Filters	p. 601
The Frequency Approach	p. 603
Filter Design	p. 609
Summary	p. 616
Appendix: Statistical Tables	p. 621
Index	p. 643
About the Authors	p. 653
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