Statistics for Research

With a Guide to SPSS

George Argyrous

• Publisher: SAGE Publications Ltd
• Year: 2011
• ISBN:
  9781446245163
• Edition: 3

This fully updated edition of Statistics for Research explains statistical concepts in a straight-forward and accessible way using practical examples from a variety of disciplines. If you?re looking for an easy-to-read, comprehensive introduction to statistics with a guide to SPSS, this is the book for you!

The new edition features:

- Clear explanations of all the main techniques of statistical analysis

- A brand new student-friendly, easy-to-navigate design

- Even more step-by-step screenshots of SPSS commands and outputs

- An extensive glossary of terms, ideal for those new to statistics

- End of chapter exercises to help you put your learning into practice

- A new, fully updated companion website (www.uk.sagepub.com/argyrous3) with comprehensive student and lecturer resources including additional, discipline specific examples and online readings and WebCT/Blackboard quizzes.

This is the ideal textbook for any course in statistical methods across the health and social sciences and a perfect starter book for students, researchers and professionals alike.

PART 1

An introduction to statistical analysis

ONE

Variables and their measurement

Learning objectives

At the end of this chapter you will to able to:

• identify the cases of interest to a research study
• identify the variables of interest to a research study
• understand the issues involved in conceptualizing and operationalizing a variable
• understand the difference between nominal, ordinal, and interval/ratio levels of measurement
• identify the dependent and independent variables in a theoretical model
• know the different classes of statistical techniques

This book helps people analyse quantitative information. Before detailing the ‘hands-on’ analysis we will explore in later chapters, this introductory chapter will discuss some of the background conceptual issues that are precursors to statistical analysis. The most important of these background issues is the determination of research questions.

Research Question

A research question states the aim of a research project in terms of cases of interest and the variables upon which these cases are thought to differ.

A few examples of research questions are:

‘What is the age distribution of the students in my statistics class?’
‘Is there a relationship between the health status of the students in my statistics class and their sex?’
‘Is any relationship between the health status and the sex of students in my statistics class affected by the age of the students?’

We begin with very clear, precisely stated, research questions such as these to guide our research, and to ensure we do not end up with a jumble of information that does not create any real knowledge. We need a clear research question (or questions) in mind before undertaking statistical analysis to avoid the situation where huge amounts of data are gathered unnecessarily and do not lead to any meaningful results. I suspect that a great deal of the confusion associated with statistical analysis actually arises from imprecision in the research questions that are meant to guide it. It is very difficult to select the relevant type of analysis to undertake on a given set of data, given the many possible analyses we could employ, if we are not certain of our objectives. If we don’t know why we are undertaking research in the first place, then it follows that we will not know what to do with research data once we have gathered them. Conversely, if we are clear about the research question(s), the statistical techniques to apply follow almost as a matter of course.

Each of the research questions above identifies the entities that I wish to investigate. In each question these entities are students in my statistics class, who are thus the units of analysis – the cases of interest – to my study.

Case

A case is an entity that displays or possesses the traits of a variable.

In this example, as in many others, the cases are individual people. It is important to bear in mind, however, that this is not always so. For example, if I am interested in retention rates for high schools in a particular area, the cases will be high schools. It is individual high schools that are ‘stamped’ with a label indicating their respective retention rate.

In the research questions listed above, all the students in my statistics class constitute my target population (sometimes called a universe).

Population

A population is the set of all possible cases of interest.

In determining our population of interest, we usually specify the point in time that defines the population – am I interested in my currently enrolled statistics students, or those who also completed my course last year? We also specify, where relevant, the geographic region over which the population spreads.

For reasons we will investigate later, we may not be able to, or not want to, investigate the entire population of interest. Instead we may select only a subset of the population, and this subset is called a sample.

Sample

A sample is a set of cases that does not include every member of the population.

For example, it may be too costly or time-consuming to include every student in my study. I may instead choose only those students in my statistics class whose last name begins with ‘A’, and thus be only working with a sample.

