Exploratory and Descriptive Statistics

Julie Scott Jones,John Goldring

• Publisher: SAGE Publications Ltd
• Year: 2022
• ISBN:
  9781529710908
• Edition: 1
• Topic: Social Sciences
• Subtopic: Social Science Research & Methodology
• Index: Social Sciences

Nervous about statistics? This guide offers you a clear, straight to the point break down of exploratory and descriptive statistics and its potential. Anchored by lots of examples and exercises to enhance your learning, this book will give you the know-how and confidence needed to succeed on your quantitative research journey.

1 Introducing Descriptive and Exploratory Statistics

Chapter Overview

• What is this book about? 2
• What’s in each chapter? 2
• New to statistical analysis? this book is for you! 4
• So, what are descriptive statistics? 4
• What no statistical testing? 9
• Sounds like inferential statistics are more important 9
• Types of descriptive statistics 10
• One variable or two? 15
• So, what can I do with descriptive statistics? 16
• Why not try exploratory data analysis 20
• Further Reading 22

What is this book about?

This book focuses on the uses (and some abuses) of what are called ‘descriptive and exploratory statistics’ and can be read as a stand-alone book on this subject. However, it is one of a series within the SAGE Quantitative Methods Toolkit, and there will be references throughout to other volumes in the series that cover relevant themes in greater depth than this book does. This volume (Number 3 in the series) builds on Volumes 1 (Beginning Quantitative Research) and 2 (Survey Research and Sampling), which you may find useful to read prior to this one, although there will be brief recaps of key material within this book. Likewise, Volumes 5 (Archival and Secondary Data Analysis) and 8 (Inferential Statistics) of this series develop further themes explored in this book, so you may find it useful to read these to develop your knowledge even further.

This book has seven chapters, each of which explores a key element of descriptive and exploratory statistics. We use IBM SPSS and MS Excel throughout and provide handy ‘how-to’ guides and accompanying screenshots to show how each software package does all the heavy lifting, meaning you don’t have to. If you like to read books in a linear way, then each chapter of this book obviously builds on and links to the next. If you are a complete newcomer to this topic, then you should certainly do this, otherwise you may get confused; you will find that your confidence with the topic (and knowledge) will build with each chapter. However, if you already have some knowledge and understanding of the topic, you may wish to ‘dip’ into specific chapters.

What’s in each chapter?

Chapter 1 discusses the definitions of and the differences between descriptive, exploratory and inferential statistics. It then explores why and how we can use descriptive and exploratory statistics both in their own right and as a precursor to inferential statistics. Chapter 1 should be your starting point if you are reading this paragraph and thinking ‘I haven’t a clue what descriptive, inferential or exploratory statistics means!’

Chapter 2 outlines how to access data from which to conduct statistical analysis, identifying both primary and secondary sources, before discussing some key principles of data management. This is the chapter for you if you have a research paper to do that involves accessing, cleaning and manipulating quantitative data, and you have never done it before. If you are clueless as to how to find good sources of data, then this chapter will help. On the other hand, it may be that you already have a good source of data but it is in the ‘wrong’ software format, or you feel overwhelmed by the fact that the data set has more than 10,000 cases and 700 variables. Don’t worry, Chapter 2 will help you. Chapter 3 identifies the different ways we can choose to measure social concepts (which is a fundamental challenge for all researchers) and the consequences (good and bad) of those measurement choices. It introduces the concept of ‘variables’ and units of measurement. It is easy for students to get confused with different types of variables and to struggle with the concept of measurement; you may have already had a class on interval versus nominal variables or continuous versus categorical-level data and come out of it none the wiser. The whole thing may seem like a parade of words with little real meaning to you; try Chapter 3 before you decide never to attend another stats class, it will help. Chapters 4 and 5 build on Chapter 3, so don’t start with them if you have not covered measurement before. Chapter 4 discusses categorical data, both nominal and ordinal; it defines, classifies and illustrates this type of data. It shows you how to analyse such data and acknowledge its limitations. There are many examples to help you understand. Chapter 5 does a similar thing with interval-level or continuous data. If you have done a bit of stats already, you may just dip into these chapters to refresh or reinforce your understanding; however, if you are like many students and struggle to understand the difference between ordinal-level data that is categorical and interval-level data that is continuous, then you may want to read both the chapters. It is worth noting that often students understand the differences between types of measurement but struggle to understand the greater significance of these differences; that is, why do the differences matter: if this is you, then take your time and read these chapters. Chapter 6 focuses on how to visualise our data, using different types of graphs. If you don’t know the difference between pie, bar and stacked charts or struggle to understand why your tutor gets annoyed when you produce a colourful pie chart for the variable ‘age’ in your data, then this is the chapter for you. How you visualise your data is a skill in itself, and effective visualisations can communicate powerful stories about your data with less need for detailed discussion. Students often don’t understand the power of good visualisation of data and how visualising your data effectively can assist the understanding and analysis of your data. Before you submit that research report with the same old frequency tables or poorly labelled pie charts, read this chapter. Chapter 7, the final chapter, discusses how to construct powerful narratives or ‘stories’ from your data. When your tutor asks you to discuss your findings at the end of your research report, you may think it is sufficient to summarise the key ‘headlines’ from your data analysis. Hopefully, you would support this discussion of analysis with some literature, but often students rush this element because they think the data findings themselves are the central focus. However, finding out that, for example, there is a rising trend on campus for plant-based diets among female students is not necessarily that interesting unless we can frame it into a wider narrative: is the trend common across a range of universities or indeed are women nationally participating in this trend? If it is a wider trend, is it to do with gender, age or educational level? Students often struggle to do this; when your tutor writes in her feedback ‘You needed to develop this’ or ‘Why is this relevant?’ she is identifying that you could have constructed a greater narrative for your data and it is time to try Chapter 7.

