Practical Statistics for Geographers and Earth Scientists

Nigel Walford

• Publisher: Wiley
• Year: 2011
• ISBN:
  9781119957027
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geography
• Index: Geography

Practical Statistics for Geographers and Earth Scientists provides an introductory guide to the principles and application of statistical analysis in context. This book helps students to gain the level of competence in statistical procedures necessary for independent investigations, field-work and other projects. The aim is to explain statistical techniques using data relating to relevant geographical, geospatial, earth and environmental science examples, employing graphics as well as mathematical notation for maximum clarity. Advice is given on asking the appropriate preliminary research questions to ensure that the correct data is collected for the chosen statistical analysis method. The book offers a practical guide to making the transition from understanding principles of spatial and non-spatial statistical techniques to planning a series analyses and generating results using statistical and spreadsheet computer software.

• Learning outcomes included in each chapter
• International focus
• Explains the underlying mathematical basis of spatial and non-spatial statistics
• Provides an geographical, geospatial, earth and environmental science context for the use of statistical methods
• Written in an accessible, user-friendly style

Datasets available on accompanying website at www.wiley.com/go/Walford

Section 1

First principles

1

What's in a number?

Chapter 1 provides a brief review of the development of quantitative analysis in Geography, Earth and Environmental Science and related disciplines. It also discusses the relative merits of using numerical data and how numbers can be used to represent qualitative characteristics. A brief introduction to mathematical notation and calculation is provided to a level that will help readers to understand subsequent chapters. Overall this introductory chapter is intended to define terms and to provide a structure for the remainder of the book.

Learning outcomes

This chapter will enable readers to:

• outline the difference between quantitative and qualitative approaches, and their relationship to statistical techniques;
• describe the characteristics of numerical data and scales of measurement;
• recognize forms of mathematical notation and calculation that underlie analytical procedures covered in subsequent chapters;
• plan their reading of this text in relation to undertaking an independent research investigation in Geography and related disciplines.

1.1 Introduction to quantitative analysis

Quantitative analysis comprises one of two main approaches to researching and understanding the world around us. In simple terms quantitative analysis can be viewed as the processing and interpretation of data about things, sometimes called phenomena, which are held in a numerical form. In other words, from the perspective of Geography and other Earth Sciences, it is about investigating the differences and similarities between people and places that can be expressed in terms of numerical quantities rather than words. In contrast, qualitative analysis recognizes the uniqueness of all phenomena and the important contribution towards understanding that is provided by unusual, idiosyncratic cases as much as by those conforming to some numerical pattern. Using the two approaches together should enable researchers to develop a more thorough understanding of how processes work that lead to variations in the distribution of phenomena over the Earth's surface than by employing either methodology on its own.

If you are reading this book as a student on a university or college course, there will be differences and similarities between you and the other students taking the same course in terms of such things as your age, height, school level qualifications, home town, genetic make-up, parental annual income and so on. You will also be different because each human being, and for that matter each place on the Earth, is unique. There is no one else exactly like you, even if you have an identical twin, nor is there any place exactly the same as where you are reading this book. You are different from other people because your own attitudes, values and feelings have been moulded by your upbringing, cultural background and physical characteristics. In some ways, it is the old argument of nature versus nurture, but in essence we are unique combinations of both sets of factors. You may be reading this book in your room in a university hall of residence, and there are many such places in the various countries of the world and those in the same institution often seem identical, but the one where you are now is unique. Just as the uniqueness of individuals does not prevent analysis of people as members of various different groups, so the individuality of places does not inhibit investigation of their distinctive and shared characteristics.

What quantitative analysis attempts to do is concentrate on those factors that seem to be important in producing differences and similarities between individual phenomena and to disregard those producing aberrant outcomes. Confusion between quantitative and qualitative analysis may arise because the qualitative characteristics of people and places are sometimes expressed in numerical terms. For example, areas in city may be assigned to a series of categories, such as downtown, suburbs, shopping mall, commercial centre, housing estate and so on, to which numerical codes can be attached, or a person's gender may be labelled as male or female with equivalent numerical values such as 1 or 2. Just as qualitative characteristics can be turned into numerical codes, so too can numerical measurements be converted, either singly or in combination, into descriptive labels. Many geodemographic descriptions of neighbourhoods, such as (e.g. Old people, detached houses; Larger families, prosperous suburbs; Older rented terraces; and Council flats, single elderly) are based on having taken a selection of different socioeconomic and demographic numerical counts for different locations and combined them in an analytical melting pot so as to produce a label describing what the places are like.

