Statistics Without Maths for Psychology

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I have always been interested by the development of numerical abilities in children and more specifically, by trying to understand why some children, although of normal intelligence, do present big difficulties in learning math. In that paper, I wanted to take the problem in its root by testing preschoolers who had not been exposed yet to math instruction and see whether, at that age already, we could identify the children who were developing more poorly the bases for math learning. One of the problems with that kind of research is that we want to test many factors but the participants have only limited sustained attention abilities. So, we need to select carefully the tasks we want to propose and to make them as short as possible and put them in an attractive context. The results showed a very strong correlation between the performance in the tasks testing the central executive capacity and those measuring the numerical development. I was really surprised to see that difference between two groups matched in terms of age and non-verbal IQ but defined as under or above the median on these working memory measures led to two groups completely different in terms of their numerical development, those being below the median split presenting a developmental delay of nearly one year, which is enormous at that young age. Thus, a 5-minute task testing the child’s ability in working memory could already provide a very good indicator of the child’s risk to present a difficult cognitive development, in particular (but not only) in the numerical domain. Personal reflection boxes bring statistics to life through interviews with researchers, showing their important role in psychological discoveries. Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk First published 1999 Second edition published 2002 Third edition published 2004 Fourth edition published 2007 Fifth edition published 2011 © Pearson Education Limited 1999, 2011 The rights of Christine P. Dancey and John Reidy to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. Pearson Education is not responsible for the content of third party internet sites. ISBN: 978-0-273-72602-9 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Dancey, Christine P. Statistics without maths for psychology / Christine P. Dancey, John Reidy. — 5th ed. p. cm. ISBN 978-0-273-72602-9 (pbk.) 1. SPSS for Windows. 2. Mathematical statistics. 3. Psychology—Statistical methods. I. Reidy, John. II. Title. BF39.D26 2011 150.7′27—dc22 2010053187 10 14

Examples from the literature highlight a key piece of research in the area. Chapter summaries enable you to revise the main points of the chapter after you’ve read it. Numerous examples in each chapter illustrate the key points. Gain a thorough understanding of introductory statistics, data analysis & application of statistical concepts dgi]ZVcVanh

Basics Starting SPSS Working with data Data entry Saving your data Inputting data for between-participants and within-participants designs Within-participants designs British Psychological Society standards in Quantitative Methods in Psychology The British Psychological Society (BPS) accredits psychology degree programmes across the UK. It has set guidelines as to which major topics should be covered within quantitative methods in psychology. We have listed these topics below and indicated where in this textbook each is covered most fully. Dr David Field, University of Reading Christine P. Dancey is a Professor of Psychology at the University of East London John Reidy is a Senior Lecturer in the Department of Psychology, Sociology & Politics at Sheffield Hallam University Frequency histogram The frequency histogram is a useful way of graphically illustrating your data. Often researchers are interested in the frequency of occurrence of values in their sample data. For example, if study, so you need to obtain far more participants than you think you need, to make sure you have enough participants in each cell. X2 is always positive (because a squared number is always positive). Whereas DF roughly equates to the number of participants in most statistical analyses, it does not in X2, as DF is calculated by number of rows minus 1 (r " 1) multiplied by number of columns minus 1 (c " 1). In this case, you can see that a 2 ¨ 2 X2 will always have DF 2 1 because (r " 1) 2 (c " 1) 2 (2 " 1) 2 (2 " 1) 2 1.

