DISCOVERING STATISTICS USING IBM SPSS STATISTICS CATISFIED CUSTOMERS DISCOVERING STATISTICS USING IBM SPSS STATISTICS AND SEX AND DRUGS AND ROCK ‘N’ ROLL 4TH EDITION ANDY FIELD SAGE Publications Ltd 1 Oliver’s Yard 55 City Road London EC1Y 1SP SAGE Publications Inc. 2455 Teller Road Thousand Oaks, California 91320 SAGE Publications India Pvt Ltd B 1/I 1 Mohan Cooperative Industrial Area Mathura Road New Delhi 110 044 SAGE Publications Asia-Pacific Pte Ltd 3 Church Street #10-04 Samsung Hub Singapore 049483 Editor: Michael Carmichael Development editor: Robin Lupton Digital content assistant: Tanushri Shukla Production editor: Ian Antcliff Copyeditor: Richard Leigh Proofreaders: Louise Harnby; Kate Harrison; Anna Gilding; Jennifer Hinchliffe Indexer: David Rudeforth Marketing manager: Ben Griffin-Sherwood Cover design: Wendy Scott Typeset by: C&M Digitals (P) Ltd, Chennai, India Printed: in Canada by Transcontinental Printing Inc Printed on paper from sustainable resources © Andy Field 2013 First edition published 2000 Second edition published 2005 Third edition published 2009. Reprinted 2009, 2010, 2011 (twice), 2012 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted in any form, or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction, in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. Library of Congress Control Number: 2012944559 British Library Cataloguing in Publication data A catalogue record for this book is available from the British Library ISBN 978-1-4462-4917-8 ISBN 978-1-4462-4918-5 (pbk) CONTENTS Preface How to use this book Acknowledgements Dedication Symbols used in this book Some maths revision 1 Why is my evil lecturer forcing me to learn statistics? 1.1. What will this chapter tell me? ① 1.2. What the hell am I doing here? I don’t belong here ① 1.2.1. The research process ① 1.3. Initial observation: finding something that needs explaining ① 1.4. Generating theories and testing them ① 1.5. Collect data to test your theory ① 1.5.1. Variables ① 1.5.2. Measurement error ① 1.5.3. Validity and reliability ① 1.5.4. Correlational research methods ① 1.5.5. Experimental research methods ① 1.5.6. Randomization ① 1.6. Analysing data ① 1.6.1. Frequency distributions ① 1.6.2. The centre of a distribution ① 1.6.3. The dispersion in a distribution ① 1.6.4. Using a frequency distribution to go beyond the data ① 1.6.5. Fitting statistical models to the data ① 1.7. Reporting data ① 1.7.1. Dissemination of research ① 1.7.2. Knowing how to report data ① 1.7.3. Some initial guiding principles ① 1.8. Brian’s attempt to woo Jane ① 1.9. What next? ① 1.10. Key terms that I’ve discovered 1.11. Smart Alex’s tasks 1.12. Further reading 2 Everything you never wanted to know about statistics 2.1. What will this chapter tell me? ① 2.2. Building statistical models ① 2.3. Populations and samples ① 2.4. Statistical models ① 2.4.1. The mean as a statistical model ① 2.4.2. Assessing the fit of a model: sums of squares and variance revisited ① 2.4.3. Estimating parameters ① 2.5. Going beyond the data ① 2.5.1. The standard error ① 2.5.2. Confidence intervals ② 2.6. Using statistical models to test research questions ① 2.6.1. Null hypothesis significance testing ① 2.6.2. Problems with NHST ② 2.7. Modern approaches to theory testing ② 2.7.1. Effect sizes ② 2.7.2. Meta-analysis ② 2.8. Reporting statistical models ② 2.9. Brian’s attempt to woo Jane ① 2.10. What next? ① 2.11. Key terms that I’ve discovered 2.12. Smart Alex’s tasks 2.13. Further reading 3 The IBM SPSS Statistics environment 3.1. What will this chapter tell me? ① 3.2. Versions of IBM SPSS Statistics ① 3.3. Windows versus MacOS ① 3.4. Getting started ① 3.5. The data editor ① 3.5.1. Entering data into the data editor ① 3.5.2. The variable view ① 3.5.3. Missing values ① 3.6. Importing data ① 3.7. The SPSS viewer ① 3.8. Exporting SPSS output ① 3.9. The syntax editor ③ 3.10. Saving files ① 3.11. Retrieving a file ① 