Statistics Without Maths for Psychology

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Supporting resources Visit www.pearsoned.co.uk/dancey to find valuable online resources Companion Website for students: ■ Multiple choice questions for each chapter to test your understanding ■ SPSS datasets for each chapter ■ Extra datasets and exercises ■ An interactive flowchart to help you choose your method of analysis ■ A list of where to find core content in the book outlined by the British Psychological Society ■ Links to useful resources on the web ■ A handy guide to report writing For instructors: ■ A testbank of at least 20 questions per chapter ■ Downloadable PowerPoint slides of all the figures from the book Also – The Companion Website provides the following features: ■ A Syllabus and Profile Manager ■ Online help and search functions ■ Email results functions For more information please contact your local Pearson Education sales representative or visit www.pearsoned.co.uk/dancey test of independence: r ¬ c What if you have more than two levels? It is perfectly possible to have more rows and columns. We still have two categorical variables, but this time we have more categories to choose from. X2 can handle this quite easily. Let’s assume, staying with our smoke/drink example, that we have three levels of smoke: heavy smokers, light smokers and non-smokers. We could also have heavy drinkers, light drinkers and teetotallers (see Table 9.8). This is a 3 ¨ 3 contingency table, for obvious reasons. The calculations are worked out in exactly the same way as we have described for the 2 ¨ 2 table. The degrees of freedom, however, will be different. Remember: DF 2 (c " 1) ¨ (r " 1) So: 2 ¨ 2 2 4 Inferential tests, which show us whether the relationship between the variables is likely to have been due to sampling error, assuming the null hypothesis is true. Effect size: `2 can be converted to a statistic called Cramer’s V – this is interpreted in the same way as any other correlation coefficient. Luckily, this is available through SPSS.

Although we have updated many examples from the literature, we have left in some early studies because they illustrate exactly the points made in the text. Some reviewers thought there should be more challenging activities and/or multiple choice questions. Therefore, we have added activities which are based on examples from the literature, and require students to interpret the material, in their own words. They can then compare their interpretation with the authors’ interpretation. Other improvements are more definitions within the first few introductory chapters, and detail on meeting the assumptions of the tests. Since writing earlier editions of this book, we have received numerous reviews, the vast majority of which have been very positive. Over the years the reviewers have been incredibly helpful in ensuring that the book has improved and best meets the needs of students and lecturers alike. The improvements we have made in this fifth edition are a result of feedback we have received both from reviewers and from students. We would like to thank all those who have taken the time and effort to provide us with feedback and we would urge you to keep doing so. We hope that students who read the book will not only learn from it, but also enjoy our explanations and examples. We also hope that as a result of reading this book students will feel confident in their ability to perform their own statistical analyses. inferences, Journal of Speech, Language and Hearing Research, 52, 359–72 (Blake, M.L. 2009), Reprinted with permission from Inferencing processes after right hemisphere brain damage: Maintenance of inferences by M.L. Blake. Journal of Speech, Language and Hearing Research, 53, 359–72. Copyright 2009 by American Speech-Language-Hearing Association. All Rights Reserved; Table on page 229 from Counting on working memory when learning to count and to add: a pre-school study, Developmental Psychology, 45 (6), 1630–1643 (Noel, M-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 256 from Method of delivery and subjective distress: women’s emotional responses to childbirth practices, Journal of Reproductive and Infant Psychology, 18 (2), 153–62 (Maclean, L.I., McDermott, M.R. and May, C.P. 2000), © Society for Reproductive and Infant Psychology reprinted by permission of (Taylor & Francis Ltd, http://www.tandf.co.uk/journals) on behalf of Society for Reproductive and Infant Psychology; Table on page 287 from Efficacy of a Camp-Based Intervention for Childhood Traumatic Grief, Research on Social Work Practice, 19, 19–30 (McClatchey, I.S., Vonk, M.E. and Palardy, G. 2009), Reprinted by permission of SAGE Publications; Tables on page 311 from The effects of cigarette smoking and abstinence on auditory verbal learning, Human Psychopharmacology: Clinical and Experimental, 23, 621–627 (Soar, K., Dawkins, L., Begum, H. and Parrott, A.C. 2008); Table on page 312 from Differential effects of age on involuntary and voluntary autobiographical memory, Psychology and Aging, 24 (2), 397–411 (Schlagman, S., Kliegel, M., Schulz, J. and Kvavilashvili, L. 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/a0015785. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 416 from Barriers to engagement in sleep restriction and stimulus control in chronic insomnia, Journal of Consulting and Clinical Psychology, 76 (5), 820–828 (Vincent, N., Lewycky, S. and Finnegan, H. 2008), Copyright © 2009 by the American Psychological Association. Reproduced with permission. The official citation that should be used in referencing this material is doi:10.1037/0022-006X.76.5.820. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 447 from An evaluation study of the young empowered sisters (YES!) program: promoting cultural assets among African American adolescent girls through a culturally relevant school-based intervention, Journal of Black Psychology, 34, 281–308 (Thomas, O., Davidson, W. and McAdoo, H. 2008), Reprinted by permission of SAGE Publications; Table on page 475 from Developing a measure of sluggish cognitive tempo for children: content validity, factor structure, and reliability, Psychological Assessment, 21 (3), 380–9 (Penny, A.M., Waschbusch, D.A., Klein, R.M., Corkum, P. and Eskes, G. 