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SAGE was founded in 1965 by Sara Miller McCune to support
the dissemination of usable knowledge by publishing innovative
and high-quality research and teaching content. Today, we
publish over 900 journals, including those of more than 400
learned societies, more than 800 new books per year, and a
growing range of library products including archives, data, case
studies, reports, and video. SAGE remains majority-owned by
our founder, and after Sara’s lifetime will become owned by
a charitable trust that secures our continued independence.
Los Angeles | London | New Delhi | Singapore | Washington DC | Melbourne
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SAGE Publications Ltd Andy Field 2016
1 Oliver’s Yard
55 City Road First published 2016
London EC1Y 1SP
Apart from any fair dealing for the purposes of research or
SAGE Publications Inc. private study, or criticism or review, as permitted under the
2455 Teller Road Copyright, Designs and Patents Act, 1988, this publication may
Thousand Oaks, California 91320 be reproduced, stored or transmitted in any form, or by any
means, only with the prior permission in writing of the
SAGE Publications India Pvt Ltd publishers, or in the case of reprographic reproduction, in
B 1/I 1 Mohan Cooperative Industrial Area accordance with the terms of licences issued by the Copyright
Mathura Road Licensing Agency. Enquiries concerning reproduction outside
New Delhi 110 044 those terms should be sent to the publishers.
SAGE Publications Asia-Pacific Pte Ltd
3 Church Street
#10-04 Samsung Hub
Singapore 049483
Library of Congress Control Number: 2016936610
Editor: Mark Kavanagh
Development editor: Robin Lupton
British Library Cataloguing in Publication data
Production editor: Ian Antcliff
Copyeditor: Richard Leigh
A catalogue record for this book is available from
Proofreader: Andy Baxter
the British Library
Indexer: David Rudeforth
Marketing manager: Ben Griffin-Sherwood
Cover design: Wendy Scott
Typeset by: C&M Digitals (P) Ltd, Chennai, India
Printed and bound in Great Britain
by Bell and Bain Ltd, Glasgow
ISBN 978-1-4462-1044-4
ISBN 978-1-4462-1045-1 (pbk)
At SAGE we take sustainability seriously. We print most of our products in the UK. These are produced using FSC papers and boards. We
undertake an annual audit on materials used to ensure that we monitor our sustainability in what we are doing. When we print overseas,
we ensure that sustainable papers are used, as measured by the PREPS grading system.
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CCoonntteennttss
HOW TO USE THIS BOOK xv
Prologue: The Dying Stars 1
1 Why you need science 7
2 Reporting research, variables and measurement 39
3 Summarizing data 75
4 Fitting models (central tendency) 111
5 Presenting data 157
6 z-scores 189
7 Probability 215
8 Inferential statistics: Going beyond the data 257
9 Robust estimation 297
10 Hypothesis testing 331
11 Modern approaches to theory testing 361
12 Assumptions 395
13 Relationships 429
14 The general linear model 477
15 Comparing two means 527
16 Comparing several means 567
17 Factorial designs 633
Epilogue: The genial night 677
Appendix 685
Glossary 699
References 727
INDEX 733
ACKNOWLEDGEMENTS 743
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EExxtteennddeedd CCoonntteennttss
HOW TO USE THIS BOOK xv
Who is the book aimed at? xv
How do I teach with a book that has a fictional narrative? xv
Can I dip into the book? xvi
What online resources are there? xvi
Prologue: The Dying Stars 1
1 Why you need science: The beginning and the end 7
1.1. Will you love me now? 10
1.2. How science works 14
1.2.1. The research process 14
1.2.2. Science as a life skill 21
1.3. Research methods 21
1.3.1. Correlational research methods 22
1.3.2. Experimental research methods 24
1.3.3. Practice, order and randomization 27
1.3.4. Piecing it all together 31
1.4. Why we need science 34
Key terms 36
JIG:SAW’s puzzles 36
2 Reporting research, variables and measurement: Breaking the law 39
2.1. Writing up research 43
2.2. Maths and statistical notation 49
2.3. Variables and measurement 55
2.3.1. The conspiracy unfolds 55
2.3.2. Qualitative and quantitative data 57
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2.3.3. Levels of measurement 60
2.3.4. Measurement error 66
2.3.5. Validity and reliability 68
Key terms 70
JIG:SAW’s puzzles 70
3 Summarizing data: She loves me not? 75
3.1. Frequency distributions 81
3.1.1. Tabulated frequency distributions 81
3.1.2. Grouped frequency distributions 89
3.1.3. Graphical frequency distributions 94
3.1.4. Idealized distributions 100
3.1.5. Histograms for nominal and ordinal data 100
3.2. Throwing shapes 103
Key terms 107
JIG:SAW’s puzzles 107
4 Fitting models (central tendency): Somewhere in the middle 111
4.1. Statistical models 116
4.1.1. From the dead 116
4.1.2. Why do we need statistical models? 117
4.1.3. Sample size 118
4.1.4. The one and only statistical model 120
4.2. Central tendency 124
4.2.1. The mode 126
4.2.2. The median 128
4.2.3. The mean 129
4.3. The ‘fit’ of the mean: variance 135
4.3.1. The fit of the mean 136
4.3.2. Estimating the fit of the mean from a sample 141
4.3.3. Outliers and variance 148
4.4. Dispersion 149
4.4.1. The standard deviation as an indicator of dispersion 149
4.4.2. The range and interquartile range 151
Key terms 155
JIG:SAW’s puzzles 155
5 Presenting data: Aggressive perfector 157
5.1. Types of graphs 161
5.2. Another perfect day 162
5.3. The art of presenting data 166
5.3.1. What makes a good graph? 166
5.3.2. Bar graphs 170
5.3.3. Line graphs 172
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5.3.4. Boxplots (box–whisker diagrams) 173
5.3.5. Graphing relationships: the scatterplot 176
5.3.6. Pie charts 177
Key terms 181
JIG:SAW’s puzzles 182
6 z-scores: The wolf is loose 189
6.1. Interpreting raw scores 193
6.2. Standardizing a score 196
6.3. Using z-scores to compare distributions 200
6.4. Using z-scores to compare scores 206
6.5. z-scores for samples 209
Key terms 212
JIG:SAW’s puzzles 212
7 Probability: The bridge of death 215
7.1. Probability 218
7.1.1. Classical probability 219
7.1.2. Empirical probability 225
7.2. Probability and frequency distributions 228
7.2.1. The discs of death 228
7.2.2. Probability density functions 230
7.2.3. Probability and the normal distribution 233
7.2.4. The probability of a score greater than x 236
7.2.5. The probability of a score less than x: The tunnels of death 238
7.2.6. The probability of a score between two values:
The catapults of death 242
7.3. Conditional probability: Deathscotch 248
Key terms 255
JIG:SAW’s puzzles 255
8 Inferential statistics: Going beyond the data: Humiliative 257
8.1. Estimating parameters 262
8.2. How well does a sample represent the population? 267
8.2.1. Sampling distributions 267
8.2.2. The standard error 271
8.2.3. The central limit theorem 274
8.3. Confidence intervals 278
8.3.1. Calculating confidence intervals 281
8.3.2. Calculating other confidence intervals 286
8.3.3. Confidence intervals in small samples 287
8.4. Inferential statistics 291
Key terms 296
JIG:SAW’s puzzles 296
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