3.12. Brian’s attempt to woo Jane ① 3.13. What next? ① 3.14. Key terms that I’ve discovered 3.15. Smart Alex’s tasks 3.16. Further reading 4 Exploring data with graphs 4.1. What will this chapter tell me? ① 4.2. The art of presenting data ① 4.2.1. What makes a good graph? ① 4.2.2. Lies, damned lies, and … erm … graphs ① 4.3. The SPSS chart builder ① 4.4. Histograms ① 4.5. Boxplots (box–whisker diagrams) ① 4.6. Graphing means: bar charts and error bars ① 4.6.1. Simple bar charts for independent means ① 4.6.2. Clustered bar charts for independent means ① 4.6.3. Simple bar charts for related means ① 4.6.4. Clustered bar charts for related means ① 4.6.5. Clustered bar charts for ‘mixed’ designs ① 4.7. Line charts ① 4.8. Graphing relationships: the scatterplot ① 4.8.1. Simple scatterplot ① 4.8.2. Grouped scatterplot ① 4.8.3. Simple and grouped 3-D scatterplots ① 4.8.4. Matrix scatterplot ① 4.8.5. Simple dot plot or density plot ① 4.8.6. Drop-line graph ① 4.9. Editing graphs ① 4.10. Brian’s attempt to woo Jane ① 4.11. What next? ① 4.12. Key terms that I’ve discovered 4.13. Smart Alex’s tasks 4.14. Further reading 5 The beast of bias 5.1. What will this chapter tell me? ① 5.2. What is bias? ① 5.2.1. Assumptions ① 5.2.2. Outliers ① 5.2.3. Additivity and linearity ① 5.2.4. Normally distributed something or other ① 5.2.5. Homoscedasticity/homogeneity of variance ② 5.2.6. Independence ② 5.3 Spotting bias ② 5.3.1. Spotting outliers ② 5.3.2. Spotting normality ① 5.3.3. Spotting linearity and heteroscedasticity/heterogeneity of variance ② 5.4. Reducing bias ② 5.4.1. Trimming the data ② 5.4.2. Winsorizing ① 5.4.3. Robust methods ③ 5.4.4. Transforming data ② 5.5. Brian’s attempt to woo Jane ① 5.6. What next? ① 5.7. Key terms that I’ve discovered 5.8. Smart Alex’s tasks 5.9. Further reading 6 Non-parametric models 6.1. What will this chapter tell me? ① 6.2. When to use non-parametric tests ① 6.3. General procedure of non-parametric tests in SPSS ① 6.4. Comparing two independent conditions: the Wilcoxon rank-sum test and Mann–Whitney test ① 6.4.1. Theory ② 6.4.2. Inputting data and provisional analysis ① 6.4.3. The Mann–Whitney test using SPSS ① 6.4.4. Output from the Mann–Whitney test ① 6.4.5. Calculating an effect size ② 6.4.6. Writing the results ① 6.5. Comparing two related conditions: the Wilcoxon signed-rank test ① 6.5.1. Theory of the Wilcoxon signed-rank test ② 6.5.2. Running the analysis ① 6.5.3. Output for the ecstasy group ① 6.5.4. Output for the alcohol group ① 6.5.5. Calculating an effect size ② 6.5.6. Writing the results ① 6.6. Differences between several independent groups: the Kruskal–Wallis test ① 6.6.1. Theory of the Kruskal–Wallis test ② 6.6.2. Follow-up analysis ② 6.6.3. Inputting data and provisional analysis ① 6.6.4. Doing the Kruskal–Wallis test in SPSS ① 6.6.5. Output from the Kruskal–Wallis test ① 6.6.6. Testing for trends: the Jonckheere–Terpstra test ② 6.6.7. Calculating an effect size ② 6.6.8. Writing and interpreting the results ① 6.7. Differences between several related groups: Friedman’s ANOVA ① 6.7.1. Theory of Friedman’s ANOVA ② 6.7.2. Inputting data and provisional analysis ① 6.7.3. Doing Friedman’s ANOVA in SPSS ① 6.7.4. Output from Friedman’s ANOVA ① 6.7.5. Following-up Friedman’s ANOVA ② 6.7.6. Calculating an effect size ② 6.7.7. Writing and interpreting the results ① 6.8. Brian’s attempt to woo Jane ① 6.9. What next? ① 6.10. Key terms that I’ve discovered 6.11. Smart Alex’s tasks 6.12. Further reading 7 Correlation 7.1. What will this chapter tell me? ① 7.2. Modelling relationships ① 7.2.1. A detour into the murky world of covariance ① 7.2.2. Standardization and the correlation coefficient ① 7.2.3. The significance of the correlation coefficient ③ 7.2.4. Confidence intervals for r ③ 7.2.5. A word of warning about interpretation: causality ① 7.3. Data entry for correlation analysis using SPSS ① 7.4. Bivariate correlation ① 7.4.1. General procedure for