Suppose that I do take this sample of students from my statistics class. I will observe that these students differ from each other in many ways: they may differ in terms of sex, height, age, attitude towards statistics, religious affiliation, health status, etc. In fact, there are many ways in which the cases in my study may differ from each other, and each of these possible expressions of difference is a variable.

Variable

A variable is a condition or quality that can differ from one case to another.

The opposite notion to a variable is a constant, which is simply a condition or quality that does not vary among cases. The number of cents in a United States dollar is a constant: every dollar note will always exchange for 100 cents. Most research, however, is devoted to understanding variables – whether (and why) a variable takes on certain traits for some cases and different traits for other cases.

The conceptualization and operationalization of variables

Where do variables come from? Why do we choose to study particular variables and not others? The choice of variables to investigate is affected by a number of complex factors, three of which I will emphasize here.

1. Theoretical framework. Theories are ways of interpreting the world and reconciling ourselves to it, and even though we may take for granted that a variable is worthy of research, it is in fact often a highly charged selection process that directs one’s attention to it. We may be working within an established theoretical tradition that considers certain variables to be central to its world-view. For example, Marxists consider ‘economic class’ to be a variable worthy of research, whereas another theoretical perspective might consider this variable to be uninteresting. Analysing the world in terms of economic class means not analysing it in other ways, such as social groups. This is neither good nor bad: without a theory to order our perception of the world, research will often become a jumble of observations that do not tie together in a meaningful way. We should, though, acknowledge the theoretical preconceptions upon which our choice of variables is based.
2. Pre-specified research agenda. Sometimes the research question, and thereby the variables to be investigated, is not determined by the person analysing the data. For example, a consultant may contract to undertake research that has terms of reference set in advance by the contracting body. In such a situation the person or people actually doing the research might have no choice over the variables to be investigated and how they are to be defined, since they are doing work for someone else.
3. Curiosity-driven research. Sometimes we might not have a clearly defined theoretical framework to operate in, nor clear directives from another person or body as to the key concepts to be investigated. Instead we want to investigate a variable purely on the basis of a hunch: a loosely conceived feeling that something useful or important might be revealed if we study a particular variable. This can be as important a reason for undertaking research as theoretical imperatives. Indeed, when moving into a whole new area of research, into which existing theories have not ventured, simple hunches can be fruitful motivations.

These three motivations are obviously not mutually exclusive. For example, even if another person determines the research question, that person will almost certainly be operating within some theoretical framework. Whatever the motivation, though, social inquiry will initially direct us to particular variables to be investigated. At this initial stage a variable is given a conceptual definition.

Conceptual Definition

The conceptual definition (or nominal definition) of a variable uses literal terms to specify the qualities of a variable.

A conceptual definition is much like a dictionary definition: it provides a working definition of the variable so that we have a general sense of what it ‘means’. For example, I might define ‘health’ conceptually as ‘an individual’s state of well-being’.

It is clear, though, that if I now instruct researchers to go out and measure people’s ‘state of well-being’, they would leave scratching their heads. The conceptual definition of a variable is only the beginning; we also need a set of rules and procedures – operations – that will allow us to actually ‘observe’ a variable for individual cases. What will we look for to identify someone’s health status? How will the researchers record how states of well-being vary from one person to the next? This is the problem of operationalization.

Operational Definition

The operational definition of a variable specifies the procedures and criteria for taking a measurement of that variable for individual cases.

A statement such as ‘a student’s health status is measured by how far in metres they can walk without assistance in 15 minutes’ provides one operati...

Table of contents

• Cover Page
• About the Author
• Title
• Copyright
• Dedication
• Table of Contents
• Extended Contents
• Preface
• Part 1 An introduction to statistical analysis
• Part 2 Descriptive statistics: Graphs and tables
• Part 3 Descriptive statistics: Numerical measures
• Part 4 Inferential statistics: Tests for a mean
• Part 5 Inferential statistics: Tests for frequency distributions
• Part 6 Inferential statistics: Other tests of significance
• Part 7 Advanced topics
• Appendix
• Key equations
• Glossary
• Answers
• Index