Statistical Analysis of Geographical Data

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.

Autorentext

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

Zusammenfassung
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.

Inhalt

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: zscores 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 tdistribution 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: onesample ztest 56

5.1.2 pvalues 60

5.1.3 General procedure for hypothesis testing 61

5.2 Comparing means from small samples: onesample ttest 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: ttest with unknown population variances assumed equal 64

5.4.3 Comparing means: ttest with unknown population variances assumed unequal 68

5.4.4 ttest for use with paired samples (paired ttest) 71

5.4.5 Comparing variances: Ftest 74

5.5 Nonparametric hypothesis testing 75

5.5.1 Parametric and nonparametric tests 75

5.5.2 Mannwhitney Utest 75

Exercises 79

6 Comparing distributions: the Chisquared test 81

6.1 Chisquared test with one sample 81

6.2 Chisquared test for two samples 84

Exercises 87

7 Analysis of variance 89

7.1 Oneway analysis of variance 90

7.2 Assumptions and diagnostics 99

7.3 Multiple comparison tests after analysis of variance 101

7.4 Nonparametric 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 productmoment 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 Leastsquares linear regression 121

9.2 Scatter plots 122 9.3 Choosing the ...