Statistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography. It covers a wide range of topics including graphical and numerical description of datasets, probability, calculation of confidence intervals, hypothesis testing, collection and analysis of data using analysis of variance and linear regression. Taking a clear and logical approach, this book examines real problems with real data from the geographical literature in order to illustrate the important role that statistics play in geographical investigations. Presented in a clear and accessible manner the book includes recent, relevant examples, designed to enhance the reader’s understanding.

Table of Contents:
Preface xi 1 Dealing with data 1 1.1 The role of statistics in geography 1 1.1.1 Why do geographers need to use statistics? 1 1.2 About this book 3 1.3 Data and measurement error 3 1.3.1 Types of geographical data: nominal, ordinal, interval, and ratio 3 1.3.2 Spatial data types 5 1.3.3 Measurement error, accuracy and precision 6 1.3.4 Reporting data and uncertainties 7 1.3.5 Significant figures 9 1.3.6 Scientific notation (standard form) 10 1.3.7 Calculations in scientific notation 11 Exercises 12 2 Collecting and summarizing data 13 2.1 Sampling methods 13 2.1.1 Research design 13 2.1.2 Random sampling 15 2.1.3 Systematic sampling 16 2.1.4 Stratified sampling 17 2.2 Graphical summaries 17 2.2.1 Frequency distributions and histograms 17 2.2.2 Time series plots 21 2.2.3 Scatter plots 22 2.3 Summarizing data numerically 24 2.3.1 Measures of central tendency: mean, median and mode 24 2.3.2 Mean 24 2.3.3 Median 25 2.3.4 Mode 25 2.3.5 Measures of dispersion 28 2.3.6 Variance 29 2.3.7 Standard deviation 30 2.3.8 Coefficient of variation 30 2.3.9 Skewness and kurtosis 33 Exercises 33 3 Probability and sampling distributions 37 3.1 Probability 37 3.1.1 Probability, statistics and random variables 37 3.1.2 The properties of the normal distribution 38 3.2 Probability and the normal distribution: z‐scores 39 3.3 Sampling distributions and the central limit theorem 43 Exercises 47 4 Estimating parameters with confidence intervals 49 4.1 Confidence intervals on the mean of a normal distribution: the basics 49 4.2 Confidence intervals in practice: the t‐distribution 50 4.3 Sample size 53 4.4 Confidence intervals for a proportion 53 Exercises 54 5 Comparing datasets 55 5.1 Hypothesis testing with one sample: general principles 55 5.1.1 Comparing means: one‐sample z‐test 56 5.1.2 p‐values 60 5.1.3 General procedure for hypothesis testing 61 5.2 Comparing means from small samples: one‐sample t‐test 61 5.3 Comparing proportions for one sample 63 5.4 Comparing two samples 64 5.4.1 Independent samples 64 5.4.2 Comparing means: t‐test with unknown population variances assumed equal 64 5.4.3 Comparing means: t‐test with unknown population variances assumed unequal 68 5.4.4 t‐test for use with paired samples (paired t‐test) 71 5.4.5 Comparing variances: F‐test 74 5.5 Non‐parametric hypothesis testing 75 5.5.1 Parametric and non‐parametric tests 75 5.5.2 Mann–whitney U‐test 75 Exercises 79 6 Comparing distributions: the Chi‐squared test 81 6.1 Chi‐squared test with one sample 81 6.2 Chi‐squared test for two samples 84 Exercises 87 7 Analysis of variance 89 7.1 One‐way analysis of variance 90 7.2 Assumptions and diagnostics 99 7.3 Multiple comparison tests after analysis of variance 101 7.4 Non‐parametric methods in the analysis of variance 105 7.5 Summary and further applications 106 Exercises 107 8 Correlation 109 8.1 Correlation analysis 109 8.2 Pearson’s product‐moment correlation coefficient 110 8.3 Significance tests of correlation coefficient 112 8.4 Spearman’s rank correlation coefficient 114 8.5 Correlation and causality 116 Exercises 117 9 Linear regression 121 9.1 Least‐squares linear regression 121 9.2 Scatter plots 122 9.3 Choosing the line of best fit: the ‘least‐squares’ procedure 124 9.4 Analysis of residuals 128 9.5 Assumptions and caveats with regression 130 9.6 Is the regression significant? 131 9.7 Coefficient of determination 135 9.8 Confidence intervals and hypothesis tests concerning regression parameters 137 9.8.1 Standard error of the regression parameters 137 9.8.2 Tests on the regression parameters 138 9.8.3 Confidence intervals on the regression parameters 139 9.8.4 Confidence interval about the regression line 140 9.9 Reduced major axis regression 140 9.10 Summary 142 Exercises 142 10 Spatial statistics 145 10.1 Spatial data 145 10.1.1 Types of spatial data 145 10.1.2 Spatial data structures 146 10.1.3 Map projections 149 10.2 Summarizing spatial data 157 10.2.1 Mean centre 157 10.2.2 Weighted mean centre 157 10.2.3 Density estimation 158 10.3 Identifying clusters 159 10.3.1 Quadrat test 159 10.3.2 Nearest neighbour statistics 162 10.4 Interpolation and plotting contour maps 162 10.5 Spatial relationships 163 10.5.1 Spatial autocorrelation 163 10.5.2 Join counts 164 Exercises 171 11 Time series analysis 173 11.1 Time series in geographical research 173 11.2 Analysing time series 174 11.2.1 Describing time series: definitions 174 11.2.2 Plotting time series 175 11.2.3 Decomposing time series: trends, seasonality and irregular fluctuations 179 11.2.4 Analysing trends 180 11.2.5 Removing trends (‘detrending’ data) 186 11.2.6 Quantifying seasonal variation 187 11.2.7 Autocorrelation 189 11.3 Summary 190 Exercises 190 Appendix A: Introduction to the R package 193 Appendix B: Statistical tables 205 References 241 Index 243