The major focus of this book is on quantitative analysis as applied to Geography and other Earth Sciences. However, this should not be taken to imply that quantitative analysis is in some definitive sense regarded as “better”, or even more scientific, than qualitative analysis. Nor are these approaches mutually exclusive, since researchers from many disciplines have come to appreciate the advantages of combining both forms of analysis in recent years. This book concentrates on quantitative analysis since for many students, and perhaps researchers, dealing with numbers and statistics is difficult, and trying to understand what these can usefully tell us about the “real” Geography or Earth Science topics that interest us is perplexing. Why should we bother with numbers and statistics, when all we want to do is to understand the process of globalization in political economy, or to explain why we are experiencing a period of global temperature increase, or to identify areas vulnerable to natural hazards?

We can justify bothering with numbers and statistics to answer such research questions in a number of different ways. As with most research, when we actually try to explain things such as globalization, global warming and the occurrence of natural hazards, the answers often seem like commonsense and perhaps even rather obvious. Maybe this is a sign of “good” research because it suggests the process of explaining such things is about building on what has become common knowledge and understanding. If this is true, then ongoing academic study both rests upon and questions the endeavours of previous generations of researchers, and puts across complex issues in ways that can be generally understood. Yet despite the apparent certainty with which the answers to research questions might be conveyed, these are often underlain by an analysis of numerical information that is anything but certain. It is likely that the results of the research are correct, but they may not be. Using statistical techniques gives us a way of expressing this uncertainty and of hedging our bets against the possibility that our particular set of results has only arisen by chance. At some time in the future another researcher might come along and contradict our findings.

But what do we really mean by the phrase “the results of the research ”. For the “consumers”of research, whether the public at large or particular professional groups, the findings, results or outcomes of research are often some piece of crucial factual information. The role of such information is to either confirm facts that are already known or believed, or to fulfil the unquenchable need for new “facts ”. For the academic, these detailed factual results may be of less direct interest than the implications of the research findings, perhaps with regard to some overarching theory. The student undertaking a research investigation as part of the programme of study sits somewhere, perhaps uncomfortably between these two positions. Realistically, many undergraduate students recognize that their research endeavours are unlikely to contribute significantly to theoretical advance, although obviously there are exceptions. Yet they also recognize that their tutors are unlikely to be impressed simply by the presentation of new factual information. Further, such research investigations are typically included in undergraduate degree programmes in order to provide students with a training that prepares them for a career where such skills as collecting and assimilating information will prove beneficial, whether this be in academia or more typically in other professional fields. Students face a dilemma to which there is no simple answer. They need to demonstrate that they have carried out their research in a rigorous scientific manner using appropriate quantitative and qualitative techniques, but they do not want to overburden the assessors with an excess of detail that obscures the implications of their results.

In the 1950s and 1960s a number of academic disciplines “discovered” quantitative analysis and few geography students of the last five decades can fail to have heard of the so-called “quantitative revolution”in their subject area, and some may not have forgiven the early pioneers of this approach. There was, and to some extent still is, a belief that the principles of rigour, replication and respectability enshrined in scientific endeavour sets it apart from, and possibly above, other forms of more discursive academic enquiry. The adoption of the quantitative approach was seen implicitly, and in some cases explicitly, as providing the passport to recognition as a scientific discipline. Geography and other Earth Sciences were not alone, although perhaps were more sluggish than some disciplines, in seeking to establish their scientific credentials. The classical approach to geographical enquiry followed on from the colonial and exploratory legacies of the 18th and 19th centuries. This permeated regional geography in the early 20th century and concentrated on the collection of factual information about places. Using this information to classify and categorize places seemed to correspond with the inductive scientific method that served the purpose of recognizing pattern and regularity in the occurrence of phenomena. However, the difficulty of establishing inductive laws about intrinsically unique places and regions led other geographers to search for ways of applying the deductive scientific method, which was also regarded as more rigorous. The deductive method involves devising hypotheses with reference to existing conditions and testing them using empirical evidence obtained through the measurement and observation of phenomena.

