Statistics for Geography and Environmental Science

Richard Harris, Claire Jarvis

• Publisher: Routledge
• Year: 2014
• ISBN:
  9781317904397
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geography
• Index: Geography

Statistics are important tools for validating theory, making predictions and engaging in policy research. They help to provide informed commentary about social and environmental issues, and to make the case for change. Knowledge of statistics is therefore a necessary skill for any student of geography or environmental science.

This textbook is aimed at students on a degree course taking a module in statistics for the first time. It focuses on analysing, exploring and making sense of data in areas of core interest to physical and human geographers, and to environmental scientists. It covers the subject in a broadly conventional way from descriptive statistics, through inferential statistics to relational statistics but does so with an emphasis on applied data analysis throughout.

1
Data, statistics and geography

Chapter overview

The aim of this chapter is to convince you that studying statistics is a good idea for any student of geography, environmental science or geographical information science.

Our argument is that data collection and analysis are central to the functioning of contemporary society. It follows that knowledge of data handling and of statistics is a necessary skill to contribute to social and scientific debate.

We present statistics as a reflective practice, a way of approaching research that requires a clear and manageable research question to be formulated, a means to answer that question, knowledge of the assumptions of each test used, an understanding of the consequences of violating those assumptions, and awareness of the researcher’s own prejudices when doing the research.

At their simplest, statistics are used to form basic numeric summaries of the processes, events or activities that the data represent. Yet, this is only the starting point for analysis. Statistics can also go beyond a sample of data, to help decide whether information gleaned from the sample is true more generally. Statistics ask if one ‘thing’ is related to another, or if the one causes the other.

We do not claim that statistics are the only way of doing research. But, they are important tools for validating theory, making predictions, helping to make sense of the world, engaging in policy research, offering informed commentary about social and environmental issues, and to help make the case for change.

Learning objectives

By the end of this chapter you will be able to:

• Appreciate the importance of studying statistics as a student of geography, environmental or geographical information science.
• Define what is meant by geographical data and analysis.
• Give a working definition of the difference between geographical and non geographical forms of analysis.
• Summarise some debates surrounding the use of numbers and statistics in human and social geography.
• Have an appreciation of the impact of spatial association when using statistics for geographical enquiry.

1.1 Statistics: a brief introduction

Students tend to be uneasy about statistics. This is hardly surprising. Statistics involve the language of mathematics, of formulae and notation – a language that is mystifying to new learners and worryingly intolerant of mistakes. Concepts such as ‘degrees of freedom’ are less intuitive than they ought to be and frequent use of the Greek alphabet is like shorthand for ‘keep away!’ Yes, learning statistics is a challenge. But the problem is deeper than that: statistics seem innately off-putting:

[E]very year it seems that the majority of students, who apparently grasp many nonstatistical concepts with commensurate ease, struggle to understand statistics.

(Dancey and Reidy 2004, p.1)

Of course, there are exceptions. It is a generalisation to say, ‘Students tend to be uneasy about statistics.’ We have not met all students to ask them. Even if we had, each individual’s response to the question ‘do you like statistics?’ would depend on a range of factors including time of day, their understanding of the last stats class, peer pressure, other work commitments, whether they thought a ‘yes’ would get us to go away, and so on.

However, we are not suggesting every student is uneasy about statistics. We know there is variation between each individual’s attitude and aptitude. Our observation is simply of a general trend and is based on experience. Admittedly, there is a risk that our experience is unusual. There could be widespread fondness for statistics in places other than the Universities of Bristol and Leicester (the institutions in which we work). If so, our generalisation is wrong. But that would surprise us. We believe we have encountered enough sufficiently typical students to remain confident in our assertion that ‘students tend to be uneasy about statistics’.

