Introduction

No one wants to be just another statistic. Perhaps this is because of the way that statistical descriptions of society often seem to obscure the individual lives that they represent, or perhaps it is because many of the statistics that we hear reported enumerate events that we would like to avoid such as divorce, violent crime and mortality. However, statistics play an important role in the social world. They provide information which bodies such as local authorities or national governments can potentially use to make policy decisions, or which can be used to evaluate the effectiveness of existing policies. Increasingly data and statistics about institutions such as schools, hospitals and police forces have been made available to the general public. This type of data is often published on the basis that it allows individuals to make informed decisions - for example about which secondary school might be best for their child, or which hospital to go to for a hip operation. However, there is also an argument that these types of statistics fulfil a political purpose in reducing the power of professionals by making their performance more visible and allowing for comparisons to be made. This proliferation of statistics has also led to increasing debate about how these figures are constructed. There is a growing recognition that, although numbers are often thought of as 'hard facts' when compared with more subjective case studies or individual narratives, in reality every published statistic is the result of a number of different decisions about how something should be categorized and counted, or not counted. As statistics become ever more ubiquitous, aided by the power and immediacy of the world wide web, so it becomes even more essential that as citizens we possess the statistical literacy to make informed judgements about how to interpret them and how to decode their political purpose.

To understand how to calculate percentages, how to decipher a table and how to interpret a graph requires a feel for numbers. Many people lack confidence in their numerical abilities and many students studying for degrees in the social sciences have been overheard saying 'I'm no good with numbers.' However, the vast majority of people already have a very sound understanding of number. There is no question that people would rather have a 10 per cent pay rise than a 2.5 per cent pay rise. People would rather win a £10 bet placed on the 100 to one outsider than the two to one favourite in a horse race.

This book is not about sophisticated mathematical techniques or complicated formulae. It is about building on the basic understandings we all have about numbers and introducing some straightforward techniques for using numbers to describe the social world. In addition to providing a wide range of examples of how statistics are used in society, the book also aims to describe the nature of some of the main government social surveys in Britain. This book is therefore more about politics than it is about algebra or sums.

The word 'statistics' comes from German and originally referred to pieces of information about the state, particularly its military strength. With the birth of industrialism came an interest in social data. For the early Victorians, 'statisticians' were those who collected social information about the inhabitants of emerging capitalist societies. The first volumes of the Journal of the Royal Statistical Society were full of articles describing the social conditions of the time. Gradually the word 'statistics' was restricted to quantitative information of that kind, and came to be synonymous with what we would now call 'data', spreading its meaning beyond social data to biological and other types of data. Finally, as theoretical advances were made, particularly in the theory of sampling and of the regularities which random subsets of data display, statistics swapped disciplinary camps and came under the provenance of mathematics.

Mathematical statisticians have solved some very important problems in the area of sampling theory. They can tell us, with some precision, how likely it is that a property of a small sample drawn at random from a larger population holds true for that larger population. In general, they have elaborated the process of inference, i.e. generalizing from small samples. Because people who teach mathematical statistics are justly proud of these achievements, inferential statistics tends to occupy a large place in their courses and many books on quantitative data analysis focus almost exclusively on these topics.

However, this book does not set out to be a course in statistical theory. It seeks to restore the emphasis to data analysis and to the detective work involved in sifting through and piecing together numerical evidence about the social world. The techniques which are presented here are designed to help the researcher look at batches of numbers and make sense of them. Some of the best of these techniques were put forward by John Tukey, whose hero is Sherlock Holmes, and whose maxim is 'Seeing is believing.' In fact, Tukey probably did little more than to formalize the kind of logic in use by practising statisticians the world over. The main original sourcebooks are Tukey's Exploratory Data Analysis (1977) and Mosteller and Tukey's Data Analysis and Regression (1977). A more recent edition including many of the original techniques is Hoaglin, Mosteller and Tukey (2006). The group of techniques that have come to be known as Exploratory Data Analysis (EDA) provide the data analyst with a set of techniques with which to explore numerical data and to gain an understanding of its most salient features through emphasizing graphical display.

Anyone who is eventually going to make a career analysing data must be able to answer the question 'Is your sample size big enough for you to be fairly sure of that?' This is, however, a second-order question in comparison with 'What do these data say?' or 'Might that result be spurious?' This book therefore aims to keep a balance between introducing the main techniques needed for understanding the patterns or stories within the data and discussing how to check whether the patterns that appear are also likely to be found within the wider population of interest. This second edition of Exploring Data therefore retains the original book's emphasis on exploring and understanding the patterns to be found within sets of data but also includes an introduction to inferential statistics.

How to use this book

The book is divided into three parts. The first part covers various techniques for examining variables one at a time. The second part covers relationships between two variables. And - you've guessed it - the third covers situations in which a third variable is brought into the picture. Here three stands in for many; once you understand how to manipulate three variables together, you are ready to understand in principle how to extend the techniques to many variables. In many cases the later chapters in the book build on material introduced earlier; however, some chapters are relatively free standing. While some readers may want to work through the book chapter by chapter others may prefer to tackle topics in a different order. We have therefore suggested at or near the beginning of each chapter which others are required reading.

Data analysis is not a spectator sport. No amount of reading about it substitutes for doing it. The exercises at the end of each chapter are therefore an integral part of the book, and should not be skipped. Sometimes they allow illustration of a point which the example used in the chapter did not show. Read the suggested answers that are provided on the accompanying website www.polity.co.uk/exploringdata, but don't be put off if you did something different, or came to rather different conclusions. One of the most important rules of data analysis is that there is no one model that best or uniquely fits a set of data.

Most of the chapters also have an associated appendix that introduces a major data source. They have been put on the accompanying website so that they can be referred to quickly and easily and can be updated as the major government surveys and sources of data are themselves revised and changed.

While the book starts by suggesting some simple pencil and paper techniques for understanding data, the computer has now become an important part of the data analyst's armoury. At the time of writing, a statistical computer package called SPSS (the Statistical Package for the Social Sciences) is widely used by social scientists in the UK and provides a fast, efficient and well-documented interactive package for data analysis (Norusis, 2005). The book therefore includes basic instructions as to how the various techniques described can be accomplished with SPSS (version 13). However, the book is not primarily intended as an instruction manual for the SPSS package and the sections on SPSS can therefore be ignored if you do not have access to it. There are a series of datasets which are used for the computer exercises and which can be used for further exploratory work of your own devising. They are listed and documented on the accompanying website. The datasets have all been deposited at the ESRC Data Archive at the University of Essex, and it is straightforward to download them via the internet.

Key terms are in bold type in the text when they first appear or where they are given a clear...