(BQ) Part 1 book Statistics without maths for psychology has contents: Variables and research design, descriptive statistics, probability, sampling and distributions, hypothesis testing and statistical significance, issues of significance, measures of association,...and other contents.
Find more at www.downloadslide.com ‘This is a clearly written and beautifully presented text The style is ideal for those who are new or nervous about statistics, as it supports their understanding in a friendly and easy to follow way.’ SEVENTH EDITION Dr Jennifer Murray, Edinburgh Napier University ‘In teaching statistics to undergraduates for a number of years, I have found this textbook provides an accessible yet sophisticated grounding in conceptual and practical aspects of quantitative psychology I recommend it without reservation.’ Professor Richard Rowe, University of Sheffield Statistics without Maths for Psychology, 7th edition, will help you gain the confidence to apply statistical concepts and use SPSS to analyse data within your studies and future independent research This new edition has been fully revised and is suitable for use with SPSS version 23 and earlier Key features: • Full-colour design and screenshots of the steps you need to take when using SPSS to help build an understanding of and confidence in analysing data • Up-to-date examples from the literature to keep you informed of current research • Activities related to the literature help you learn how to understand and interpret research findings • Interviews with researchers bring statistics to life showing their important role in psychological discoveries • Multiple choice questions at the end of each chapter enable you to check your understanding and progress Suitable for students taking a course in psychology, applied psychology, social science and other related fields Christine P Dancey is Emeritus Professor of Psychology at the University of East London John Reidy is Head of Academic Operations in the Department of Psychology, Sociology and Politics at Sheffield Hallam University Christine Dancey and John Reidy SEVENTH EDITION Dancey and Reidy www.pearson-books.com Statistics without Maths for Psychology Highly praised for its clear, straightforward approach, Statistics without Maths for Psychology, 7th edition, provides a comprehensive and accessible introduction to statistics and SPSS This widely used and trusted textbook is packed with examples, activities and questions to help you test your learning and deepen your understanding in a practical and manageable way Statistics without Maths for Psychology Front cover image © Miyoung Han / EyeEm / Getty Images CVR_DANCE_07_28856.indd 20/03/2017 09:38 Find more at www.downloadslide.com Statistics Without Maths for Psychology F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com 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 BPS guidelines on the teaching of quantitative methods in psychology Which chapters? Descriptive and summary statistics 3, and Probability theory and The normal distribution 3, and Statistical inference and Confidence intervals Mean and error bar graphs Non-parametric alternatives to t-tests 16 Tests of proportions Cramer’s Phi as a measure of association in contingency tables — McNemar’s test of change — Bivariate correlation and linear regression and 12 The analysis of variance 10, 11 and 15 Non-parametric alternatives to one factor analyses of variance 16 The choice of an appropriate statistical analysis F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com Statistics Without Maths for Psychology Seventh Edition Christine P Dancey University of East London John Reidy Sheffield Hallam University Harlow, England • London • New York • Boston • San Francisco • Toronto • Sydney Dubai • Singapore • Hong Kong • Tokyo • Seoul • Taipei • New Delhi Cape Town • São Paulo • Mexico City • Madrid • Amsterdam • Munich • Paris • Milan F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com PEARSON EDUCATION LIMITED Edinburgh Gate Harlow CM20 2JE United Kingdom Tel: +44 (0)1279 623623 Web: www.pearson.com/uk First published 1999 (print) Second edition 2002 (print) Third edition 2004 (print) Fourth edition 2008 (print) Fifth edition 2011 (print) Sixth edition 2014 (print and electronic) Seventh edition published 2017 (print and electronic) © Pearson Education Limited 1999, 2002, 2004, 2008, 2011 (print) © Pearson Education Limited 2014, 2017 (print and electronic) 