Statistical Methods for Geography; A Student's Guide

by Rogerson, Peter

• ISBN13: 9781412907965
• ISBN10: 1412907969
• Edition: 2nd
• Format: Paperback
• Copyright: 2006-01-27
• Publisher: Sage Publications Ltd

Summary

"The First Edition of Statistical Methods for Geography provided an excellent introduction to the statistical analysis of spatial data. The second edition is even better - providing more material on probability and on descriptive statistics as well as more exercises. I would recommend this strongly as a text for introductory statistics courses in geography. It is currently the best on the market by far."  - A. Stewart Fotheringham, National University of Ireland, Maynooth The Second Edition of this bestselling text has been completely revised and updated. It provides a systematic introduction to the principal methods and techniques that students must understand to complete a statistics course.Features new to this edition include: More introductory material especially in a new chapter on descriptive statistics, and much-expanded introductory chapters More exercises and illustrative examples within the chapters SPSS for Windows and EXCEL used to illustrate the applied use of the methods A companion Web site for lecturers and students is available at www.sagepub.co.uk/rogerson . The password-protected lecturer section contains answers to questions from the book. There are also downloadable-datasets and study skills for students.

Author Biography

Peter A. Rogerson is Professor of Geography at the University at Buffalo, USA

Table of Contents

Preface	p. xii
Preface to the second edition	p. xv
Introduction to Statistical Methods for Geography	p. 1
Introduction	p. 1
The Scientific method	p. 1
Exploratory and confirmatory approaches in geography	p. 4
Probability and statistics	p. 4
Probability	p. 4
Statistics	p. 5
Probability paradoxes	p. 6
Geographical applications of probability and statistics	p. 8
Descriptive and inferential methods	p. 13
The nature of statistical thinking	p. 14
Special considerations for spatial data	p. 15
Modifiable areal unit problem	p. 16
Boundary problems	p. 16
Spatial sampling procedures	p. 17
Spatial autocorrelation	p. 17
Structure of the book	p. 17
Datasets	p. 19
Mobile phone signal strength in Erie County, New York, US	p. 19
House sales in Tyne and Wear	p. 20
Descriptive Statistics	p. 23
Types of data	p. 23
Visual descriptive methods	p. 24
Measures of central tendency	p. 27
Measures of variability	p. 29
Other numerical measures for describing data	p. 30
Coefficient of variation	p. 30
Skewness	p. 31
Kurtosis	p. 31
Standard scores	p. 32
Descriptive spatial statistics	p. 32
Mean center	p. 32
Median center	p. 33
Standard distance	p. 34
Relative distance	p. 34
Illustration of spatial measures of central tendency and dispersion	p. 35
Angular data	p. 36
Descriptive statistics in SPSS for Windows 12.0	p. 39
Data input	p. 39
Descriptive analysis	p. 39
Exercises	p. 41
Probability and Discrete Probability Distributions	p. 47
Introduction	p. 47
Sample spaces, random variables, and probabilities	p. 47
Binomial processes and the binomial distribution	p. 49
The geometric distribution	p. 53
The Poisson distribution	p. 55
The hypergeometric distribution	p. 59
Application to residential segregation	p. 61
Application to the space-time clustering of disease	p. 61
Binomial tests in SPSS for Windows 12.0	p. 63
Exercises	p. 63
Continuous Probability Distributions and Probability Models	p. 69
Introduction	p. 69
The uniform or rectangular distribution	p. 69
The normal distribution	p. 72
The exponential distribution	p. 77
Summary of discrete and continuous distributions	p. 82
Probability models	p. 82
The intervening opportunities model	p. 84
A model of migration	p. 88
The future of the human population	p. 89
Exercises	p. 90
Inferential Statistics: Confidence Intervals, Hypothesis Testing and Sampling	p. 93
Introduction to inferential statistics	p. 93
Confidence intervals	p. 93
Confidence intervals for the mean	p. 93
Confidence intervals for the mean when the sample size is small	p. 96
Confidence intervals for proportions	p. 97
Hypothesis testing	p. 97
Hypothesis testing and one-sample z-tests of the mean	p. 97
One-sample t-tests	p. 101
One-sample tests for proportions	p. 103
Two-sample tests: differences in means	p. 105
Two-sample tests: differences in proportions	p. 108
Distributions of the random variable and distributions of the test statistic	p. 109
Spatial data and the implications of nonindependence	p. 111
Further discussion of the effects of deviations from the assumptions	p. 112
One-sample test of proportions: binomial distribution - assumption of constant or equal success probabilities	p. 113
One-sample test of proportions: binomial distribution - assumption of independence	p. 114
Two-sample difference of means test: assumption of independent observations	p. 115
Two-sample difference of means test: assumption of homogeneity	p. 117
Sampling	p. 117
Spatial sampling	p. 118
Sample size considerations	p. 119