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/a0016600. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on pages 477–8 from Selectivity of executive function deficits in mild cognitive impairment, Neuropsychology, 23 (5), 607–18 (Brandt, J., Aretouli, E., Neijstrom, E., Bandeen-Roche, K., Samek, J., Manning, K. & Albert, M.S. 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/a0015851. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 532 from Faith in intuition is associated with decreased latent inhibition in a sample of high-achieving adolescents, Psychology of Aesthetics, Creativity and the Arts, 3 (1), 28–34 (Kaufman, S., B. 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/a0014822. No further reproduction or distribution is permitted without written permission from the American Psychological Association; Table on page 533 from The Association Between the Negative Cry Conduct t-test analyses of the single DVs Conduct X2 analyses of the DVs followed by t-tests None of the above We wrote this book primarily for our students, most of whom disliked mathematics, and could not understand why they had to learn mathematical formulae when their computer software performed the calculations for them. They were not convinced by the argument that working through calculations gave them an understanding of the test – neither were we. We wanted them to have a conceptual understanding of statistics and to enjoy data analysis. Over the past decade we have had to adapt our teaching to large groups of students, many of whom have no formal training in mathematics. We found it was difficult to recommend some of the traditional statistics textbooks – either they were full of mathematical formulae, and perceived by the students as dull or boring, or they were simple, statistical cookbook recipes, which showed them how to perform calculations, but gave them no real understanding of what the statistics meant. We therefore decided to write this book, which seeks to give students a conceptual understanding of statistics while avoiding the distraction of formulae and calculations. Another problem we found with recommending statistics textbooks was the over-reliance on the probability value in the interpretation of results. We found it difficult to convince them to take effect size, and confidence intervals, into consideration when the textbooks that were available made no mention of the debates around hypothesis testing, but simply instructed students to say p < 0.05 is significant and p > 0.05 is not significant! We hope in writing this book that students will become more aware of such issues. We also wanted to show students how to incorporate the results of their analysis into laboratory reports, and how to interpret results sections of journal articles. Until recently, statistics books ignored this aspect of data analysis. Of course, we realise that the way we have written our example ‘results sections’ will be different from the way that other psychologists would write them. Students can use these sections to gain confidence in writing their own results, and hopefully they will build on them, as they progress through their course. We have tried to simplify complex, sometimes very complex, concepts. In simplifying, there is a trade-off in accuracy. We were aware of this when writing the book, and have tried to be as accurate as possible, while giving the simplest explanation. We are also aware that some students do not use SPSS (an IBM company*) for their data analysis. IBM® SPSS® Statistics, however, is the most commonly used statistical package for the social sciences, and this is why the text is tied so closely to SPSS. Students not using this package should find the book useful anyway. This edition of the book has been updated for use with SPSS version 18 and earlier. SPSS Statistics was previously known as PASW and this PASW name is still reflected in the screenshot visuals you will see; however, please note the text will always refer to SPSS. The information and explanation provided and detail in the screenshot are relevant for all versions of SPSS. For the fifth edition of this book, we have updated our chapters, and included some information about the authors of articles which we have drawn upon in the writing of this book – and have included photos of them – strictly with their permission, of course. We also asked them why they had chosen their particular research topic, and whether they had encountered any problems in the running of the experiment/study. We thought this would enrich the text. *SPSS was acquired by IBM in October 2009.There are a number of features in this book to help you learn the concepts being covered (in technical terms these are called ‘pedagogic’ features). These are explained below, but before we explain these we will give you a general overview of what to expect in each chapter. In each chapter we will highlight what is to come and then we will explain the statistical concepts underlying the particular topics for that chapter. Once we have covered the statistical concepts you will be given step-by-step guides to conducting analyses using SPSS Statistics. Towards the end of each chapter you will be provided with a means of testing your knowledge, followed by some pointers to further reading. We will now describe some of the features found in the chapters in more detail. At the beginning of every chapter there is a Chapter overview. These overviews provide you with information about what is contained in each chapter and what you should have achieved from working through it. Sometimes we will also highlight what you need to know beforehand to be able to get the most from the chapter. You should make sure that you read these (it is very easy to get into the habit of not doing this) as they will set the scene for you and prepare your mind for the concepts coming up in the book. At the end of each chapter there are Summaries which outline the main concepts that were covered. These are important for consolidating what you have learned and help put the concepts learned later in the chapter back in the context of the earlier concepts. You will also find SPSS Statistics exercises, activities and multiple choice questions. We cannot stress enough the