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 The print publication is protected by copyright Prior to any prohibited reproduction, storage in a retrieval system, distribution or transmission in any form or by any means, electronic, mechanical, recording or otherwise, permission should be obtained from the publisher or, where applicable, a licence permitting restricted copying in the United Kingdom should be obtained from the Copyright Licensing Agency Ltd, Barnard’s Inn, 86 Fetter Lane, London EC4A 1EN The ePublication is protected by copyright and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased, or as strictly permitted by applicable copyright law Any unauthorised distribution or use of this text may be a direct infringement of the authors’ and the publisher’s rights and those responsible may be liable in law accordingly 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 The screenshots in this book are reprinted by permission of Microsoft Corporation Pearson Education is not responsible for the content of third-party internet sites ISBN: 978-1-292-12885-6 (print) 978-1-292-12889-4 (PDF) 978-1-292-13027-9 (ePub) British Library Cataloguing-in-Publication Data A catalogue record for the print edition is available from the British Library Library of Congress Cataloging-in-Publication Data Dancey, Christine P., author | Reidy, John, author Statistics without maths for psychology / Christine P Dancey, University of East London, John Reidy, Sheffield Hallam University Seventh Edition | New York : Pearson, [2017] | Revised edition of the authors' Statistics without maths for psychology, 2014 LCCN 2016059329| ISBN 9781292128856 (print) | ISBN 9781292128894 (pdf) ISBN 9781292130279 (epub) LCSH: SPSS for Windows | Mathematical statistics | Psychology Statistical methods LCC BF39 D26 2017 | DDC 150.1/5195 dc23 LC record available at https://lccn.loc.gov/2016059329 10 21 20 19 18 17 Print edition typeset in 10/12pt Times New Roman PS Pro by SPi Global Printed in Slovakia by Neografia NOTE THAT ANY PAGE CROSS REFERENCES REFER TO THE PRINT EDITION F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com Christine would like to dedicate this book to Donna Wiles and Linda Perkins Our close friendship and support for each other is very important to me You are both strong, beautiful and fantastic people Thanks a million, for everything John would like to dedicate this book to Ollie … super schnotz (100% Schnauzer) F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com Brief contents Preface xvi xx Guided tour Acknowledgements xxii 10 11 12 13 14 15 16 Variables and research design Introduction to SPSS 25 Descriptive statistics 42 Probability, sampling and distributions 97 Hypothesis testing and statistical significance 134 Correlational analysis: Pearson’s r 174 Analyses of differences between two conditions: the t-test 217 Issues of significance 246 Measures of association 265 Analysis of differences between three or more conditions 298 Analysis of variance with more than one IV 328 Regression analysis 377 Analysis of three or more groups partialling out effects of a covariate 414 Introduction to factor analysis 446 Introduction to multivariate analysis of variance (MANOVA) 481 Non-parametric statistics 516 Answers to activities and SPSS exercises 551 Appendix 1: Table of z-scores and the proportion of the standard normal distribution falling above and below each score 592 Appendix 2: Table r to zr 595 Index F00 Statistics Without Maths for P 28856 Contents.indd 597 30/03/2017 21:26 Find more at www.downloadslide.com F00 Statistics Without Maths for P 28856 Contents.indd 30/03/2017 21:26 Find more at www.downloadslide.com Contents Preface xvi Guided tour xx Acknowledgements xxii Variables and research design Chapter overview 1.1 Why teach statistics without mathematical formulae? 