Is that how you feel? If so, you are not alone. That said, if you understand all you have read so far, then you might be closer to understanding statistics than you previously imagined. Because, in the preceding paragraphs, we laid out a basic principle of statistics: to learn from a sample (of students we have met), something we have confidence will be generally true for other members of the population too (the student population, though we have not met them all), whilst at the same time being mindful of variation (the fact that some students like statistics more than others). The formulae of statistics may seem abstract and confusing, yet all they really do is define and quantify what is meant by confidence and variation, offer ways of detecting a trend, establish how general the trend is, and offer tools to describe and explain what we have found out.

Ultimately geographical data analysis and statistics are about ideas and concepts. These matter far more than the formulae do. The concepts are ways to think about and do research. It is far better you ‘get behind’ these ideas than get stuck in the quagmire of equations. It is easy enough to download free statistical software that can do the calculations for you.

However, we are not convinced that a complete avoidance of equations really helps you learn. Whilst a computer may do the calculation, to know when and why it is made remain important. When you are familiar with their language, equations and notation are the most succinct and least ambiguous way of expressing calculations and concepts. As authors, our responsibility is to help you learn. Nevertheless, you can breathe easy for a while – you will not find any equations in this chapter! Instead, we discuss what we mean by geographical data analysis, make a case for why studying statistics is important (even if you have no intention of using them ever again) and consider some of the practical problems involved in employing statistical techniques in geographical research.

1.2 Why you should study statistics

A good question is ‘why?’ Why do you need to study statistics? Are they really relevant to your learning, to your research plans?

Reasons for human geographers

Questions about the use of numbers and statistics in, especially, human geography have been influenced by the ‘cultural turn’ of the social sciences and humanities. We address some of the issues later in this chapter. For now we make a simple appeal to the more philosophically sceptical student. Data collection and analysis are central to the functioning of contemporary societies, underpinning systems of science, governance and production. This is evident by listening to a news channel: have the Dow Jones indices risen or fallen; what is the crime rate in your locality; how many pupils passed examinations this year; what impact did that have on school ‘performance tables’; has the government met targets on reducing carbon emissions; who is topping the baseball league; what are the waiting times at your local hospital; was this the wettest or hottest summer on record; how long should we wait before saying that an outbreak of seasonal flu has passed. . .? It follows that knowledge of statistics is an entry into debate, informed critique and the possibility of change.

Consider the following text that appeared on the website of the new economics foundation (nef), ‘an independent think-and-do tank that inspires and demonstrates real economic well-being’:

What gets counted, counts. nef is redefining approaches to value and measurement so that those things that matter most to people, communities and to achieving a sustainable planet are made visible and measurable.

Practices of measurement and valuation are still often focused narrowly and on the short term. Sometimes things that are easy to count, outputs, are the things that get measured and thereby valued. Instead nef believes measures should be focused on outcomes and how lives, communities or the environment changes as a result of policy.

(www.neweconomics.org)

This is a very positive agenda and one we embrace. At the same time, we recognise that some see counting as part of the problem: it classifies, it separates, it labels in ways that can reflect narrow political interests. However, to withdraw to a position where lack of knowledge prevents informed criticism is utterly self-defeating: it leaves the status quo free from effective challenge.

As Barnes and Hannah (2001, p.379) note:

geographers should take numbers and statistics seriously [. . .] because they are a crucial component in the construction of social reality.

We need not like the reality and can raise important questions about how, why and for whom our worlds are ‘organised, controlled, manipulated, studied, and known’ (Surveillance Studies Network 2006). But it is best to do so from an informed position. We cannot enter the debate without the requisite knowledge and understanding to do so. In short, there is little sense in standing on the sidelines, even if learning statistics is not an enticing prospect. Dorling (2003, pp.369–370) understands this, writing:

Statistics are duller than ditch water. In and of themselves they tend to be of interest to people who are not very interesting. [!] To me, it is only when statistics are set in wider context that they begin to come to life [. . .] Suppose you are interested in the issue of poverty. Poverty rates are statistics [. . .] If you are interested in why higher levels of poverty persist in some places and not others [. . .] you are unlikely to get far without the numbers and methods which make up statistics.

