reading

Cover
Title Page
Preface
1 Dealing with data
1. 1.1 The role of statistics in geography
2. 1.2 About this book
3. 1.3 Data and measurement error
4. Exercises
2 Collecting and summarizing data
1. 2.1 Sampling methods
2. 2.2 Graphical summaries
3. 2.3 Summarizing data numerically
4. Exercises
3 Probability and sampling distributions
1. 3.1 Probability
2. 3.2 Probability and the normal distribution: z‐scores
3. 3.3 Sampling distributions and the central limit theorem
4. Exercises
4 Estimating parameters with confidence intervals
1. 4.1 Confidence intervals on the mean of a normal distribution: the basics
2. 4.2 Confidence intervals in practice: the t‐distribution
3. 4.3 Sample size
4. 4.4 Confidence intervals for a proportion
5. Exercises
5 Comparing datasets
1. 5.1 Hypothesis testing with one sample: general principles
2. 5.2 Comparing means from small samples: one‐sample t‐test
3. 5.3 Comparing proportions for one sample
4. 5.4 Comparing two samples
5. 5.5 Non‐parametric hypothesis testing
6. Exercises
6 Comparing distributions
1. 6.1 Chi‐squared test with one sample
2. 6.2 Chi‐squared test for two samples
3. Exercises
7 Analysis of variance
1. 7.1 One‐way analysis of variance
2. 7.2 Assumptions and diagnostics
3. 7.3 Multiple comparison tests after analysis of variance
4. 7.4 Non‐parametric methods in the analysis of variance
5. 7.5 Summary and further applications
6. Exercises
8 Correlation
1. 8.1 Correlation analysis
2. 8.2 Pearson’s product‐moment correlation coefficient
3. 8.3 Significance tests of correlation coefficient
4. 8.4 Spearman’s rank correlation coefficient
5. 8.5 Correlation and causality
6. Exercises
9 Linear regression
1. 9.1 Least‐squares linear regression
2. 9.2 Scatter plots
3. 9.3 Choosing the line of best fit: the ‘least‐squares’ procedure
4. 9.4 Analysis of residuals
5. 9.5 Assumptions and caveats with regression
6. 9.6 Is the regression significant?
7. 9.7 Coefficient of determination
8. 9.8 Confidence intervals and hypothesis tests concerning regression parameters
9. 9.9 Reduced major axis regression
10. 9.10 Summary
11. Exercises
10 Spatial Statistics
1. 10.1 Spatial Data
2. 10.2 Summarizing Spatial Data
3. 10.3 Identifying Clusters
4. 10.4 Interpolation and Plotting Contour Maps
5. 10.5 Spatial Relationships
6. Exercises
11 Time series analysis
1. 11.1 Time series in geographical research
2. 11.2 Analysing time series
3. 11.3 Summary
4. Exercises
Appendix A: Introduction to the R package
1. A.1 Obtaining R
2. A.2 Simple calculations
3. A.3 Vectors
4. A.4 Basic statistics
5. A.5 Plotting data
6. A.6 Multiple figures
7. A.7 Reading and writing data
8. A.8 Summary
Appendix B: Statistical tables
References
Index
End User License Agreement