1.2 Variables 1.3 Levels of measurement 1.4 Research designs 1.5 Between-participants and within-participants designs Summary Multiple choice questions References Answers to multiple choice questions Introduction to SPSS Chapter overview 2.1 Basics 2.2 Starting SPSS 2.3 Working with data 2.4 Data entry 2.5 Saving your data 2.6 Inputting data for between-participants and within-participants designs 2.7 Within-participants designs Summary SPSS exercises Descriptive statistics Chapter overview 3.1 Samples and populations 3.2 Measures of central tendency F00 Statistics Without Maths for P 28856 Contents.indd 1 16 20 21 24 24 25 25 25 25 30 31 34 36 39 40 40 42 42 42 45 30/03/2017 21:26 Find more at www.downloadslide.com CHAPTER 9 Measures of association 283 In your report, you would show the frequency counts in the form of a * crosstabulation table, and also give the x2 value, DF and associated probability level The textual part of your report might read as follows: A * x2 was carried out to discover whether there was a significant relationship between smoking and drinking The x2 value of 12.12 had an associated probability value of 0.001, DF = 1, showing that such an association is extremely unlikely to have arisen as a result of sampling error Cramer’s V was found to be 0.33 – thus nearly 11% of the variation in frequencies of smoking can be explained by drinking It can therefore be concluded that there is a significant association between smoking and drinking Have you broken the assumptions for x ? If you have, then Fisher’s Exact Probability Test will be on your output, and the line saying Cells with expected frequency will tell you the percentage of cells that you have with an expected frequency of less than In this case, instead of reporting the values in the paragraph above, you report the exact probability level given by Fisher’s (e.g Fisher’s Exact Probability = 0.66) Fisher’s does not have a value like a t-test or x2 The following output shows you what to expect if you have more than 25% of cells with an expected frequency of less than The first section of the output is simply the categories and frequency values: DO YOU DRINK* DO YOU SMOKE CROSSTABULATION Count drink * smoke Crosstabulation smoke drink Total 1.00 2.00 1.00 60 34 94 2.00 65 35 100 Total We then have the test statistics: Chi-Square Tests Value df Asymptotic Significance (2-sided) Pearson Chi-Square 943a 332 Continuity Correctionb 281 596 1.057 304 Likelihood Ratio Exact Sig (2-sided) Exact Sig (1-sided) 662 312 Fisher’s Exact Test Linear-by-Linear Association 934 N of Valid Cases 100 334 a cells (50.0%) have expected count less than The minimum expected count is 2.10 b Computed only for a table Warning: assumptions broken, therefore use Fisher’s Exact Test (the emboldened row) M09 Statistics Without Maths for P 28856.indd 283 29/03/2017 16:59 Find more at www.downloadslide.com 284 Statistics without maths for psychology The emboldened row shows the probability of obtaining a value of 0.94 when the null hypothesis is assumed to be true - 66% for a two-tailed hypothesis, and 31% for a one-tailed hypothesis Symmetric Measures Nominal by Nominal N of Valid Cases Value Approximate Significance Phi 2.097 332 Cramer’s V 097 332 This is the measure of effect 100 The textual part of your report might read as follows: Since 50% of the cells had an expected frequency of less than 5, the appropriate statistical test was Fisher’s Exact Probability This gave p = 0.66 for a two-tailed hypothesis The value of Cramer’s V was 0.10, showing that the relationship between smoking and drinking was almost zero The conclusion, therefore, is that there is no evidence to suggest an association between drinking and smoking A * x2 square is easy to work out by hand once you are used to it, but we will not ask you to it The instructions on how to perform a * x2 analysis on SPSS were given earlier (see page 301) Caution! You cannot tell how many people are going to fall into each category when you start your 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 (r - 1) multiplied by number of columns minus (c - 1) In this case, you can see that a * x2 will always have DF = because (r - 1) = (c - 1) = (2 - 1) = (2 - 1) = Activity 9.5 Cramer’s V is: (a) A measure of difference (b) A correlation coefficient (c) An equivalent statistic to Fisher’s Exact Probability Test (d) A CV value M09 Statistics Without Maths for P 28856.indd 284 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association 285 9.4 x2 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 * contingency table, for obvious reasons The calculations are worked out in exactly the same way as we have described for the * table The degrees of freedom, however, will be different Remember: DF = (c - 1) * (r - 1) So: * = It is also possible to have more than three levels (e.g * or * 3), but interpretation then becomes a problem We not just want to say ‘there is a significant relationship between variable A and variable B’ We would also like to be able to say something about the direction of the relationship For instance, in our smoke/drink example, we