running correlations in SPSS ① 7.4.2. Pearson’s correlation coefficient ① 7.4.3. Spearman’s correlation coefficient ① 7.4.4. Kendall’s tau (non-parametric) ① 7.4.5. Biserial and point-biserial correlations ③ 7.5. Partial correlation ② 7.5.1. The theory behind part and partial correlation ③ 7.5.2. Partial correlation in SPSS ③ 7.5.3. Semi-partial (or part) correlations ② 7.6. Comparing correlations ③ 7.6.1. Comparing independent rs ③ 7.6.2. Comparing dependent rs ③ 7.7. Calculating the effect size ① 7.8. How to report correlation coefficients ① 7.9. Brian’s attempt to woo Jane ① 7.10. What next? ① 7.11. Key terms that I’ve discovered 7.12. Smart Alex’s tasks 7.13. Further reading 8 Regression 8.1. What will this chapter tell me? ① 8.2. An introduction to regression ① 8.2.1. The simple linear model ① 8.2.2. The linear model with several predictors ② 8.2.3. Estimating the model ② 8.2.4. Assessing the goodness of fit, sums of squares, R and R2 ① 8.2.5. Assessing individual predictors ① 8.3. Bias in regression models? ② 8.3.1. Is the model biased by unusual cases? ② 8.3.2. Generalizing the model ② 8.3.3. Sample size in regression ③ 8.4. Regression using SPSS: One Predictor ① 8.4.1. Regression: the general procedure ① 8.4.2. Running a simple regression using SPSS ① 8.4.3. Interpreting a simple regression ① 8.4.4. Using the model ① 8.5. Multiple regression ② 8.5.1. Methods of regression ② 8.5.2. Comparing models ② 8.5.3. Multicollinearity ② 8.6. Regression with several predictors using SPSS ② 8.6.1. Main options ② 8.6.2. Statistics ② 8.6.3. Regression plots ② 8.6.4. Saving regression diagnostics ② 8.6.5. Further options ② 8.6.6. Robust regression ② 8.7. Interpreting multiple regression ② 8.7.1. Descriptives ② 8.7.2. Summary of model ② 8.7.3. Model parameters ② 8.7.4. Excluded variables ② 8.7.5. Assessing multicollinearity ② 8.7.6. Bias in the model: casewise diagnostics ② 8.7.7. Bias in the model: assumptions ② 8.8. What if I violate an assumption? Robust regression ② 8.9. How to report multiple regression ② 8.10. Brian’s attempt to woo Jane ① 8.11. What next? ① 8.12. Key terms that I’ve discovered 8.13. Smart Alex’s tasks 8.14. Further reading 9 Comparing two means 9.1. What will this chapter tell me? ① 9.2. Looking at differences ① 9.2.1. An example: are invisible people mischievous? ① 9.2.2. Categorical predictors in the linear model ① 9.3. The t-test ① 9.3.1. Rationale for the t-test ① 9.3.2. The independent t-test equation explained ① 9.3.3. The paired-samples t-test equation explained ① 9.4. Assumptions of the t-test ① 9.5. The independent t-test using SPSS ① 9.5.1. The general procedure ① 9.5.2. Exploring data and testing assumptions ① 9.5.3. Compute the independent t-test ① 9.5.4. Output from the independent t-test ① 9.5.5. Calculating the effect size ② 9.5.6. Reporting the independent t-test ① 9.6. Paired-samples t-test using SPSS ① 9.6.1. Entering data ① 9.6.2. Exploring data and testing assumptions ① 9.6.3. Computing the paired-samples t-test ① 9.6.4. Calculating the effect size ① 9.6.5. Reporting the paired-samples t-test ① 9.7. Between groups or repeated measures? ① 9.8. What if I violate the test assumptions? ② 9.9. Brian’s attempt to woo Jane ① 9.10. What next? ① 9.11. Key terms that I’ve discovered 9.12. Smart Alex’s tasks 9.13. Further reading 10 Moderation, mediation and more regression 10.1. What will this chapter tell me? ① 10.2. Installing custom dialog boxes in SPSS ② 10.3. Moderation: interactions in regression ③ 10.3.1. The conceptual model ③ 10.3.2. The statistical model ② 10.3.3. Centring variables ② 10.3.4. Creating interaction variables ② 10.3.5. Following up an interaction effect ② 10.3.6. Running the analysis ② 10.3.7. Output from moderation analysis ② 10.3.8. Reporting moderation analysis ② 10.4. Mediation ② 10.4.1. The conceptual model ② 10.4.2. The statistical model ② 10.4.3. Effect sizes of mediation ③ 10.4.4. Running the analysis ② 10.4.5. Output