importance of working through these when you finish each chapter. They are designed to test your knowledge and to help you actively work with the information that you have learned. The best way to learn about things is to do them. The answers to the multiple choice questions are also provided at the very end of each chapter so that you can check your progress. If you have answered questions incorrectly go back and read the relevant part of the chapter to ensure that you have a good understanding of the material. The answers to the SPSS Statistics exercises are provided at the end of the book. Check these and if you have different answers go back and try to work out where you might have gone wrong. Often it might be that you have input the data incorrectly into SPSS Statistics. There are additional multiple choice questions and SPSS Statistics exercises on the companion website and so please do make use of these also. Within each chapter there are a number of features designed to get you thinking about what you have been reading. There are Discussion points which help you to explore different ideas or theories in more detail. There are also a number of Activity boxes which provide additional opportunities for you to test your understanding of the theories and ideas being discussed. It is important to complete the activities as we have placed these to ensure that you are actively engaging with the material. Our experience has shown that actively working with material helps learning (and makes reading more enjoyable). You will also find a number of Example boxes where we provide a concrete example of what we are discussing. Providing such concrete examples helps students understand the concepts more easily. There are also lots of examples from the psychological literature which show how active psychology researchers use the statistical techniques which have been covered in the chapters. Where appropriate we have included as many diagrams and pictures as we can as these will help you to understand (and remember) the text more easily. The thought of giving you endless pages of text without breaking it up is not worth thinking about. This would probably lead to a lot of Zzzzzz. On a serious note though, remember that the pictures are not there to be pretty nor just to break up the text. Please consult these along with reading the text and this will help you learn and understand the concept under discussion. Occasionally in the book you will come across Caution boxes. These are there to warn you of possible problems or issues related to certain techniques or statistical concepts. These are useful in many ways as they are designed to help you to understand some of the limits of statistical tests and they serve as a reminder that we have to think carefully about how we analyse our data. Where in a chapter we want to show you how to use SPSS Statistics we provide annotated screenshots. These will show you which buttons to click in SPSS Statistics as well as how and where to move information around to get the analyses that you want. Finally, at the end 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. Sampling error SPSS: obtaining measures of central tendency Graphically describing data SPSS: generating graphical descriptives Scattergrams SPSS: generating scattergrams Sampling error and relationships between variables The normal distribution Variation or spread of distributions SPSS: obtaining measures of variation Other characteristics of distributions Non-normal distributions SPSS: displaying the normal curve on histograms Writing up your descriptive statistics

For uncorrelated DVs, how do we examine the relative contributions of the individual DVs to the combined DVs when our IV has only two conditions? (a) Conduct separate t-tests and adjust V to keep down the familywise error rate (b) Look at the multivariate effect size of the combined DVs (c) Check that Box’s M is significant (d) Both (a) and (b) above 9. If we had three DVs and found a multivariate difference, what level of V would we set for each t-test to keep the overall V at 5%? (a) (b) (c) (d) Basics Starting SPSS Working with data Data entry Saving your data Inputting data for between-participants and within-participants designs Within-participants designs More definitions explain the key terms you need to understand statistics Up-to-date examples from the literature keep you informed of current research NEW interviews with researchers bring statistics to life NEW full-colour design makes it even easier to follow the steps in SPSS NEW SPSS exercises allow you to learn by using the software Full guidance on using version 18 of SPSS, as well as earlier versions of the software 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. In Chapter 6 you learned how to analyse the relationship between two variables, using Pearson’s r. This test was useful in giving a measure of the association between two continuous variables. You have seen how to represent such relationships on scattergrams, or scatterplots. You learned what was meant by a correlation coefficient, and that r is a natural effect size. This chapter also discusses relationships, or associations, but this time we are going to discuss how to analyse relationships between categorical variables. The measure of association that we are going to discuss in this chapter, `2 or chi-square (pronounced kye-square), measures the association between two categorical variables. You learnt about categorical variables in Chapter 1. If, for instance, we classify people into groups based on which colour blouse or shirt they are wearing, this is a categorical category. In the same way, if we classify people by ethnic group, religion or the country in which they live, these are all categorical judgements; it does not make sense to order them numerically. In this chapter then, you will learn how to: N

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 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. Definition Exploratory data analyses are where we explore the data that we have collected in order to describe it in more detail. These techniques simply describe our data and do not try to draw conclusions about any underlying populations. 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