Quantitative and Statistical Approaches to Geography

Quantitative and Statistical Approaches to Geography: A Practical Manual is a practical introduction to some quantitative and statistical techniques of use to geographers and related scientists. This book is composed of 15 chapters, each begins with an outline of the purpose and necessary mechanics of a technique or group of techniques and is concluded with exercises and the particular approach adopted. These exercises aim to enhance student's ability to use the techniques as part of the process by which sound judgments are made according to scientific standards while tackling complex problems. After a brief introduction to the principles of quantitative and statistical geography, this book goes on dealing with the topics of measures of central tendency; probability statements and maps; the problem of time-dependence, time-series analysis, non-normality, and data transformations; and the elements of sampling methodology. Other chapters cover the confidence intervals and estimation from samples, statistical hypothesis testing, analysis of contingency tests, and non-parametric tests for independent and dependent samples. The final chapters consider the evaluation of correlation coefficients, regression prediction, and choice and limitations of statistical techniques. This book is of value to undergraduate geography students.

1. Introduction. Quantification in a Context

Exercise 1 : Problems of measurement in the invention of shape indices for landforms

Exercise 2: Scientific method in the analysis of the Roman road network in England and Wales

2. Measures of Central Tendency

Exercise 3: Application of histograms and use of the mode in the reconstruction and dating of glacier fluctuations in Swedish Lappland

Exercise 4: Comparison of measures of central tendency in the study of a fan of erratics in the Central Lowlands of Scotland

3. Measures of dispersion

Exercise 5: Application of dispersion diagrams and measures of dispersion in the study of British rainfall patterns

4. Probability Statements and Probability Maps

Exercise 6: Use of tables of the normal distribution function for making elementary probability statements

Exercise 7: Construction of a probability map of atmospheric pollution for north-west Europe

5. The Problem of Time-Dependence and Time-Series Analysis

Exercise 8: Running means and the analysis of birth and death rates in preindustrial Norway

6. The Problem of Non-Normality and Data Transformations

Exercise 9: Use of transformations and probability paper in the analysis of the wealth of nations at a world scale

7. Elements of sampling methodology

Exercise 10: Application of sampling techniques in the extraction of information from soil maps in north Wales

8. Confidence Intervals and Estimation from Samples

Exercise 11: Use of tables of the t distribution and the calculation of confidence intervals around sample means

Exercise 12: Use of confidence intervals in the evaluation of models of vegetation succession in the Jotunheimen Mountains of southern Norway

9. Statistical Hypothesis Testing Based on Students t

Exercise 13: Hypothesis testing about the upper limit of agriculture on the North York Moors (north-east England) using Student's t-tests

10. x2 Tests and The Analysis of Contingency Tables

Exercise 14: Hypothesis testing about the location of Eskimo settlements on the coast of Baffin Island, Canada, using x2 tests

Exercise 15: Analysis of spatial variation of water quality in the River Exe drainage basin (south-west England) using x2 tests

11. Further Non-Parametric Tests for Independent Samples

Exercise 16: A comparative study of hobby farms and commercial farms in Ontario, Canada, using Kolmogorov-Smirnov tests

Exercise 17: Do regions exist? Testing the distinctiveness of planning regions in South Wales using Kruskal-Wallis analysis of variance by ranks

12. Non-Parametric Tests for Dependent (matched) Samples

Exercise 18: Form and origin of saw-tooth moraines in Bödalen, Norway, investigated by Wilcoxon tests and Mann-Whitney tests

Exercise 19: Recent trends in causes of death in some advanced Western societies characterized by application of Friedman analysis of variance by ranks

13. The Strength of Relationships: Correlation Coefficients

Exercise 20: An investigation into the processes forming modern beach ridges on Jura, Scottish Inner Hebrides, using Pearson's correlation coefficient

Exercise 21: Analysis of indicators of economic development for Latin American countries by application of Spearman's rank correlation coefficient

14. The Form of Relationships and Prediction by Regression

Exercise 22: Prediction of annual temperatures from sea-ice conditions off Iceland using regression analysis

Exercise 23: Application of regression to the description and analysis of urban population densities in London and Chicago

15. Conclusion: Choice and Limitations of Statistical Techniques

Exercise 24: Choosing an appropriate technique for particular purposes Further Reading

References

Answers to Numerical Questions

Appendix: Statistical Tables

A. Tables of the z statistic (the normal distribution function)

B. Tables of random sampling numbers

C. Tables of the Student / statistic

D. Tables of the x2 statistic

E. Tables of the Kolmogorov-Smirnov D statistic

F. Tables of the Mann-Whitney U statistic

G. Tables of the Kruskal-Wallis H statistic

Ç. Tables of the Wilcoxon T statistic

I. Tables of the Friedman x2 statistic

J. Tables of the Spearman rank correlation coefficient

Index