Statistical Analysis of Geographical Data (eBook)

An Introduction

Simon James Dadson (Autor)

eBook Download: PDF

2017
John Wiley & Sons (Verlag)
978-1-118-52511-1 (ISBN)

Infos

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.

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

Inhalt

Title Page 5
Copyright Page 6
Contents 7
Preface 13
Chapter 1 Dealing with data 15
1.1 The role of statistics in geography 15
1.1.1 Why do geographers need to use statistics? 15
1.2 About this book 17
1.3 Data and measurement error 17
1.3.1 Types of geographical data: nominal, ordinal, interval, and ratio 17
1.3.2 Spatial data types 19
1.3.3 Measurement error, accuracy and precision 20
1.3.4 Reporting data and uncertainties 21
1.3.5 Significant figures 23
1.3.6 Scientific notation (standard form) 24
1.3.7 Calculations in scientific notation 25
Exercises 26
Chapter 2 Collecting and summarizing data 27
2.1 Sampling methods 27
2.1.1 Research design 27
2.1.2 Random sampling 29
2.1.3 Systematic sampling 30
2.1.4 Stratified sampling 31
2.2 Graphical summaries 31
2.2.1 Frequency distributions and histograms 31
2.2.2 Time series plots 35
2.2.3 Scatter plots 36
2.3 Summarizing data numerically 38
2.3.1 Measures of central tendency: mean, median and mode 38
2.3.2 Mean 38
2.3.3 Median 39
2.3.4 Mode 39
2.3.5 Measures of dispersion 42
2.3.6 Variance 43
2.3.7 Standard deviation 44
2.3.8 Coefficient of variation 44
2.3.9 Skewness and kurtosis 47
Exercises 47
Chapter 3 Probability and sampling distributions 51
3.1 Probability 51
3.1.1 Probability, statistics and random variables 51
3.1.2 The properties of the normal distribution 52
3.2 Probability and the normal distribution: z-scores 53
3.3 Sampling distributions and the central limit theorem 57
Exercises 61
Chapter 4 Estimating parameters with confidence intervals 63
4.1 Confidence intervals on the mean of a normal distribution: the basics 63
4.2 Confidence intervals in practice: the t-distribution 64
4.3 Sample size 67
4.4 Confidence intervals for a proportion 67
Exercises 68
Chapter 5 Comparing datasets 69
5.1 Hypothesis testing with one sample: general principles 69
5.1.1 Comparing means: one-sample z-test 70
5.1.2 p-values 74
5.1.3 General procedure for hypothesis testing 75
5.2 Comparing means from small samples: one-sample t-test 75
5.3 Comparing proportions for one sample 77
5.4 Comparing two samples 78
5.4.1 Independent samples 78
5.4.2 Comparing means: t-test with unknown population variances assumed equal 78
5.4.3 Comparing means: t-test with unknown population variances assumed unequal 82
5.4.4 t-test for use with paired samples (paired t-test) 85
5.4.5 Comparing variances: F-test 88
5.5 Non-parametric hypothesis testing 89
5.5.1 Parametric and non-parametric tests 89
5.5.2 Mann–whitney U-test 89
Exercises 93
Chapter 6 Comparing distributions: the Chi-squared test 95
6.1 Chi-squared test with one sample 95
6.2 Chi-squared test for two samples 98
Exercises 101
Chapter 7 Analysis of variance 103
7.1 One-way analysis of variance 104
7.2 Assumptions and diagnostics 113
7.3 Multiple comparison tests after analysis of variance 115
7.4 Non-parametric methods in the analysis of variance 119
7.5 Summary and further applications 120
Exercises 121
Chapter 8 Correlation 123
8.1 Correlation analysis 123
8.2 Pearson’s product-moment correlation coefficient 124
8.3 Significance tests of correlation coefficient 126
8.4 Spearman’s rank correlation coefficient 128
8.5 Correlation and causality 130
Exercises 131
Chapter 9 Linear regression 135
9.1 Least-squares linear regression 135
9.2 Scatter plots 136
9.3 Choosing the line of best fit: the ‘least-squares’ procedure 138
9.4 Analysis of residuals 142
9.5 Assumptions and caveats with regression 144
9.6 Is the regression significant? 145
9.7 Coefficient of determination 149
9.8 Confidence intervals and hypothesis tests concerning regression parameters 151
9.8.1 Standard error of the regression parameters 151
9.8.2 Tests on the regression parameters 152
9.8.3 Confidence intervals on the regression parameters 153
9.8.4 Confidence interval about the regression line 154
9.9 Reduced major axis regression 154
9.10 Summary 156
Exercises 156
Chapter 10 Spatial Statistics 159
10.1 Spatial Data 159
10.1.1 Types of Spatial Data 159
10.1.2 Spatial Data Structures 160
10.1.3 Map Projections 163
10.2 Summarizing Spatial Data 171
10.2.1 Mean Centre 171
10.2.2 Weighted Mean Centre 171
10.2.3 Density Estimation 172
10.3 Identifying Clusters 173
10.3.1 Quadrat Test 173
10.3.2 Nearest Neighbour Statistics 176
10.4 Interpolation and Plotting Contour Maps 176
10.5 Spatial Relationships 177
10.5.1 Spatial Autocorrelation 177
10.5.2 Join Counts 178
Exercises 185
Chapter 11 Time series analysis 187
11.1 Time series in geographical research 187
11.2 Analysing time series 188
11.2.1 Describing time series: definitions 188
11.2.2 Plotting time series 189
11.2.3 Decomposing time series: trends, seasonality and irregular fluctuations 193
11.2.4 Analysing trends 194
11.2.5 Removing trends (‘detrending’ data) 200
11.2.6 Quantifying seasonal variation 201
11.2.7 Autocorrelation 203
11.3 Summary 204
Exercises 204
Appendix A: Introduction to the R package 207
A.1 Obtaining R 207
A.2 Simplecalculations 207
A.3 Vectors 210
A.4 Basicstatistics 211
A.5 Plottingdata 211
A.6 Multiplefigures 213
A.7 Readingand writing data 216
A.8 Summary 218
Appendix B: Statistical tables 219
References 255
Index 257
EULA 267

Produkt-Details

• Erscheint lt. Verlag: 14.3.2017
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Allgemeines / Lexika
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geografie / Kartografie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Technik
• Schlagworte: Analysis of Variance • calculation of confidence intervals • collection and analysis of data • confidence intervals • earth sciences • geographical investigations statistics • geographical literature • Geographie • Geography • Geowissenschaften • graphical description of datasets • hypothesis testing • linear regression • numerical description of datasets • physical geography • Physiogeographie • Probability • Simon James Dadson • statistical analysis in geography • Statistical Analysis of Geographical Data: An Introduction • Statistics • Statistics Analysis of Geographical Data • Statistik • Statistische Analyse • uncertainty analysis
• ISBN-10: 1-118-52511-6 / 1118525116
• ISBN-13: 978-1-118-52511-1 / 9781118525111