List of Tables

Chapter 01
1. Table 1.1 Prefixes used to indicate powers of 10.
Chapter 02
1. Table 2.1 Geography test scores.
2. Table 2.2 Frequency distribution for test scores.
3. Table 2.3 Concentration of lead (Pb) in pine trees (ppm).
4. Table 2.4 Calculation of variance and standard deviation for lead concentrations in pine trees.
5. Table 2.5 Rainfall data in Glasgow and London.
6. Table 2.6 Weekly food expenditure in two suburbs of a city.
Chapter 05
1. Table 5.1 Beach pollution.
2. Table 5.2 Summary of rainfall data in Glasgow and London.
3. Table 5.3 Comparison of lake acidity before and after pollution reduction programme.
4. Table 5.4 Job security data.
5. Table 5.5 Ranked job security data.
Chapter 06
1. Table 6.1 Museum visitor ages.
2. Table 6.2 Contingency table for museum visitor ages.
3. Table 6.3 River habitat biodiversity.
4. Table 6.4 Contingency table for stream habitat biodiversity showing observed counts and calculated row and column totals.
5. Table 6.5 Contingency table for stream habitat biodiversity showing expected frequencies.
6. Table 6.6 Distribution of graffiti by building type.
7. Table 6.7 Distribution of bird seed availability.
8. Table 6.8 Effects of preschool education on literacy.
Chapter 07
1. Table 7.1 Crop yield data for single factor analysis of variance.
2. Table 7.2 ANOVA table for crop yield analysis of variance.
3. Table 7.3 Average A‐Level point scores for schools in three areas.
4. Table 7.4 Slope angles and lithology.
Chapter 08
1. Table 8.1 July rainfall and corn yield in Iowa, USA.
2. Table 8.2 Calculations for Pearson’s product‐moment correlation coefficient between July rainfall and corn yield in Iowa, USA.
3. Table 8.3 Property prices in Oxford, UK.
4. Table 8.4 Species–area relationship for birds of the Solomon Archipelago.
Chapter 09
1. Table 9.1 Tree height and girth data.
2. Table 9.2 Calculations to estimate parameters of best‐fit linear model to trees data using least squares procedure.
3. Table 9.3 ANOVA table for regression between tree height and diameter.
4. Table 9.4 Species richness and pH for lowland stream reaches.
5. Table 9.5 Pollutant concentration away from a disused mine.
Chapter 10
1. Table 10.1 R packages for plotting and analysing spatial data.
2. Table 10.2 Parameters of the Ordnance Survey Great Britain projection (OSGB36).
3. Table 10.3 Data for London Boroughs (2013/14 figures).
Chapter 11
1. Table 11.1 Mean monthly temperature data (°C) for Oxford, UK, 1961–1990.
2. Table 11.2 Mean monthly precipitation data (mm/month) for Oxford, UK, 1961–1990.
Appendix A
1. Table A.1 Plotting options in R.
Appendix B
1. Table B.1 z‐Table.
2. Table B.2 t‐Distribution.
3. Table B.3 Critical values of the F‐distribution.
4. Table B.4 Critical values of the U‐distribution.
5. Table B.5 Critical values of the χ² distribution.

