Statistical Analysis of Geographical Data

Simon J. Dadson is Associate Professor of Physical Geography at Oxford University and Tutor in Geography at Christ Church.

• Preface xi1 Dealing with data 11.1 The role of statistics in geography 11.1.1 Why do geographers need to use statistics? 11.2 About this book 31.3 Data and measurement error 31.3.1 Types of geographical data: nominal, ordinal, interval, and ratio 31.3.2 Spatial data types 51.3.3 Measurement error, accuracy and precision 61.3.4 Reporting data and uncertainties 71.3.5 Significant figures 91.3.6 Scientific notation (standard form) 101.3.7 Calculations in scientific notation 11Exercises 122 Collecting and summarizing data 132.1 Sampling methods 132.1.1 Research design 132.1.2 Random sampling 152.1.3 Systematic sampling 162.1.4 Stratified sampling 172.2 Graphical summaries 172.2.1 Frequency distributions and histograms 172.2.2 Time series plots 212.2.3 Scatter plots 222.3 Summarizing data numerically 242.3.1 Measures of central tendency: mean, median and mode 242.3.2 Mean 242.3.3 Median 252.3.4 Mode 252.3.5 Measures of dispersion 282.3.6 Variance 292.3.7 Standard deviation 302.3.8 Coefficient of variation 302.3.9 Skewness and kurtosis 33Exercises 333 Probability and sampling distributions 373.1 Probability 373.1.1 Probability, statistics and random variables 373.1.2 The properties of the normal distribution 383.2 Probability and the normal distribution: z‐scores 393.3 Sampling distributions and the central limit theorem 43Exercises 474 Estimating parameters with confidence intervals 494.1 Confidence intervals on the mean of a normal distribution: the basics 494.2 Confidence intervals in practice: the t‐distribution 504.3 Sample size 534.4 Confidence intervals for a proportion 53Exercises 545 Comparing datasets 555.1 Hypothesis testing with one sample: general principles 555.1.1 Comparing means: one‐sample z‐test 565.1.2 p‐values 605.1.3 General procedure for hypothesis testing 615.2 Comparing means from small samples: one‐sample t‐test 615.3 Comparing proportions for one sample 635.4 Comparing two samples 645.4.1 Independent samples 645.4.2 Comparing means: t‐test with unknown population variances assumed equal 645.4.3 Comparing means: t‐test with unknown population variances assumed unequal 685.4.4 t‐test for use with paired samples (paired t‐test) 715.4.5 Comparing variances: F‐test 745.5 Non‐parametric hypothesis testing 755.5.1 Parametric and non‐parametric tests 755.5.2 Mann–whitney U‐test 75Exercises 796 Comparing distributions: the Chi‐squared test 816.1 Chi‐squared test with one sample 816.2 Chi‐squared test for two samples 84Exercises 877 Analysis of variance 897.1 One‐way analysis of variance 907.2 Assumptions and diagnostics 997.3 Multiple comparison tests after analysis of variance 1017.4 Non‐parametric methods in the analysis of variance 1057.5 Summary and further applications 106Exercises 1078 Correlation 1098.1 Correlation analysis 1098.2 Pearson’s product‐moment correlation coefficient 1108.3 Significance tests of correlation coefficient 1128.4 Spearman’s rank correlation coefficient 1148.5 Correlation and causality 116Exercises 1179 Linear regression 1219.1 Least‐squares linear regression 1219.2 Scatter plots 1229.3 Choosing the line of best fit: the ‘least‐squares’ procedure 1249.4 Analysis of residuals 1289.5 Assumptions and caveats with regression 1309.6 Is the regression significant? 1319.7 Coefficient of determination 1359.8 Confidence intervals and hypothesis tests concerning regression parameters 1379.8.1 Standard error of the regression parameters 1379.8.2 Tests on the regression parameters 1389.8.3 Confidence intervals on the regression parameters 1399.8.4 Confidence interval about the regression line 1409.9 Reduced major axis regression 1409.10 Summary 142Exercises 14210 Spatial statistics 14510.1 Spatial data 14510.1.1 Types of spatial data 14510.1.2 Spatial data structures 14610.1.3 Map projections 14910.2 Summarizing spatial data 15710.2.1 Mean centre 15710.2.2 Weighted mean centre 15710.2.3 Density estimation 15810.3 Identifying clusters 15910.3.1 Quadrat test 15910.3.2 Nearest neighbour statistics 16210.4 Interpolation and plotting contour maps 16210.5 Spatial relationships 16310.5.1 Spatial autocorrelation 16310.5.2 Join counts 164Exercises 17111 Time series analysis 17311.1 Time series in geographical research 17311.2 Analysing time series 17411.2.1 Describing time series: definitions 17411.2.2 Plotting time series 17511.2.3 Decomposing time series: trends, seasonality and irregular fluctuations 17911.2.4 Analysing trends 18011.2.5 Removing trends (‘detrending’ data) 18611.2.6 Quantifying seasonal variation 18711.2.7 Autocorrelation 18911.3 Summary 190Exercises 190Appendix A: Introduction to the R package 193Appendix B: Statistical tables 205References 241Index 243