How to Make Sense of Statistics

Stephen Gorard

• Publisher: SAGE Publications Ltd
• Year: 2021
• Print ISBN: 9781526413826, 9781526413819
• eBook ISBN: 9781529755855
• Edition: 1
• Topic: Social Sciences
• Subtopic: Probability & Statistics
• Index: Social Sciences

In a new textbook designed for students new to statistics and social data, Stephen Gorard focuses on non-inferential statistics as a basis to ensure students have basic statistical literacy. 

Understanding why we have to learn statistics and seeing the links between the numbers and real life is a crucial starting point. Using engaging, friendly, approachable language this book will demystify numbers from the outset, explaining exactly how they can be used as tools to understand the relationships between variables. 

This text assumes no previous mathematical or statistical knowledge, taking the reader through each basic technique with step-by-step advice, worked examples, and exercises. Using non-inferential techniques, students learn the foundations that underpin all statistical analysis and will learn from the ground up how to produce theoretically and empirically informed statistical results.

Part I Introduction

1 Why we use numbers in research

Introduction

This is a book about using and understanding numbers in social science research. It differs from other resources you may come across, by presenting the process of using numbers as being simpler, and more powerfully liberating, than is usually portrayed. It encourages all academics, researchers and students to use and understand the use of numbers in research. This is not a book about the conduct of research in general, or the process of numeric data collection more specifically. It does not require entering a scary paradigm called quantitative research, or making any kind of epistemological commitment, whatever that is (see the glossary for explanations of terms set in bold). Everyone can use numbers in research easily, just as they do in their everyday life. The focus of the book is on the use of numbers that we have good access to, rather than on any hypothetical numbers that we cannot see, or which might not even exist. This is not a book about maths, and there are no complex sections of equations or algebra. The examples presented mostly require only elementary arithmetic to understand them. Instead, the use of numbers, as dealt with here, requires imagination, care, appropriate scepticism and lots of critical judgement. Using numbers in this way is rewarding, valuable for society and enjoyable for the researcher. There is nothing to be scared of.

Why everyone needs to know something about the use of numbers

It is not really possible to live your life without using numbers in some way. You may use numbers when handling money, telling the time, planning your day, booking a train, concert ticket or holiday, checking your speed, battery life, fridge temperature, or the weather forecast, watching a game show or home improvement programme, weighing ingredients for cooking, weighing yourself, checking your activity tracker, playing board games or cards, buying shoes, or just calling a telephone number. The examples are endless. Numbers are one of the types of information that are key to understanding and control in our lives. Eschewing them would be absurd, and would make having a co-operative life in society almost impossible.

Everyone knows this. Many, perhaps most, people use the numbers that are important in their lives in an uncomplicated manner, without too much problem, and without obvious resistance. This is true even if the same people say that they are not good at, or cannot abide, maths. Numbers of the kind we use regularly are not maths. To take just one example, you can take your partner’s temperature if they are ill without being or becoming a mathematician. Again, everyone knows this. And everyone, even a mathematician, may miss their bus, forget they had something in the oven, or not notice that they have been given the incorrect change in a shop. Mistakes such as these do not just occur with numbers, and are perhaps an inevitable part of the everyday. They do not mean that the person involved cannot or should not use numbers. Most of us routinely process a huge amount of numeric information successfully, often without even realising it.

However, when some people become social science researchers an odd thing can happen. Numbers can become a focus for divisive but needless arguments about their validity. Many practising social science researchers seem to reject the use of the same sort of numbers that they are happy with in their non-social-science lives. And then they try to defend that rejection on the basis of talk about paradigms, methods identities, and epistemologies (Ralston et al., 2016). It is often the researchers who are least confident in maths, or have most anxiety about statistics, who are most likely to defend their non-use of numbers in research through an appeal to the supposed illegitimacy of statistics.

Whatever the reasons, this is not a sustainable position. It is not possible to do real-life social research without encountering numbers in the same way as we all do when we are not researching. It is as crucial to be appropriately critical of the use of numbers in research as it is in everyday life. The sceptical approach, encouraged in this book, is completely contrary to just rejecting all use of numbers. In order to decide whether to trust some numeric information or not, to be able to discriminate between the trustworthy research and the rest, we need to understand quite a bit about how those numbers are used and how they behave.