could see, from looking at the cells, that the significant relationship referred to the positive association between drinking and smoking When we have larger contingency tables, it can be difficult to disentangle all the various relationships Also, for the test statistic to be reliable, remember: • No more than 25% of cells should have an expected frequency of less than • No cell should contain less than (if they do, you may be able to collapse cells, i.e ex-smokers and smokers could be added together to form one group; however, sometimes it is not possible to collapse cells in this way, because the cells not have enough in common) You may be wondering why we have to meet these assumptions It is because we assume that we are sampling from a normal population If the expected cell sizes are so small, it is unlikely that we are sampling from a normal population Our test statistic will be unreliable unless we meet the assumptions Check that participants not appear in more than one cell Remember that we are checking to see if the numbers of participants in each cell are independent – obviously they will not be if they are the same participants! So the same participants must not respond more than once The total of the cell frequencies must equal the number of participants There is no reason why the x2 test cannot be used with quantitative variables – it is just that, with quantitative data, other tests, such as the parametric ones, will be more powerful Table 9.8 * contingency table Heavy smokers Light smokers Non-smokers Heavy drinkers Light drinkers Teetotallers M09 Statistics Without Maths for P 28856.indd 285 29/03/2017 16:59 Find more at www.downloadslide.com 286 Statistics without maths for psychology Activity 9.6 True or false? (a) x2 needs to have equal numbers of participants in each cell (b) Each participant must contribute to every cell (c) You must have 650% of your cells with an expected frequency of in order to perform x2 (d) The same participant can count in more than one category 9.4.1 x2: a one- or two-tailed test? There are debates among statisticians as to whether we should use one- or two-tailed tests You cannot go wrong if you use a two-tailed test, because you are less likely to declare a result significant when using such a test Some people think you should always use a two-tailed hypothesis when using x2 The test itself is one-tailed: the x2 value will be the same whether the figures look like this: 22 36 40 15 or this: 40 22 15 36 36 15 22 40 Like this: 15 40 36 22 or this: The sampling distribution of x2 is always positive That is, because x2 value is a squared figure, it is always positive This is what we mean by saying that the test itself is one-tailed: it gives you values only in the positive range – it is impossible to obtain a negative x2 value However, your hypothesis can be two-tailed (there is an association, but you are not predicting the direction of the association) or, more likely, one-tailed (you predict the direction of the association, e.g smoking and cancer are related in a positive way or, in a one-variable x2, brand A chocolate is preferred significantly more often than the other brands) However, one-tailed tests should be formulated on the basis of previous theory – not just because you felt that chocolate A was better than all the other bars Some people feel that if we use a one-tailed test, and then the relationship is found to be opposite to the one we are predicting, then we have ‘lost out’, but of course that is the case with any one-tailed prediction (see section 5.11, for more on this) If we have good reason to specify a direction of the association, then it is quite valid to use a one-tailed hypothesis, but you must decide before you your analysis (i.e you have to think carefully about whether your hypothesis is one- or two-tailed before the study) M09 Statistics Without Maths for P 28856.indd 286 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association 287 Personal reflection Doctoral Candidate and NSF Graduate Research Fellow Daniel Sullivan, M.A Department of Psychology University of Kansas ARTICLE: Collectivism and the meaning of suffering (Sullivan, Landau, Kay and Rothschild, 2012) Daniel Sullivan says: “ For this particular study, we were looking at whether one group of people – namely, parents in the US – might differentially interpret one form of suffering – namely, the suffering of children – based on whether they were in a more collectivist