Geography and to a lesser extent the other Earth Sciences have emerged from a period of self-reflection on the scientific nature of their endeavour with an acceptance that various philosophies can coexist and further their collective enterprise. Thus, many university departments include physical geographers and Earth scientists, adhering to generally positivist scientific principles, working alongside human geographers following a range of traditions including humanism, Marxism and structuralism as well as more positivist social science. The philosophical basis of geographical and Earth scientific enquiry has received a further twist in recent decades on account of the growing importance of information and communications technology (ICT). Hence, students in academic departments need to be equipped with the skills not only to undertake research investigations in these areas, but also to handle geographical and spatial data in a digital environment.

Johnston (1979) commented that statistical techniques provide a way of testing hypotheses and the validity of empirical measurements and observations. However, the term statistics is used in a number of different ways. In general usage, it typically refers to the results of data collection by means of censuses and surveys that are published in books, over the Internet or on other media. The associated term “ official statistics”is usually reserved for information that has been collected, analysed and published by national, regional or local government and are therefore deemed to have a certain authority and a connotation of conveying the “truth ”. This belief may be founded upon a presumption of impartiality and rigour, although such neutrality of method or intent cannot realistically be justified or assumed in all instances. Statistics also refers to a branch of mathematics that may be used in scientific investigations to substantiate or refute the results of scientific research. In this sense statistics also has a double meaning, either comprising a series of techniques ranging from simple summarizing measures to complex models involving many variables, or the term may refer to the numerical quantities produced by these techniques. All these senses of the term statistics are relevant to this text, since published statistics may well contribute to research investigations, and statistical techniques and the measures associated with them are an essential part of quantitative analysis. Such techniques are applied to numerical data and serve two general purposes: to confirm or otherwise the significance of research results towards the accumulation of knowledge with respect to a particular area of study; and to establish whether empirical connections between different characteristics for a given set of phenomena are likely to be genuine or spurious.

Different areas of scientific study and research have over the years carved out their own particular niches. For example, in simplistic terms the Life Sciences are concerned with living organisms, the Chemical Sciences with organic and inorganic materials, Political Science with national and international government, Sociology with social groups and Psychology with individuals”mental condition. When these broad categories have become too general then often subdivision occurred with the emergence of fields in the Life Sciences such as cell biology, biochemistry, physiology, etc. Geography and the other Earth Sciences do not seem to fit easily into this seemingly straightforward partitioning of scientific subject matter, since their broad perspective leads to an interest in all the things covered by other academic disciplines, even to the extent of Earth Scientists transferring their allegiance to examine terrestrial processes on other planetary and celestial bodies. No doubt if, or when, ambient intelligent life is found on other planets,“human” geographers will be there investigating its spatial arrangement and distribution. It is commonly argued that the unifying focus of Geography is its concern for the spatial and earthly context in which those phenomena of interest to other disciplines make their home. Thus, for example human geographers are concerned with the same social groups as the sociologist, but emphasize their spatial juxtaposition and interaction rather than the social ties that bind them, although geographers cannot disregard the latter. Similarly, geochemists focus on the chemical properties of minerals not only for their individual characteristics but also for how assemblages combine to form different rocks in distinctive locations. Other disciplines may wonder what Geography and Earth Science add to their own academic endeavour, but geographers and Earth scientists are equally certain that if their area of study did not exist, it would soon need to be invented.

The problem that all this raises for geographers and Earth scientists is how to define and specify the units of observation, the things that are of interest to them, and them alone. One possible solution that emerged during the quantitative revolution was that geography was pre-eminently the science of spatial analysis and therefore it should be concerned with discovering the laws that governed spatial processes. A classical example of this approach in human geography was the search for regions or countries where the collections of settlements conformed to the spatial hierarchy anticipated by central place theory. Physical geographers and Earth scientists also became interested in spatial patterns. Arguably they had more success in associating the occurrence of environmental phenomena with underlying explanatory processes, as evidenced by the development plate tectonics theory in connection with the spatial pattern of earthquake and volcanic zones around the Earth. According to this spatial analytic approach, once the geographer and Earth scientist have identified some spatially distributed phenomena, such as settlements, hospitals, earthquakes or volcanoes, then their investigation can proceed by measuring distance and determining pattern.