On the other hand, some commentators and funders have suggested that there should be more statistical (‘quantitative’) studies in social science research, because this form of evidence is said to be intrinsically preferable and of higher quality than other forms. This is again completely the wrong way of looking at it. One reason to encourage a greater awareness of statistical techniques among all researchers is that so-called ‘quantitative’ work is currently often very poor, but it can have considerable real-life impact while being largely unchecked by a wider, more cautious, readership.

There are other reasons why all researchers should learn something about techniques for research involving numbers. All researchers need to read and use the research of others, because all new studies involve some consideration of prior work in that field. This is impossible to do unless researchers know something about the conduct of research with numbers. Otherwise they may just accept all numeric research as valid, which is a big mistake, or reject all research with numbers, which is prejudiced and an even bigger mistake. Or they may accept/reject results on the basis of ideology, or whether they are happy with what the research reports having found. This would be the biggest mistake of all. It is not a social science approach to research.

The supposed schism between research using numbers (so-called ‘quantitative’) and research not using numbers (so-called qualitative) is at fault for much of this. There is no need to use such divisive terms to describe your research (Gorard with Taylor, 2004). These terms are generally used either by people who do not do research, and so have not realised that once you start researching everything is or could be useful data. Or these terms are used as defences by people who want to avoid dealing with research of one kind or another, because they do not want to work at a reasonable scale (Chapter 10), or perhaps do not see the need for judgement in analysing results (Chapter 8). Everyone reads text in much the same way, and everyone checks their change in a shop in much the same way. Researchers should just report what they did, and what they discovered (Chapter 21).

So, this book suggests a better and more fruitful way forward.

The format and structure of the book

The book is based on a wide range of simple worked examples and exercises that introduce the various topics, terms and techniques for using numbers, gradually, and in an order that will build up your knowledge and skills. Some of the ideas may seem very simple for some readers at the outset, but it is often useful to re-examine our basic understanding of the foundations of research. Some of the later ideas, such as logistic regression techniques, may seem difficult at first for some readers unused to working with numbers. However, whatever your prior experience, working through each chapter in turn should lead to a logical and ordered understanding, even though each substantive chapter is also intended to be readable on its own.

Each substantive chapter starts with a summary of its contents or purpose, and includes exercises for the reader, some simple worked examples, and at least one example of real-life social science research using the ideas in that chapter. The chapters end, where appropriate, with notes on the exercises for use by readers, or by lecturers using the text as the basis for a course, a further exercise usually based on datasets available on the accompanying website, and notes on a few suggestions for further reading. The further reading is based on resources that I have seen. There will be many other useful books, articles and websites.

A note on software

The graphs and other outputs from the examples in this book are based on working with software in widespread use, such as Excel and SPSS. These programs can help you to do the calculations for your numeric analyses easily. Excel is more widely available for most users, while SPSS provides more help with a wider range of analyses such as factor analysis, logistic regression and other more advanced regression models. However, reading the book does not depend on using either of these programs, or any other available software such as R or Stata. Nor is the book intended to be a manual on how to use any of them. There is a list of useful and simple resources for setting up and using analytical software (particularly SPSS) at the end of Chapter 3.

Each worked example has a related box that contains the steps needed to produce the example outputs, including a summary of the SPSS syntax (a sequence of steps, like computer code, to produce an analysis). The advantage of syntax is that readers can repeat each analysis while changing the names of the variables to suit their own research. Readers who want to can simply skip these bits, just by skipping the inset boxes. For those who want to pursue it, the datasets described are available to play with on the website accompanying this book. Use this material in the book or ignore it as you wish (it is all boxed off, separate from the main flow of the text). Maybe ignore it the first time, and then go back and try out some of the worked examples.