or individualist mindset I wanted a method that would make this issue very real for our parent participants; I wanted to relate the suffering of children back to their own personal experience Of course, parents sometimes make children suffer through punishments, so could there be a way to realistically examine in the lab the circumstances under which parents might be more willing to this? My wife grew up in a state where corporal punishment of children in schools is legal, and she told me that her parents had to make a choice when she entered school as to whether she would be suspended or spanked in the event that she got into trouble I had not personally experienced this, but it immediately struck me as an interesting way to make this issue real for the parents in my study: make them choose whether their own child would be punished corporally or not In this case, the stats followed the method I found an interesting method to engage my participants, and then decided the Chi-square would be one appropriate technique for analyzing the resulting data ” Example from the literature Collectivism and the meaning of suffering Sullivan, Landau, Kay and Rothschild (2012) focused on the way individuals and communities interpret suffering A person, or a particular community, might interpret an instance of suffering by believing the suffering was just a chance event (having a car crash and happening to be in the wrong place at the wrong time) or they might believe the suffering is a punishment because the sufferer has contravened social norms, e.g that having HIV or AIDS is a punishment for being promiscuous The authors state that collectivist cultures will be more likely to interpret suffering repressively than will individualist cultures As part of this study, parents of at least one child were recruited into the study Parents were assessed as to whether they were ‘individualist self-construal’ or ‘collectivist self-construal’ They were then measured as to their support for corporal punishment in schools Then the parents were presented with a forced choice asking them which they would allow their own child to receive (in the event of some major misdemeanour) The choice was either suspension from school, or corporal punishment The results are as follows: M09 Statistics Without Maths for P 28856.indd 287 29/03/2017 16:59 Find more at www.downloadslide.com 288 Statistics without maths for psychology Choice Condition Individualist self-construal Collectivist self-construal Suspension 46 41 Corporal punishment 18 The authors carried out a * chi-square test They said (p 1035): ‘We obtained a significant result, x2 (1) = 3.92, p = 05 c participants overwhelmingly preferred suspension for their child over corporal punishment (77% chose suspension) Importantly, however, the number of participants who chose corporal punishment in the collectivist self-construal condition was more than double the number who chose corporal punishment in the individualist self-construal condition.’ Activity 9.7 Using the information in the authors’ * contingency table, run the analysis in SPSS Check your results with the authors Using this information, write a few brief sentences interpreting the results – you should be able to add some of your own interpretation to that of the authors! Sometimes in the literature you will find researchers who have used Yates’ correction for continuity This is a slight adjustment to the formula, used when we have small expected frequencies, in a * table In the late 1980s, psychologists were routinely advised to use Yates’ correction, but now many people feel it is unreasonable and unnecessary to this (see Howell, 2010, for debate on this issue) You will sometimes see a x2 value, corrected for continuity We recommend that, as introductory students, you not worry about such corrections when you carry out your own analysis Note, however, that some of the journal articles you read will report the use of Yates’ correction Example from the literature * chi-square: Everyday memory in children with developmental coordination disorder (DCD) Chen et al (2013) investigated the everyday memory function in children with DCD, and explored the specific profile of everyday memory across different domains They evaluated 19 children with DCD and 19 typically developing (TD) children by measuring their everyday memory performance using the Rivermead Behavioral Memory Test for Children (RBMT) Based on their scores, children were