Effects Attributed to Ecstasy Use and Measures of Cognition and Mood Among Users, Experimental and Clinical Psychopharmacology, 17 (5), 326–36 (Fisk, J.E., Montgomery, C. and Murphy, P.N. 2009), Copyright © 2009 by the American Psychological Association. Reproduced with permission. The official citation that should be used in referencing this material is doi:10.1037/a0017038. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 534 from The Association Between the Negative Effects Attributed to Ecstasy Use and Measures of Cognition and Mood Among Users, Experimental and Clinical Psychopharmacology, 17 (5) (Fisk, J.E., Montgomery, C. and Murphy, P.N. 2009), Copyright © 2009 by the American Psychological Association. Reproduced with permission. The official citation that should be used in referencing this material is doi:10.1037/a0017038. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 539 from Cognitive Executive Function in Down’s Syndrome, British Journal of Clinical Psychology, 45, 5–17 (Rowe, J., Lavender, A. and Turk, V. 2006), Reproduced with permission from the British Journal of Clinical Psychology © The British Psychological Society; Table on page 548 from Dog-assisted Therapy in the Treatment of Chronic Schizophrenia in Patients, Anthrozoos, 22 (2), 149–59 (Villalta-Gill, V., Roca, M., Gonzalez, N., Domenec, E., Escanilla, C.A., Asensio, M.R., Esteban, M.E., Ochoa, S., Haro, J.M. and Schi-Can Group 2009), Berg Publishers, an imprint of A&C Black Publishers Ltd. The companion website, available at www.pearsoned.co.uk/dancey, is updated with interactive features including: • An interactive hyperlinked flow chart guiding you through each step of choosing an analysis • An expanded bank of Multiple Choice Questions allowing you to test your knowledge of each chapter • Extra data sets and exercises for each chapter to allow you to put what you’ve learnt into practice SPSS sections guide you through how to use the software for each process, with annotated, fullcolour screenshots to demonstrate what should be happening on screen. 3.4 Graphically describing data Once you have finished a piece of research, it is important that you get to know your data. One of the best ways of doing this is through exploratory data analysis (EDA). EDA essentially consists of exploring your data through graphical techniques. It is used to get a greater understanding of how participants in your study have behaved. The importance of such graphical techniques was highlighted by Tukey in 1977 in a classic text called Exploratory Data Analysis. Graphically illustrating your data should, therefore, be one of the first things you do with it once you have collected it. In this section we will introduce you to the main techniques for exploring your data, starting with the frequency histogram. We will then go on to explain stem and leaf plots and box plots. Another way of applying probabilities to research: hypothesis testing Null hypothesis Logic of null hypothesis testing The significance level Statistical significanceTables Tables on pages 78 and 117 from Effects of physical positions on sleep architectures and post-nap functions among habitual nappers, Biological Psychology, 83, 207–13 (Zhao, D., Zhang, Q., Fu, M., Tang, Y. and Zhao, Y. 2010). With permission from Elsevier; Table on page 201 from Counting on Working Memory When Learning to Count and to Add: A Preschool Study, Developmental Psychology, 45 (6), 1630–1643 (Noël, P. 2009), Copyright © 2009 by the American Psychological Association. Reproduced with permission. The official citation that should be used in referencing this material is doi:10.1037/a0016224. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 202 from Perceived stigma, illness intrusiveness and quality of life in men and women with irritable bowel syndrome, Psychology, Health and Medicine, 7 (4), 381–95 (Dancey, C.P., Hutton-Young, S.A., Moye, S. and Devins, G.M. 2002), Reprinted by permission of the publisher (Taylor & Francis Ltd, http://www.informaworld.com); Table on page 227 from Inferencing processes after right hemisphere brain damage: maintenance of Variables and research design Introduction to SPSS Descriptive statistics Probability, sampling and distributions Hypothesis testing and statistical significance Correlational analysis: Pearson’s r Analyses of differences between two conditions: the t-test Issues of significance Measures of association Analysis of differences between three or more conditions Analysis of variance with more than one IV Regression analysis Analysis of three or more groups partialling out effects of a covariate Introduction to factor analysis Introduction to multivariate analysis of variance (MANOVA) Non-parametric statistics

Dr Marie-Pascale Noël, Catholic University of Louvain, Louvain-La-Neuve, Belgium. ARTICLE: Counting on working memory when learning to count and to add: a preschool study.Appendix 1: Table of z-scores and the proportion of the standard normal distribution falling above and below each score Only the DVs should be normally distributed All DVs and all IVs should be normally distributed All DVs and all possible linear combinations of the DVs should be normally distributed All of the above Working memory and arithmetic As described in Chapter 6, page 201, Noël (2009) measured how much limited working memory capacity constrains early numerical development. Four- and 5-year old children provided measurements on various aspects of working memory, and arithmetical ability; 38 of the children were in the second year of kindergarten (K2) and 42 were in the third year (K3). As part of that study, the two kindergarten classes were compared on cognitive, numerical and other tests. The groups were compared by t-tests, using one-tailed hypotheses (it would be expected that children in the K3 class would do better than those in the K2 class). Look at the table below, reproduced in full. The authors have given exact p-values and 95% confidence limits around the mean difference between the groups. This is good practice. Although they have not given an effect size, it’s easy to calculate since you have all the information you need. Guided tour of the book and website The chapter overview gives you a feel for what will be covered and what you should have learnt by the end of the topic. CHAPTER 9 Measures of association Multivariate statistics Why use multivariate analyses of variance? Multivariate analysis of variance Logic of MANOVA Assumptions of MANOVA Which F-value? Post-hoc analyses of individual DVs Correlated DVs How to write up these analyses SPSS: conducting MANOVA with one between-participants IV and two DVs Within-participants designs SPSS: one within-participants IV and two DVs

Screenshots Screenshots on page 26, page 27, page 28, page 29, page 30, page 31, page 32, page 33, page 34, page 35, page 36, page 37, page 38, page 39, page 52, page 53, page 55, page 65, page 69, page 70, page 86, page 87, page 118, page 122, page 123, page 124, page 158, page 159, page 160, page 161, page 182, page 183, page 191, page 192, page 195, page 196, page 223, page 224, page 231, page 232, page 267, page 268, page 269, page 272, page 273, page 274, page 275, page 278, page 279, page 280, page 304, page 305, page 314, page 315, page 349, page 350, page 351, page 352, page 353, page 354, page 355, page 364, page 365, page 374, page 375, page 388, page 389, page 390, page 391, page 401, page 402, page 426, page 427, page 428, page 429, page 430, page 441, page 442, page 479, page 480, page 481, page 482, page 484, page 485, page 507, page 508, page 516, page 517, page 529, page 530, page 537, page 538, page 545, page 551, page 552, page 556, page 557, page 567 and page 568, reprinted Courtesy of International Business Machines Corporation, © SPSS Inc., an IBM Company. SPSS was acquired by IBM in October 2009. Probability The standard normal distribution Applying probability to research Sampling distributions Confidence intervals and the standard error SPSS: obtaining confidence intervals Error bar charts Overlapping confidence intervals SPSS: generating error bar charts Confidence intervals around other statisticsChapter overview Why teach statistics without mathematical formulae? Variables Levels of measurement Research designs Between-participants and within-participants designs