This foray into spatial analysis was soon undermined, when it became apparent that exception rather than conformity to proposed spatial laws was the norm. Other approaches, or possibly paradigms, emerged, particularly in human geography, that sought to escape from the straightjacket of positivist science. Advocates of Marxist, behavioural, politicoeconomic and cultural geography have held sway at various times during the last 40 years. However, it is probably fair to say that none of these have entirely rejected using numerical quantities as a way of expressing geographical difference. Certainly in physical geography and Earth Science where many would argue that positivism inevitably still forms the underlying methodology, quantitative analysis has never receded into the background. Despite the vagaries of all these different approaches most geographers and Earth scientists still hold on to the notion that what interests them and what they feel other people should be reminded of is that the Earth, its physical phenomena, its environment and its inhabitants are differentiated and are unevenly distributed over space.

From the practical perspective of this text, what needs to be decided is what constitutes legitimate data for the study of Geography and Earth Science. Let us simply state that a geographical or Earth scientific dataset needs to comprise a collection of data items, facts if you prefer, that relate to a series of spatially distributed phenomena. Such a collection of data needs to relate to at least one discrete and defined section of the Earth and/or its immediate atmosphere. This definition deliberately provides wide scope for various types and sources of data with which to investigate geographical and Earth scientific questions.

The spatial focus of Geography and the Earth Sciences has two significant implications. First, the location of the phenomena or observations units, in other words where they are on or near the Earth's surface is regarded as important. For instance investigations into landforms associated with calcareous rocks need to recognize whether these are in temperate or tropical environments. The nature of such landforms including their features and structures is in part dependent upon prevailing climatic conditions either now or in the past. Second, the spatial arrangement of phenomena may in itself be important, which implies that a means of numerically quantifying the position of different occurrences of the same category of observation may be required. In this case, spatial variables such as area, proximity, slope angle, aspect and volume may form part of the data items captured for the phenomena under investigation.

1.2 Nature of numerical data

We have already seen that quantitative analysis uses numbers in two ways, as shorthand labels for qualitative characteristics to save dealing with long textual descriptions or as actual measurements denoting differences in magnitude. Underlying this distinction is a division of data items into attributes and variables. Williams (1984, p. 4) defines an attribute as “a quality … whereby items, individuals, objects, locations, events, etc. differ from one another.” He contrasted these with variables that “are measured … assigned numerical values relative to some standard – the unit of measurement (Williams, 1984, p. 5). Examples of attributes and variables from Geography and other Earth Sciences are seemingly unbounded in number and diversity, since these fields of investigation cover such a wide range of subject areas. Relevant attributes include such things as rock hardness, soil type, land use, ethnic origin and housing tenure, whereas stream discharge, air temperature, population size, journey time and number of employees are examples of geographical variables. The terms attribute and variable are sometimes confused and applied interchangeably, although we will endeavour to keep to the correct terminology here.

The subdivision of numerical data into different types can also be taken further, into what are known as the scales of measurement. The four scales are usually known as nominal, ordinal, interval and ratio and can be thought of as a sequence implying a greater degree of detail as you progress from the nominal to the ratio. However, strictly speaking the nominal is not a scale of measurement, since it only applies to attributes and therefore is an assessment of qualitative difference rather than magnitude between observations. The other three scales provide a way of measuring difference between observations to determine whether one is smaller, larger or the same as any other in the set. Box 1.1 summarizes the features of each of these measurement scales and shows how it is possible to discard information by moving from the interval/ratio to the nominal scale. Such collapsing or recoding of the values for data items may be carried out for various reasons, but may be necessary when combining a qualitative data item, such as housing tenure, with a quantitative one, such as household income in your analysis.

Box 1.1a: Scales of measurement: location of a selection of McDonalds restaurants in Pittsburgh, USA...

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Preface
• Acknowledgements
• Glossary
• Section 1: First principles
• 1: What's in a number?
• 2: Geographical data: quantity and content
• 3: Geographical data: collection and acquisition
• 4: Statistical measures (or quantities)
• 5: Frequency distributions, probability and hypotheses
• Section 2: Testing times
• 6: Parametric tests
• 7: Nonparametric tests
• Section 3: Forming relationships
• 8: Correlation
• 9: Regression
• 10: Correlation and regression of spatial data
• References
• Further Reading
• Plate
• Index