categorised as (impaired), (borderline) and (normal) The two groups were children with DCD and children categorised as TD The authors wanted to see whether the range of the RBMT scores (normal, borderline or impaired) was significantly different for the two groups Their table is reproduced as follows: M09 Statistics Without Maths for P 28856.indd 288 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association 289 The distribution of the total profile scores of the RBMT-C for normal, borderline and impaired ranges in both groups (p 691) Range Developmental coordination disorder (n = 19) Typically developing children (n = 19) N % N % Normal 47.4 18 94.6 Borderline 47.4 5.3 Impaired 5.3 0 Note RBMT-C, Rivermead Behavioral Memory Test for Children p = 006 The authors say that the frequencies of children with DCD and typically developing children were significantly different at p = 0.006 They not tell us the chi-square value Activity 9.8 Borghi and colleagues (2016) sought to evaluate whether occupational therapists’ communications change with experience Groups of occupational therapists who had different levels of experience were studied Role playing with simulated clients was the focus of the study The content of the words used by occupational therapists (called ‘utterances’) were analysed and coded In this example we are interested only in the use of the one-variable chi-square which was used to analyse the total utterances of the 85 role-plays analysed from the categories in each of the groups The categories are listed below in the first column There were three groups (columns two, three and four) with a total of 5511 utterances altogether Table 9.9 frequencies of total utterances pronounced by therapists during the 85 role-plays analysed Categories Second-year OT students Final-year OT students Process 521 571 603 1695 Personal 119 118 103 340 Occupational therapy 514 550 626 1690 25 46 63 134 Psychosocial 284 282 277 843 Emotional 322 239 248 809 1785 1806 1920 5511 Medical Total M09 Statistics Without Maths for P 28856.indd 289 Professional OTs Total 29/03/2017 16:59 Find more at www.downloadslide.com 290 Statistics without maths for psychology The one-variable chi-square will tell us whether the 5511 utterances were distributed fairly evenly or not Thus the figures used in the one variable chi-square will be the last row Carry out a one-variable chi-square analysis using the three categories in the last row (1785, 1806, 1920) Give a brief interpretation of the meaning of the results Check your results with those of the authors in the Answers section Summary • For the analysis of relationships between categorical variables, x2 is the appropriate inferential statistic • A one-variable x2 (or goodness-of-fit test) has one variable with several levels The test shows whether the frequencies in the cells are significantly different from what we would expect, assuming the null hypothesis to be true • A x2 test for independence shows whether there is a significant association between two variables (with two or more levels) The test statistic results from a calculation showing the degree by which the observed frequencies in the cells are different from the frequencies we would expect, assuming the null hypothesis to be true (i.e no relationship) • x2 has certain assumptions (see section 9.3.1) If these are broken, then for a * table, Fisher’s Exact Probability Test can be performed This is done automatically in SPSS • x2 can be converted to Cramer’s V (a correlation coefficient) to give a measure of effect This is performed automatically in SPSS Discover the website at www.pearsoned.co.uk/dancey where you can test your knowledge with multiple choice questions and activities, discover more about topics using the links to relevant websites, and explore the interactive flowchart designed to help you find the right method of analysis SPSS exercises Exercise Use the data from Sullivan et al (2012) on page 310 in order to perform a * x2 on SPSS Do your results match theirs? Exercise Perform a * analysis on your computer package Smoke Do not smoke Drink Do not drink M09 Statistics Without Maths for P 28856.indd 290 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association 291 Is there a relationship between drinking and smoking in your class? What is the x2 value? What is the probability value? What the results tell you? Exercise Thirty-three people were given an animal preference questionnaire and classified as to