Statistical Methods for Geography

Peter A. Rogerson is SUNY (State University of New York) Distinguished Professor in the Department of Geography at the University at Buffalo, Buffalo, New York, USA. He also holds an adjunct appointment in the Department of Biostatistics.

1INTRODUCTION TO STATISTICAL METHODS FOR GEOGRAPHY
1.1Introduction
1.2The scientific method
1.3Exploratory and confirmatory approaches in geography
1.4Probability and statistics
1.5Descriptive and inferential methods
1.6The nature of statistical thinking
1.7Special considerations for spatial data
1.8The structure of the book
1.9Datasets
2DESCRIPTIVE STATISTICS
2.1Types of data
2.2Visual descriptive methods
2.3Measures of central tendency
2.4Measures of variability
2.5Other numerical measures for describing data
2.6Descriptive spatial statistics
2.7Descriptive statistics in SPSS 25 for Windows
Solved exercises
Exercises
3PROBABILITY AND DISCRETE PROBABILITY DISTRIBUTIONS
3.1Introduction
3.2Sample spaces, random variables, and probabilities
3.3Binomial processes and the binomial distribution
3.4The geometric distribution
3.5The Poisson distribution
3.6The hypergeometric distribution
3.7Binomial tests in SPSS 25 for Windows
Solved exercises
Exercises
4CONTINUOUS PROBABILITY DISTRIBUTIONS AND PROBABILITY MODELS
4.1Introduction
4.2The uniform or rectangular distribution
4.3The normal distribution
4.4The exponential distribution
4.5Summary of discrete and continuous distributions
4.6Probability models
Solved exercises
Exercises
5INFERENTIAL STATISTICS: CONFIDENCE INTERVALS, HYPOTHESIS TESTING, AND SAMPLING
5.1Introduction to inferential statistics
5.2Confidence intervals
5.3Hypothesis testing
5.4Distributions of the random variable and distributions of the test statistic
5.5Spatial data and the implications of nonindependence
5.6Further discussion of the effects of deviations from the assumptions
5.7Sampling
5.8Some tests for spatial measures of central tendency and variability
5.9One-sample tests of means in SPSS 25 for Windows
5.10 Two-sample t-tests in SPSS 25 for Windows
Solved exercises
Exercises
6ANALYSIS OF VARIANCE
6.1Introduction
6.2Illustrations
6.3Analysis of variance with two categories
6.4Testing the assumptions
6.5Consequences of failure to meet assumptions
6.6 The nonparametric Kruskal–Wallis test
6.7 The nonparametric median test
6.8 Contrasts
6.9 One-way ANOVA in SPSS 25 for Windows
6.10 One-way ANOVA in Excel
Solved exercises
Exercises
7CORRELATION
7.1Introduction and examples of correlation
7.2More illustrations
7.3A significance test for r
7.4The correlation coefficient and sample size
7.5Spearman’s rank correlation coefficient
7.6Additional topics
7.7Correlation in SPSS 25 for Windows
7.8Correlation in Excel
Solved exercises
Exercises
8DATA REDUCTION: FACTOR ANALYSIS AND CLUSTER ANALYSIS
8.1 Introduction
8.2 Factor analysis and principal components analysis
8.3 Cluster analysis
8.4 Data reduction methods in SPSS 25 for Windows
Exercises
9INTRODUCTION TO REGRESSION ANALYSIS
9.1 Introduction
9.2 Fitting a regression line to a set of bivariate data
9.3 Regression in terms of explained and unexplained sums of squares
9.4 Assumptions of regression
9.5 Standard error of the estimate
9.6 Tests for ß
9.7Illustration: state aid to secondary schools
9.8 Linear versus nonlinear models
9.9 Regression in SPSS 25 for Windows
9.10 Regression in Excel
Solved exercises
Exercises
10MORE ON REGRESSION
10.1 Multiple regression
10.2 Misspecification error
10.3 Dummy variables
10.4 Multiple regression illustration: species in the Galápagos Islands
10.5 Variable selection
10.6 Regression analysis on component scores
10.7 Categorical dependent variable
10.8 A summary of some problems that can arise in regression analysis
10.9 Multiple and logistic regression in SPSS 25 for Windows
Exercises
11SPATIAL DATA, SPATIAL PATTERNS, AND SPATIAL REGRESSION
11.1 Introduction
11.2 The analysis of point patterns
11.3 Geographic patterns in areal data
11.4 Local statistics
11.5 Introduction to spatial aspects of regression
11.6 Spatial lag model and neighborhood-based explanatory variables
11.7 Spatial regression: autocorrelated errors
11.8 Geographically weighted regression
11.9 Illustration
11.10 Finding Moran’s I using SPSS 25 for Windows
11.11 Finding Moran’s I using GeoDa
11.12 Spatial Regression with GeoDa 1.4.6
Exercises
EPILOGUE
ANSWERS FOR SELECTED EXERCISES
APPENDIX A: STATISTICAL TABLES
APPENDIX B: MATHEMATICAL CONVENTIONS AND NOTATION
Bibliography
Index