Statistical Analysis of Geographical Data

An Introduction

Simon James Dadson

• Publisher: Wiley-Blackwell
• Year: 2017
• ISBN:
  9781118525142
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geology & Earth Sciences

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.

1
Dealing with data

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STUDY OBJECTIVES

• Understand the nature and purpose of statistical analysis in geography.
• View statistical analysis as a means of thinking critically with quantitative information.
• Distinguish between the different types of geographical data and their uses and limitations.
• Understand the nature of measurement error and the need to account for error when making quantitative statements.
• Distinguish between accuracy and precision and to understand how to report the precision of geographical measurements.
• Appreciate the methodological limitations of statistical data analysis.

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1.1 The role of statistics in geography

1.1.1 Why do geographers need to use statistics?

Statistical analysis involves the collection, analysis and presentation of numerical information. It involves establishing the degree to which numerical summaries about observations can be justified, and provides the basis for forming judgements from empirical data.

Take the following media headlines, for example:

We know in the next 20 years the world population will increase to something like 8.3 billion people.

Sir John Beddington, UK Government Chief Scientist¹

2010 hits global temperature high.

BBC News, 20th January 2011²

Each of these statements invites critical scrutiny. The reliability of their sources encourages us to take them seriously, but how do we know that they are correct? It is hard enough to try to predict what one human being will do in any particular year, let alone what several billion are going to do in the next 20 years. How were these predictions made? How was the rate of change of world population calculated? What were the assumptions? What does the author mean by ‘something like’? The number 8.3 billion is quite a precise number: why didn’t the author just say 8 billion or almost 10 billion?

Similarly, how do we know that 2010 is the global temperature high, when temperature is only measured at a small number of measuring stations? How would we go on to investigate whether anthropogenic warming caused the record‐breaking temperature in 2010 or whether it was just a fluke?

Statistical analysis provides some of the tools that can answer some of these questions. This book introduces a set of techniques that allow you to make sure that the statistical statements that you make in your own work are based on a sound interpretation of the data that you collect.

There are four main reasons to use statistical techniques:

• to describe and measure the things that you observe;
• to characterize measurement error in your observations;
• to test hypotheses and theories;
• to predict and explain the relationships between variables.

1.2 About this book

One of the best ways to learn any mathematical skill is through repeated practice, so the approach taken in this book uses many examples. The presentation of each topic begins with an introduction to the theoretical principles: this is then followed by a worked example. Additional exercises are given to allow the reader to develop their understanding of the topics involved.

The use of computer packages is now common in statistical analysis in geography: it removes many of the tedious aspects of statistical calculation leaving the analyst to focus on experimental design, data collection, and interpretation. Nevertheless, it is essential to understand how the properties of the underlying data affect the value of the resulting statistics or the outcome of the test under evaluation.

Two kinds of computer software are referred to in this book. The more basic calculations can be performed using a spreadsheet such as Microsoft Excel. The advantages of Excel are that its user interface is well‐known and it is almost universally available in university departments and on student computers. For more advanced analysis, and in situations where the user wishes to process large quantities of data automatically, more specialized statistical software is better. This book also refers to the open‐source statistical package called ‘R’ which is freely available from http://www.r‐project.org/. In addition to offering a comprehensive collection of well‐documented statistical routines, the R software provides a scripting facility for automation of complex data analysis tasks and can produce publication‐quality graphics.

1.3 Data and measurement error

1.3.1 Types of geographical data: nominal, ordinal, interval, and ratio

Four main types of data are of interest to geographers: nominal, ordinal, interval, and ratio. Nominal data are recorded using categories. For example, if you were to interview a group of people and record their gender, the resulting data would be on a nominal, or categorical, scale. Similarly, if an ecologist were to categorize the plant species found in ...