whether they preferred mice, spiders, bats or snakes The results were as follows: Mice Spiders Bats Snakes 10 11 What are the expected frequencies for the four cells? What is the x2 value? What is the probability value? What can you conclude from the results? Exercise Perform a x2 on the following data: Smoke Drink Do not drink Do not smoke 70 32 Report the results and explain what they mean Discussion point x2 or t-test? Look at the following newspaper cuttings and decide for each whether you would use x2 or t-test A: And there’s a chance of rain on Thursdays From Professor MJ Sir, NP (Letters, 24th July) attempts to explain GN’s findings (Letters, 22nd July) that Thursday is the wettest day of the week No explanation is needed The variation in the figures for the seven days is purely random, as any statistician can assure you The total rainfall for all seven days is 938.9, giving an average of 134.13 This average is the expected figure for each day if rainfall is distributed equally over the seven days A chi-square test may be used to compare the seven observed figures with the expected one The resultant chi-square value of 1.28 for degrees of freedom is far too small to demonstrate any significant difference from expectation In fact, chance would produce this amount of difference at least 95 times out of 100 Yours faithfully, M09 Statistics Without Maths for P 28856.indd 291 29/03/2017 16:59 Find more at www.downloadslide.com 292 Statistics without maths for psychology B: The wettest day of the week put to test From Mr AF Sir, It may seem impertinent for a simple graduate to criticise his betters, but surely Professor MJ has used the wrong statistical test in his letter (27 July) The chi-square test is used to test frequencies of occurrence In this case we have interval data and should use a t-test, requiring a knowledge of the standard deviations of the sets of data Notwithstanding this, the result will probably be similar In my view, Thursday is the wettest day as it is the first day of a Test Match The selectors use this information to pick four seamers who then prove woefully inadequate for the remaining four dry days Yours faithfully, Multiple choice questions Fisher’s Exact Probability Test is used when: (a) The calculations for x2 are too difficult (b) You have more than 25% of cells with expected frequencies of less than in a * design (c) You have more than 25% of cells with expected frequencies of less than in a * contingency table (d) You have non-categorical data Cramer’s V is: (a) (b) (c) (d) A victory sign made after performing Cramer’s statistical test A measure of effect based on standardised scores A correlational measure of effect converted from x2 A measure of difference Questions to relate to the following output: DAY OF WEEK* SEX CROSSTABULATION Count SEX day of week Total M09 Statistics Without Maths for P 28856.indd 292 Total men women tuesday am 21 210 231 wednesday am 43 127 170 evening 25 99 124 89 436 525 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association 293 Chi-Square Tests Value df Asymp Sig (2-sided) Pearson Chi-Square 19.450a 000 Likelihood Ratio 20.208 000 Linear-by-Linear Association 10.429 001 N of Valid Cases 525 a cells (.0%) have expected count less than The minimum expected count is 21.02 How many women were in the Tuesday morning group? (a) 127 (b) 43 (c) 99 (d) 210 Pearson’s x2 has an associated probability of: (a) 0.001 (b) 0.00004 (c) 0.00124 (d) None of these The number of people in this analysis is: (a) 231 (b) 170 (c) 124 (d) 525 290 people are asked which of five types of cola they prefer Results are as follows: Coca Cola Pepsi Diet Coke Cheapo Pepsi Lite 67 83 77 57 What are the expected frequencies for the cells: (a) 57 (b) 58 (c) 290 (d) None of the above Look at the following output: Chi-Square Tests Value df Asymp Sig (2-sided) Pearson Chi-Square 14.3212 00050 Likelihood Ratio 14.3722 00004 Linear-by-Linear Association 14.3521 00005 M09 Statistics Without Maths for P 28856.indd 293 29/03/2017 16:59 Find more at www.downloadslide.com 294 Statistics without maths for psychology x2 has an associated probability of: (a) 0.00005 (b) 0.00004 (c) 0.00200 (d) 0.00050 Look at the following table: Statistics Child development Psychobiology Cognitive Psychology 72 31 15 50 observed expected What is the value of the expected frequencies? (a) 32 (b) 50 (c) 42 (d) 25 A one-variable x2 is also called: (a) (b) (c) (d) Goodness-of-fit test x2 test of independence