Presented clearly, statistical information can catch the media’s eye. Here is what the BBC reported about Thomas and Dorling’s (2007) social atlas of British society, on Saturday 8 September 2007 when the book featured as a leading news item:

CLASS SEGREGATION ‘ON THE RISE’

A UK social atlas suggests that British society is becoming more segregated by class, researchers have said [. . .] It found that:

• An average child in the wealthiest 10% of neighbourhoods can expect to inherit at least 40 times as much wealth as a typical child in the poorest 10%
• In some areas, 16-to-24-year-olds are 50 times more likely to attend an elite university than in others
• In the most impoverished parts of the country young adults in this age group are almost 20 times more likely not to be in education, employment or training than those in the wealthiest neighbourhoods
• There are no large neighbourhoods where under five year olds from the highest social class spend time with any other class of children other the one just beneath them.

(http://news.bbc.co.uk/1/hi/uk/6984707.stm, after Thomas and Dorling, 2007)

People tend to be cynical about statistics but they can be used to support social action. An obvious example is how they are enacted in the debate about climate change. Statistics predicting temperature increases between 1.1 and 6.4°C over the next century, and research indicating that 2°C is the threshold beyond which there are dangerous impacts to nature, humans and the global economy, are dramatic reminders of the potential impact of global warming (Intergovernmental Panel on Climate Change 2007). They have caught the public eye and been used to mobilise political support for the reduction of carbon emissions. But, like many statistics, they have also proved contentious and some groups have rallied against them.

Reasons for GI scientists

For the user of geographical information systems, we seek to complement the textbook introductions to geographical information science. Those textbooks tend to focus on technologies to collect geographical data, show how that information is encoded and visualised by computer systems, and explain how useful knowledge can be obtained by querying, linking and manipulating the data in particular ways.

The amount of data ‘out there’ is enormous and increasing rapidly (but with uneven geographical coverage). Neogeography has emerged as a term partly about how geospatial and Internet-based technologies such as Google Maps can be used to share and to display geographical data, without expert training in GIS or cartography (see, for example, Turner 2006).

Whatever the merits of this ‘new geography’ it benefits from a shot of the old. As a baseline, the added extra of studying statistics is to address the uncertainties and ambiguities of using data analytically. A more progressive reason for studying statistics is because of the increasing integration of mapping capabilities, the visualisation of data and of statistical analysis in free-to-download software packages (Bivand et al. 2008; Rey and Anselin 2006).

Reasons for all readers

The benefit of studying statistics is in gaining a skill set that is transferable to other research methods, disciplines and walks of life. In many countries there is a recognised ‘shortage of well developed quantitative skills across the social sciences and a pressing need to build capacity’ (www.esrc.ac.uk). Careers seeking statistical expertise include actuarial work, marketing consultancy, environmental assessment, policy research, careers in government, and many more.

Studying statistics encourages an approach to research that is reflective, thoughtful and mindful of the limitations of data and their analysis. Encouraging the researcher to form a clear and manageable research question, a means to answer the question, and awareness of the assumptions, methodological limitations and the researcher’s own prejudices is a discipline conducive to all empirical work, quantitative or qualitative.

For statistical research, it is good practice to ask whether the results have both statistical and substantive meaning. Focusing on the statistical helps to avoid sensationalising events that are either potentially random or entirely predictable – to avoid claiming they are unusual when they are not.

Focusing on the substantive gets away from mechanical thinking and blithely assumi...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• Preface
• About this book
• 1 Data, statistics and geography
• 2 Descriptive statistics
• 3 The normal curve
• 4 Sampling
• 5 From description to inference
• 6 Hypothesis testing
• 7 Relationships and explanations
• 8 Detecting and managing spatial dependency
• 9 Exploring spatial relationships
• Epilogue
• Appendix
• Index