List of Illustrations

Chapter 01
1. Figure 1.1 Accuracy and precision in archery. (a) High accuracy with high precision; (b) high accuracy with low precision; (c) low accuracy but high precision; (d) low accuracy and low precision. Note that without knowing the location of the archery target (i.e. the true value of the measured quantity), cases (c) and (d) are indistinguishable from (a) and (b), respectively.
Chapter 02
1. Figure 2.1 Examples of histograms showing typical properties of frequency distributions: (a) positive skew; (b) negative skew; (c) platykurtic; (d) leptokurtic; (e) bimodal; and (f) multimodal.
2. Figure 2.2 Histogram of test score data.
3. Figure 2.3 Time series of Mauna Loa atmospheric CO₂ concentrations. Note that this dataset is built into R and can be plotted using plot(co2).
4. Figure 2.4 Scatter plot of July rainfall and corn yield in Iowa.
5. Figure 2.5 Life expectancy at birth and gross domestic product (GDP) per capita in dollars (adjusted for inflation): (a) with standard axes; and (b) with logarithmically spaced horizontal axis.
6. Figure 2.6 Histogram of lead concentration in pine trees at (a) Site A and (b) Site B.
Chapter 03
1. Figure 3.1 Theoretical form of the normal distribution.
2. Figure 3.2 Properties of the normal distribution: (a) 68% of observations lie within one standard deviation either side of the mean; and (b) 95% of observations lie within two standard deviations either side of the mean.
3. Figure 3.3 The area to the left of a particular z‐score gives the fraction of the possible values in the distribution that are lower than that z‐score. (a) z = 0; (b) z = −1; (c) z = 2.5.
4. Figure 3.4 Illustration of the central limit theorem: the more samples we draw the closer their average approximates a normal distribution.
Chapter 04
1. Figure 4.1 Comparison of t‐distribution and normal distribution: (a) comparison of the normal distribution with the t‐distribution for different numbers of degrees of freedom; and (b) area under the normal distribution compared with the area under the t‐distribution.
Chapter 07
1. Figure 7.1 Completely randomized experimental design.
2. Figure 7.2 Plots of crop yields: (a) graph of yields by consecutive plot number; and (b) boxplot grouped by level.
3. Figure 7.3 Diagnostic plots for analysis of variance: (a) residuals versus fitted values; and (b) normal probability plot of residuals.
Chapter 09
1. Figure 9.1 The relation between tree height and diameter in 31 cherry trees.
2. Figure 9.2 Illustration of the principle behind linear least squares regression.
3. Figure 9.3 Plots showing typical configurations of residuals: (a) standard, normally distributed, homoscedastic; (b) heteroscedastic; and (c) non‐linear model.
4. Figure 9.4 Diagnostic plots using residuals for tree height regression: (a) residuals against fitted values; and (b) histogram of residuals.
5. Figure 9.5 Regression by linear least squares: (a) the spread around the mean in the vertical direction; (b) the spread accounted for by the line of best fit; and (c) the residual deviation, or spread around the line of best fit.
6. Figure 9.6 Confidence intervals (95%) around predictions of tree height.
Chapter 10
1. Figure 10.1 Map showing global cities with population greater than five million people.
2. Figure 10.2 Map projections and their properties
3. Figure 10.3 Comparison of Europe plotted with (a) Mercator projection and (b) Lambert conformal conic (ETRS89‐LCC) with standard parallels at 35° N and 65° N. Note the relative sizes of different countries, especially at high latitudes.
4. Figure 10.4 Plot showing the locations of the top 30 cities in the UK by population: (a) in latitude‐longitude coordinates; and (b) projected onto GB National Grid coordinates using R.
5. Figure 10.5 Geographical distribution of the UK population. Open circles indicate individual towns. The filled grey circle is the mean centre. Solid lines are contours of population density in persons per square kilometre calculated using a 60 km averaging kernel.
6. Figure 10.6 Possible distributions of points across a region: (a) completely spatially random; (b) dispersed; and (c) clustered. Quadrat outlines are drawn with numbers indicating the number of points that lie within each quadrat.
7. Figure 10.7 Polygons showing London boroughs. Filled circles show the centres of each borough; solid grey lines connect boroughs which share a boundary. Note that the River Thames passes through the centre of the city but has been ignored for the purposes of evaluating shared boundaries. Produced using data from the Office for National Statistics licensed under the Open Government Licence v.3.0. © Crown copyright and database rights (2015) Ordnance Survey 100019153. http://data.london.gov.uk/datastore/package/statistical‐gis‐boundary‐files‐london.
8. Figure 10.8 Voting patterns in the 2012 London Mayoral election. Polygons represent London boroughs, shaded to indicate whether the majority of first preference votes was for the Labour Party candidate (shown in light grey) or the Conservative Party candidate (shown in dark grey). Produced using data from the Office for National Statistics licensed under the Open Government Licence v.3.0. © Crown copyright and database rights (2015) Ordnance Survey 100019153.
Chapter 11
1. Figure 11.1 Time series of Mauna Loa atmospheric CO₂ concentrations. Note that this dataset is built into R and can be plotted using plot (co2).
2. Figure 11.2 Time series of Oxford temperature data from Table 11.1 plotted as a time series using R.
3. Figure 11.3 Types of moving average.
4. Figure 11.4 Moving averages of Oxford rainfall data: (a) raw data; (b) three‐point centred moving average with raw data shown in grey; (c) 12‐point centred moving average with raw data shown in grey; and (d) comparison of centred (black dots) and backward (solid black line) 12‐point moving averages with raw data shown in grey.
5. Figure 11.5 Monthly climatology for Oxford for (a) temperature and (b) precipitation.
6. Figure 11.6 Typical datasets with their corresponding correlograms shown below: (a, b) CO₂ concentrations showing the effect of a trend on the correlogram; (c ,d) Oxford temperature showing the effect of a seasonal pattern in the dataset; and (e, f) Oxford rainfall showing a dataset which naturally has very little autocorrelation. The dashed line indicates the threshold for statistically significant autocorrelation.
Appendix A
1. Figure A.1 A basic plot.
2. Figure A.2 List of plotting symbols commonly used in R graphics.
3. Figure A.3 A customized plot.
4. Figure A.4 Multiple plots on a page.

Pages

This edition first published 2017
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Library of Congress Cataloging‐in‐Publication Data

Name: Dadson, Simon J.
Title: Statistical analysis of geographical data : an introduction / Simon J. Dadson.
Description: 1 edition. | Chichester, West Sussex : John Wiley & Sons, Inc., 2017. | Includes bibliographical references and index.
Identifiers: LCCN 2016043619 (print) | LCCN 2017004526 (ebook) | ISBN 9780470977033 (hardback) | ISBN 9780470977040 (paper) | ISBN 9781118525111 (pdf) | ISBN 9781118525142 (epub)
Subjects: LCSH: Geography–Statistical methods. | BISAC: SCIENCE / Earth Sciences / General.
Classification: LCC G70.3 .D35 2017 (print) | LCC G70.3 (ebook) | DDC 910.72/7–dc23
LC record available at https://lccn.loc.gov/2016043619

Statistical Analysis of Geographical Data

An Introduction

Preface