x2 * 2 * x2 10 The value of x2 will always be: (a) Positive (b) Negative (c) High (d) It depends 11 The Yates’ correction is sometimes used by researchers when: (a) (b) (c) (d) Cell sizes are huge Cell sizes are small They analyse data from * contingency tables Both (b) and (c) above Questions 12 to 14 relate to the following (partial) output, which is the result of a x2 analysis investigating the association between body shape and type of sports played: Chi-Square Tests Value df Asymp Sig (2-sided) Pearson Chi-Square 22.305a 00796 Likelihood Ratio 21.516 01055 Linear-by-Linear Association 12.162 00049 N of Valid Cases 525 a cells (.0%) have expected count less than The minimum expected count is 21.02 M09 Statistics Without Maths for P 28856.indd 294 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association Cramer’s V 09943 295 00796 a Not assuming the null hypothesis b Using the asymptotic standard error assuming the null hypothesis 12 The x2 value is: (a) 12.162 (b) 21.516 (c) 22.305 (d) 525 13 The x2 value has an exact probability level of: (a) 0.0004 (b) 0.05 (c) 0.01055 (d) 0.00796 14 The value of Cramer’s V is: (a) 0.05 (b) 0.008 (c) 0.099 (d) 0.010 15 Look at the following * contingency table, taken from 150 participants: Drink tea Drink coffee Feel terrific 70 50 Feel lousy 30 80 There is something wrong with the above, in that the numbers in the cells should: (a) (b) (c) (d) Add up to 150 Add up to 100 Be equal Be analysed by a * x2 16 485 people are asked which of five types of bird pictures they prefer to be put on a ‘stop all wars’ campaign Results are as follows: 162 M09 Statistics Without Maths for P 28856.indd 295 84 57 94 88 29/03/2017 16:59 Find more at www.downloadslide.com 296 Statistics without maths for psychology What are the expected frequencies for the cells? (a) 79 (b) 97 (c) 485 (d) 5 17 In order to find out the effect size after performing a x2 analysis, we: (a) convert Cramer’s V to x2 (b) convert x2 to Cramer’s V (c) square the x2 value (d) convert x2 to Fisher’s Z 18 Look at the following table Anxious Not anxious Dreadful job 210 150 Wonderful job 62 52 This is called a: (a) (b) (c) (d) * * * * contingency table contingency table chi-square table chi-square table 19 The general purpose for which a * x2 analysis is used is to discover whether: (a) (b) (c) (d) There is a significant association between two categorical variables There is an association between two continuous variables Two groups of participants differ on two variables None of the above 20 If you are performing a * x2 analysis and find you have broken the assumptions, then you need to: (a) (b) (c) (d) Look at the results for a Fisher’s exact probability test Look to see whether it is possible to collapse categories Investigate the possibility of a t-test Give up M09 Statistics Without Maths for P 28856.indd 296 29/03/2017 16:59 Find more at www.downloadslide.com CHAPTER 9 Measures of association 297 References Borghi, L., Johnson, I., Barlascini, L., Moja, E and Vegni, E (2016) ‘Do occupational therapists’ communication behaviours change with experience?’ Scandinavian Journal of Occupational Therapy, 23(1): 50–56 Chen, I C., Tsai, P L., Hsu, Y W., Ma, H I and Lai, H A (2013) ‘Everyday memory in children with developmental coordination disorder (DCD)’, Research in Developmental Disabilities, 34: 687–94 Howell, D C (2010) Statistical Methods for Psychology, 7th international edn Stanford, CT: Wadsworth Sullivan, D., Landau, M J., Kay, A C and Rothschild, Z K (2012) ‘Collectivism and the meaning of suffering’, Journal of Personality and Social Psychology, 103(6): 1023–39 Answers to multiple choice questions b, c, d, a, d, b, d, c, a, 10 a, 11 d, 12 c, 13 d, 14 c, 15 a, 16 b, 17 b, 18 a, 19 a, 20 b M09 Statistics Without Maths for P 28856.indd 297 29/03/2017 16:59 ... 45 3 45 5 45 6 45 7 45 9 46 2 46 6 46 7 46 8 47 6 47 6 48 0 48 0 48 1 48 1 48 1 48 2 48 2 48 3 48 5 48 9 49 0 49 2 49 3 49 4 49 6 503 506 506 508 515 515 515 516 516 517 517 5 21 5 21 523 527 530 535 30/03/2 017 21: 27 Find... F00 Statistics Without Maths for P 28856 Contents.indd 13 xiii 332 333 346 3 51 359 362 368 370 370 372 376 376 377 377 377 380 3 91 398 40 7 40 7 40 9 41 3 41 3 41 4 41 4 41 6 42 2 42 8 43 2 44 0 44 0 44 1 44 5... F00 Statistics Without Maths for P 28856 Contents.indd 10 50 53 56 66 68 70 71 73 76 80 81 82 88 90 90 91 92 95 96 97 97 97 10 1 10 8 10 8 11 1 12 0 12 1 12 2 1 24 12 7 12 7 12 8 13 0 13 3 13 3 1 34 1 34 1 34 13 9