New to statistical analysis? this book is for you!

Statistics and quantitative data analysis books can be intimidating if you have not done any statistics or quantitative data analysis before; this book draws on material that has been tried and tested over the years on students who, perhaps like you, are a little bit nervous or even anxious about having to do statistical data analysis. This book is an introduction and an overview to the topic of descriptive and exploratory statistics; it will cover the basics that you would need to conduct your own descriptive-level data analysis whether at undergraduate or postgraduate level. We are presuming that you are new to the topic or are looking for a text that will reinforce or clarify your learning. To support your learning, this book has a number of features, including the following:

• 2-Minute Recaps, where you test yourself against the clock, supporting your knowledge building
• Pause for Thought, time to stop and think, reinforcing your learning
• Reflective Exercises, where you can apply your learning via set exercises
• Get Your Hands Dirty, time to boot up the computer and do some data work

These different features will help build your conceptual knowledge whilst providing you with opportunities to practice your skills; practice is a key way that we can grow our confidence and understanding of key concepts through their application.

So, what are descriptive statistics?

A key distinction made in the field of quantitative data analysis or statistics is between descriptive and inferential statistics. To understand the difference between the two, we need to think about the basic goals of the quantitative approach; Volume 1 (Beginning Quantitative Research) of this series discusses this in much more detail if you are interested. Generally speaking, the quantitative approach draws on the scientific model of understanding the world; scientists attempt to ‘draw’ conclusions and understandings about the physical world through the development of hypotheses which they test using a range of experimental techniques. This testing leads to the development of theories or ‘laws’ about the physical world – for example, the laws of gravity or motion. The foundational element of this approach is that the physical world is knowable and understandable in an objective and quantified way. Social scientists use quantitative methods in a similar way to understand the social world, whether using experimental techniques (see Volume 4, Experimental Design) or social surveys (see Volume 2, Survey Research and Sampling).

However, in order to test hypotheses or answer research questions, social scientists first need to identify a population that they are interested in. A population refers to all the members of a specific group that we want to examine: the entire population of a country, all the students at a specific university, everyone aged 10 years old in a specific school district and so forth. Populations can be large, such as the entire population of a nation (which will be in the millions or even more than a billion) or small, such as all the schoolchildren in one town (possibly 500+) or even in one single school class (maybe 30 in total). Whoever our population are, they are the focus of our interest and study; we want to use quantitative methods (whether experiments or questionnaire-based surveys) to learn about them and possibly develop some social ‘laws’ or theories of our own. Some populations are so small that we can study them as a whole and generate parameters, which is data about a whole population. For example, we could, technically, gather data on all the students on a specific university course and generate parameters about them. To illustrate, we could gather data on all the 200 students enrolled on a single Criminology programme in one university; we could identify parameters for them such as average age, grades and so forth. The national censuses that are very common around the world try to do this for entire populations at the householder level; China’s 2010 population census was the largest census ever conducted in the world, issued to more than 40 million households and gathering data on more than 1 billion people. Generally though, we acknowledge that it is technically and practically challenging to gather data on an entire population (see Volume 2, Survey Research and Sampling, for more detail on this), which is why national censuses tend to be on a 10-year cycle. Moreover, even amongst a small population of say 200 students on a course, we may struggle to reach them all, some may be absent from class or ignore emails and so forth, thus not completing our questionnaire. To overcome this problem, we tend to focus on samples. A sample is a part of a population, for example, there are 4.9 million mothers with dependent children (Office for National Statistics [ONS], 2017a) in the UK working either full-time or part-time. This is a large population, so we would draw a sample from it in order to understand the population better. If you are struggling to visualise this, think of a cake; the whole cake is the population, a slice is the sample.

Figure 1.1 represents a population that we might want to know more about. However, it is large, so we take a sample (n) from it that we can examine as shown in Figure 1.2.

Figure 1.1 Population (N)

Figure 1.2 A sample from a population

The lighter shaded faces are our sample (n) taken from our population (N). We would generate descriptive statistics about the sample and then if our data was deemed sufficiently robust, we may be able to generalise from this sample back to our population.

Box 1.1 2-Minute Recap!

Set the timer on you...

Table of contents

• Cover
• Half Title
• Acknowledgements
• Title Page
• Copyright Page
• Contents
• Illustration List
• About the Authors
• 1 Introducing Descriptive and Exploratory Statistics
• 2 Finding Data to Describe
• 3 Measure Everything – Learn Something – Answer Nothing An Exploration Into Variables and Types of Measurement
• 4 I Am Not a Number, I Am a Categorical Variable
• 5 I Like Being Average, I Am an Interval Variable
• 6 Visualising Our Data
• 7 The Story Waiting to Be Told
• Glossary
• References
• Index