The structure of the book

A few of the topics are covered by a pair of related chapters. The first chapter of each pair contains all that you really need to know about how to conduct a specific form of analysis or preparation for analysis, presented as simply as possible. The second chapter in each pair has a slightly more difficult or technical section, generally explaining why what is in the first chapter is really all you need to know. If you are feeling tentative then you can skip these more technical chapters (Chapters 7, 10, 12, 14 and 18), and this will not affect your understanding of later chapters in the book at all. These slightly more technical chapters are for the more confident and curious readers, and also for lecturers and tutors who might want to know why the book does not contain some of the difficult stuff that so many other statistical texts do. This book emphasises throughout the kinds of true analyses with judgement that follow from the relatively simple stages of totalling, averaging or modelling your data. These true analyses requires care, creativity, logic, scepticism and dedication. But they are not overly technical.

Chapter 2 looks at what numbers are, and how to interpret them. It introduces a simple classification of two types of numbers – real and categorical.

Chapter 3 outlines the common techniques for describing and summarising one variable in a dataset at a time, in a way that is clear and simple. It introduces graphs, frequencies, percentages, modes, means, and both the absolute mean deviation and the standard deviation. Chapter 4 describes analyses with two categorical variables, including cross-tabulations and odds ratios. Chapter 5 introduces analyses with one categorical variable and one real number, including effect sizes based on the differences between means.

Chapter 6 describes how to conduct two common significance tests, and what their results mean and do not mean. Although the book as a whole suggests not conducting significance tests in your own work, this chapter should help you when reading the work of other researchers who still uses this archaic approach. Chapter 7 is a more technical chapter, explaining in more detail why significance tests do not help us and can be misleading, and are therefore not presented in the rest of the book. Shorn of significance tests and the like, it becomes much easier to use, write about and understand numbers, while nothing of any value is lost.

Chapter 8 shows how all analyses, including those with numbers, require judgement on the part of the researcher. And that finding results like those described in Chapter 6 and 7 is only the start of any analysis, not its destination. This chapter begins to describe how we can judge the trustworthiness of research findings, and then their generality and meaning.

Chapter 9 reminds readers of the importance of research design. The design of any study should stem from the research questions to be addressed, and should lead naturally to the kind of analyses that will be needed. Whether the design is appropriate for the research questions being addressed is a key judgement to make, as part of deciding how trustworthy any research finding is.

Chapter 10 introduces the ideas and terminology associated with populations and sampling – the cases we obtain our measurements from. The scale and quality of the cases used in research represent another factor to take into account when judging how trustworthy any research finding is. Chapter 11 is slightly more technical, looking at the philosophical idea of randomness, as used in random sampling, and some of the rarer and more complex methods of sampling, and why these are not usually needed.

Chapter 12 describes how to detect, report and handle missing data. How much missing data there is, of what kind, and how this is handled, is another key issue to consider when looking at how trustworthy a research finding is. Chapter 13 is more technical, explaining why the simple approaches to handling missing data in Chapter 12 are sufficient for most of us, most of the time. Chapter 14 is again slightly more technical. It expands on what a measurement is, the idea of measurement errors, and ...

Table of contents

• Cover
• Half Title
• Publisher Note
• Title Page
• Copyright Page
• Acknowledgements
• Contents
• Detailed Contents
• Illustration List
• Table List
• About the Author
• Preface
• Online resources
• Part I Introduction
• 1 Why we use numbers in research
• 2 What is a number? Issues of measurement
• Part II Basic analyses
• 3 Working with one variable
• 4 Working with tables of categorical variables
• 5 Examining differences between real numbers
• 6 Significance tests: How to conduct them and what they do not mean
• 7 Significance tests: Why we should not report them
• Part III Advanced issues for analysis
• 8 The role of judgement in analysis
• 9 Research designs
• 10 Sampling and populations
• 11 What is randomness?
• 12 Handling missing data: The importance of what we do not know
• 13 Handling missing data: More complex issues
• 14 Errors in measurements
• Part IV Modelling with data
• 15 Correlating two real numbers
• 16 Predicting measurements using simple linear regression
• 17 Predicting measurements using multiple linear regression
• 18 Assumptions and limitations in regression
• 19 Predicting outcomes using logistic regression
• 20 Data reduction techniques
• Part V Conclusion
• 21 Presenting data for your audience
• Glossary
• References
• Index