Some tests for spatial measures of central tendency and variability	p. 122
One-sample tests of means in SPSS for Windows 12.0	p. 124
Interpretation	p. 124
Two-sample t-tests in SPSS for Windows 12.0	p. 125
Data entry	p. 125
Running the t-test	p. 125
Two-sample t-tests in Excel	p. 127
Exercises	p. 128
Analysis of Variance	p. 132
Introduction	p. 132
A note on the use of F-tables	p. 135
Illustrations	p. 135
Hypothetical swimming frequency data	p. 135
Diurnal variation in precipitation	p. 137
Analysis of variance with two categories	p. 138
Testing the assumptions	p. 138
Consequences of failure to meet assumptions	p. 138
The nonparametric Kruskal-Wallis test	p. 139
Illustration: diurnal variation in precipitation	p. 139
More on the Kruskal-Wallis test	p. 140
The nonparametric median test	p. 141
Illustration	p. 141
Contrasts	p. 142
A priori contrasts	p. 143
Implications for hypothesis tests when assumptions are not met	p. 144
Normality	p. 144
Homoscedasticity	p. 144
Independence of observations	p. 145
One-way ANOVA in SPSS for Windows 12.0	p. 146
Data entry	p. 146
Data analysis and interpretation	p. 147
One-way ANOVA in Excel	p. 148
Exercises	p. 148
Correlation	p. 154
Introduction and examples of correlation	p. 154
More illustrations	p. 157
Mobility and cohort size	p. 157
Statewide infant mortality rates and income	p. 157
A significance test for r	p. 160
Illustration	p. 160
The correlation coefficient and sample size	p. 160
Spearman's rank correlation coefficient	p. 162
Additional topics	p. 162
The effect of spatial dependence on significance tests for correlation coefficients	p. 162
Modifiable area unit problem and spatial aggregation	p. 165
Correlation in SPSS for Windows 12.0	p. 165
Illustration	p. 166
Correlation in Excel	p. 167
Exercises	p. 168
Introduction to Regression Analysis	p. 170
Introduction	p. 170
Fitting a regression line to a set of bivariate data	p. 173
Illustration: income levels and consumer expenditure	p. 175
Regression in terms of explained and unexplained sums of squares	p. 176
Illustration	p. 179
Assumptions of regression	p. 180
Standard error of the estimate	p. 181
Tests for beta	p. 181
Illustration	p. 181
Illustration: state aid to secondary schools	p. 182
Linear versus nonlinear models	p. 184
Regression in SPSS for Windows 12.0	p. 186
Data input	p. 186
Analysis	p. 186
Options	p. 186
Output	p. 187
Regression in Excel	p. 187
Data input	p. 187
Analysis	p. 188
Exercises	p. 188
More on Regression	p. 192
Multiple regression	p. 192
Multicollinearity	p. 193
Interpretation of coefficients in multiple regression	p. 194
Misspecification error	p. 194
Dummy variables	p. 196
Dummy variable regression in a recreation planning example	p. 198
Multiple regression illustration: species in the Galapagos Islands	p. 200
Model 1: The kitchen-sink approach	p. 200
Missing values	p. 202
Outliers and multicollinearity	p. 204
Model 2	p. 204
Model 3	p. 206
Model 4	p. 206
Variable selection	p. 208
Categorical dependent variable	p. 209
Binary response	p. 209
A summary of some problems that can arise in regression analysis	p. 213
Multiple and logistic regression in SPSS for Windows 12.0	p. 213
Multiple regression	p. 213
Logistic regression	p. 213
Exercises	p. 218
Spatial Patterns	p. 222
Introduction	p. 222
The analysis of point patterns	p. 223
Quadrat analysis	p. 224
Nearest neighbor analysis	p. 228
Geographic patterns in areal data	p. 231
An example using a chi-squared test	p. 231
Moran's I	p. 232
Local statistics	p. 238
Introduction	p. 238
Local Moran statistic	p. 239
Getis' Gi statistic	p. 240
Finding Moran's I using SPSS for Windows 9.0	p. 240
Exercises	p. 242
Some Spatial Aspects of Regression Analysis	p. 244
Introduction	p. 244
Added-variable plots	p. 245
Spatial regression: autocorrelated errors	p. 246
Spatially varying parameters	p. 247
The expansion method	p. 247
Geographically weighted regression	p. 248
Illustration	p. 249
Ordinary least squares	p. 250
Added-variable plots	p. 251
Spatial regression: autocorrelated errors	p. 253
Expansion method	p. 254
Geographically weighted regression	p. 255
Exercises	p. 256
Data Reduction: Factor Analysis and Cluster Analysis	p. 257
Introduction	p. 257
Factor analysis and principal components analysis	p. 257
Illustration: 1990 Census data for Erie County, New York	p. 258
Regression analysis on component scores	p. 262
Cluster analysis	p. 263
More on agglomerative methods	p. 266
Illustration: 1990 Census data for Erie County, New York	p. 266
Data reduction methods in SPSS for Windows 12.0	p. 270
Factor analysis	p. 270
Cluster analysis	p. 271
Exercises	p. 273
Epilogue	p. 275
Statistical Tables	p. 277
Random digits	p. 277
Normal distribution	p. 279
Student's t-distribution	p. 280
Cumulative t-distribution	p. 281
F-distribution	p. 283
[chi superscript 2] distribution	p. 286
Mathematical Conventions and Notation	p. 287
Mathematical conventions	p. 287
Mathematical notation	p. 289
Review and Extension of Some Probability Theory	p. 293
Bibliography	p. 297
Index	p. 301
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