from mediation analysis ② 10.4.6. Reporting mediation analysis ② 10.5. Categorical predictors in regression ③ 10.5.1. Dummy coding ③ 10.5.2. SPSS output for dummy variables ③ 10.6. Brian’s attempt to woo Jane ① 10.7. What next? ① 10.8. Key terms that I’ve discovered 10.9. Smart Alex’s tasks 10.10. Further reading 11 Comparing several means: ANOVA (GLM 1) 11.1. What will this chapter tell me? ① 11.2. The theory behind ANOVA ② 11.2.1. Using a linear model to compare means ② 11.2.2. Logic of the F-ratio ② 11.2.3. Total sum of squares (SST) ② 11.2.4. Model sum of squares (SSM) ② 11.2.5. Residual sum of squares (SSR) ② 11.2.6. Mean squares ② 11.2.7. The F-ratio ② 11.2.8. Interpreting F ② 11.3. Assumptions of ANOVA ③ 11.3.1. Homogeneity of variance ② 11.3.2. Is ANOVA robust? ③ 11.3.3. What to do when assumptions are violated ② 11.4. Planned contrasts ② 11.4.1. Choosing which contrasts to do ② 11.4.2. Defining contrasts using weights ② 11.4.3. Non-orthogonal comparisons ② 11.4.4. Standard contrasts ② 11.4.5. Polynomial contrasts: trend analysis ② 11.5. Post hoc procedures ② 11.5.1. Type I and Type II error rates for post hoc tests ② 11.5.2. Are post hoc procedures robust? ② 11.5.3. Summary of post hoc procedures ② 11.6. Running one-way ANOVA in SPSS ② 11.6.1. General procedure of one-way ANOVA ② 11.6.2. Planned comparisons using SPSS ② 11.6.3. Post hoc tests in SPSS ② 11.6.4. Options ② 11.6.5. Bootstrapping ② 11.7. Output from one-way ANOVA ② 11.7.1. Output for the main analysis ② 11.7.2. Output for planned comparisons ② 11.7.3. Output for post hoc tests ② 11.8. Calculating the effect size ② 11.9. Reporting results from one-way independent ANOVA ② 11.10. Key terms that I’ve discovered 11.11. Brian’s attempt to woo Jane ① 11.12. What next? ① 11.13. Smart Alex’s tasks 11.14. Further reading 12 Analysis of covariance, ANCOVA (GLM 2) 12.1. What will this chapter tell me? ② 12.2. What is ANCOVA? ② 12.3. Assumptions and issues in ANCOVA ③ 12.3.1. Independence of the covariate and treatment effect ③ 12.3.2. Homogeneity of regression slopes ③ 12.3.3. What to do when assumptions are violated ② 12.4. Conducting ANCOVA in SPSS ② 12.4.1. General procedure ① 12.4.2. Inputting data ① 12.4.3. Testing the independence of the treatment variable and covariate ② 12.4.4. The main analysis ② 12.4.5. Contrasts 12.4.6. Other options ② 12.4.7. Bootstrapping and plots ② 12.5. Interpreting the output from ANCOVA ② 12.5.1. What happens when the covariate is excluded? ② 12.5.2. The main analysis ② 12.5.3. Contrasts ② 12.5.4. Interpreting the covariate ② 12.6. Testing the assumption of homogeneity of regression slopes ③ 12.7. Calculating the effect size ② 12.8. Reporting results ② 12.9. Brian’s attempt to woo Jane ① 12.10. What next? ② 12.11. Key terms that I’ve discovered 12.12. Smart Alex’s tasks 12.13. Further reading 13 Factorial ANOVA (GLM 3) 13.1. What will this chapter tell me? ② 13.2. Theory of factorial ANOVA (independent designs) ② 13.2.1. Factorial designs ② 13.2.2. Guess what? Factorial ANOVA is a linear model ③ 13.2.3. Two-way ANOVA: behind the scenes ② 13.2.4. Total sums of squares (SST)② 13.2.5. Model sum of squares, SSM② 13.2.6. The residual sum of squares, SSR② 13.2.7. The F-ratios ② 13.3. Assumptions of factorial ANOVA ③ 13.4. Factorial ANOVA using SPSS ② 13.4.1. General procedure for factorial ANOVA ① 13.4.2. Entering the data and accessing the main dialog box ② 13.4.3. Graphing interactions ② 13.4.4. Contrasts ② 13.4.5. Post hoc tests ② 13.4.6. Bootstrapping and other options ② 13.5. Output from factorial ANOVA ② 13.5.1. Levene’s test ② 13.5.2. The main ANOVA table ② 13.5.3. Contrasts ② 13.5.4. Simple effects analysis ③ 13.5.5. Post hoc analysis ② 13.6. Interpreting interaction graphs ② 13.7. Calculating effect sizes ③ 13.8. Reporting the results of two-way ANOVA ② 13.9. Brian’s attempt to woo Jane ① 13.10. What next? ② 13.11. Key terms that I’ve discovered 13.12. Smart Alex’s tasks