Statistical Methods for Geography

1 INTRODUCTION TO STATISTICAL METHODS FOR GEOGRAPHY 1.1 Introduction 1.2 The scientific method 1.3 Exploratory and confirmatory approaches in geography 1.4 Probability and statistics 1.5 Descriptive and inferential methods 1.6 The nature of statistical thinking 1.7 Special considerations for spatial data 1.8 The structure of the book 1.9 Datasets 2 DESCRIPTIVE STATISTICS 2.1 Types of data 2.2 Visual descriptive methods 2.3 Measures of central tendency 2.4 Measures of variability 2.5 Other numerical measures for describing data 2.6 Descriptive spatial statistics 2.7 Descriptive statistics in SPSS 25 for Windows Solved exercises Exercises 3 PROBABILITY AND DISCRETE PROBABILITY DISTRIBUTIONS 3.1 Introduction 3.2 Sample spaces, random variables, and probabilities 3.3 Binomial processes and the binomial distribution 3.4 The geometric distribution 3.5 The Poisson distribution 3.6 The hypergeometric distribution 3.7 Binomial tests in SPSS 25 for Windows Solved exercises Exercises 4 CONTINUOUS PROBABILITY DISTRIBUTIONS AND PROBABILITY MODELS 4.1 Introduction 4.2 The uniform or rectangular distribution 4.3 The normal distribution 4.4 The exponential distribution 4.5 Summary of discrete and continuous distributions 4.6 Probability models Solved exercises Exercises 5 INFERENTIAL STATISTICS: CONFIDENCE INTERVALS, HYPOTHESIS TESTING, AND SAMPLING 5.1 Introduction to inferential statistics 5.2 Confidence intervals 5.3 Hypothesis testing 5.4 Distributions of the random variable and distributions of the test statistic 5.5 Spatial data and the implications of nonindependence 5.6 Further discussion of the effects of deviations from the assumptions 5.7 Sampling 5.8 Some tests for spatial measures of central tendency and variability 5.9 One-sample tests of means in SPSS 25 for Windows 5.10 Two-sample t-tests in SPSS 25 for Windows Solved exercises Exercises 6 ANALYSIS OF VARIANCE 6.1 Introduction 6.2 Illustrations 6.3 Analysis of variance with two categories 6.4 Testing the assumptions 6.5 Consequences 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 7 CORRELATION 7.1 Introduction and examples of correlation 7.2 More illustrations 7.3 A significance test for r 7.4 The correlation coefficient and sample size 7.5 Spearman's rank correlation coefficient 7.6 Additional topics 7.7 Correlation in SPSS 25 for Windows 7.8 Correlation in Excel Solved exercises Exercises 8 DATA 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 9 INTRODUCTION 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 9.7 Illustration: 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 10 MORE ON REGRESSION 10.1 Multiple regression 10.2 Misspecification error 10.3 Dummy variables 10.4 Multiple regression illustration: species in the Galapagos 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 11 SPATIAL 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