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by Donncha Hanna and Martin Dempster
Psychology Statistics
FOR DUMmIES
‰
Psychology Statistics For Dummies®
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About the AuthorsDonncha hanna is, among other more interesting things, a lecturer at the School of Psychology, Queen’s University Belfast.
He has been teaching statistics to undergraduate students, postgraduate students and real professional people for over 10 years (he is not as old as Martin). His research focuses on mental health and the reasons why students do not like statistics; these topics are not necessarily related. He attempts to teach statistics in an accessible and easy to understand way without dumb-ing down the content; maybe one day he will succeed.
Donncha lives in Belfast with two fruit bats, a hedgehog and a human named Pamela.
martin Dempster is a Senior Lecturer in the School of Psychology, Queen’s University Belfast. He is a Health Psychologist and Chartered Statistician who has also authored A Research Guide for Health & Clinical Psychology.
He has been teaching statistics to undergraduate psychology students for over 20 years. As a psychologist he is interested in the adverse reaction that psychology students often have to learning statistics and endeavours to work out what causes this (hopefully not him) and how it can be alleviated. He tries to teach statistics in an accessible manner (which isn’t always easy).
Martin lives in Whitehead, a seaside village in Co. Antrim, Northern Ireland, which isn’t very well-known, which is why he lives there.
DedicationFrom Donncha: For my mother and father. Thank you for everything.
From martin: For Tom, who joined the world half way through the develop-ment of this book and has been a glorious distraction ever since.
Author’s AcknowledgmentsFrom Donncha: I’m very grateful to the team at Dummies Towers for their work and guidance in getting this book to print – particularly our editors Simon Bell and Mike Baker.
I would like to thank all the students, colleagues and teachers who have helped shape my thinking and knowledge about statistics (and apologise if I have stolen any of their ideas!). I must also acknowledge Pamela (who didn’t complain when I used the excuse of writing this book to avoid doing the dishes) and my sister, Aideen, who offered practical help as always. Thanks to my friend and colleague Martin Dorahy who put up with me in New Zealand where half of this book was written. And of course to Martin Dempster, without whom there would be no book.
From martin: This book is the product of at least 20 years of interaction with colleagues and students; picking up their ideas; answering their questions; and being stimulated into thinking about different ways of explaining statisti-cal concepts. Therefore, there are many people to thank – too many too list and certainly too many for me to remember (any more).
However, there are a few people who made contributions to the actual con-tent of this book. My brother, Bob, who has a much better sense of humour than me, helped with some of the examples in the book. Noleen helped me to better formulate my thinking when I was having some difficulty and sup-ported my decision to undertake this project in the first place. My mum and dad spurred me on with their ever-present encouragement. Finally, thanks to my colleague Donncha, who floated the idea of writing this book and asked me to collaborate with him on its development.
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Contents at a GlanceIntroduction ................................................................ 1
Part I: Describing Data ................................................ 7Chapter 1: Statistics? I Thought This Was Psychology! ................................................ 9Chapter 2: What Type of Data Are We Dealing With? ................................................. 19Chapter 3: Inputting Data, Labelling and Coding in SPSS ........................................... 27Chapter 4: Measures of Central Tendency ................................................................... 53Chapter 5: Measures of Dispersion ............................................................................... 73Chapter 6: Generating Graphs and Charts ................................................................... 91
Part II: Statistical Significance ................................. 111Chapter 7: Understanding Probability and Inference ............................................... 113Chapter 8: Testing Hypotheses .................................................................................... 123Chapter 9: What’s Normal about the Normal Distribution? ..................................... 139Chapter 10: Standardised Scores ................................................................................. 155Chapter 11: Effect Sizes and Power ............................................................................. 165
Part III: Relationships between Variables .................. 183Chapter 12: Correlations ............................................................................................... 185Chapter 13: Linear Regression ..................................................................................... 211Chapter 14: Associations Between Discrete Variables ............................................. 243
Part IV: Analysing Independent Groups Research Designs .......................................... 265Chapter 15: Independent t-tests and Mann-Whitney Tests ...................................... 267Chapter 16: Between-Groups ANOVA ......................................................................... 285Chapter 17: Post Hoc Tests and Planned Comparisons
for Independent Groups Designs ............................................................................... 313
Part V: Analysing Repeated Measures Research Designs ..................................................... 327Chapter 18: Paired t-tests and Wilcoxon Tests .......................................................... 329Chapter 19: Within-Groups ANOVA ............................................................................. 347Chapter 20: Post Hoc Tests and Planned Comparisons
for Repeated Measures Designs ................................................................................ 379Chapter 21: Mixed ANOVA ............................................................................................ 395
Part VI: The Part of Tens .......................................... 415Chapter 22: Ten Pieces of Good Advice For Inferential Testing .............................. 417Chapter 23: Ten Tips for Writing Your Results Section ............................................ 421
Index ...................................................................... 425
Table of ContentsIntroduction ................................................................. 1
About This Book .............................................................................................. 2What You’re Not to Read ................................................................................ 2Foolish Assumptions ....................................................................................... 3How this Book is Organised ........................................................................... 3Icons Used in This Book ................................................................................. 4Where to Go from Here ................................................................................... 5
Part I: Describing Data ................................................. 7
Chapter 1: Statistics? I Thought This Was Psychology! . . . . . . . . . . . . .9Know Your Variables .................................................................................... 10What is SPSS? ................................................................................................. 11Descriptive Statistics .................................................................................... 12
Central tendency .................................................................................. 12Dispersion ............................................................................................. 12Graphs ................................................................................................... 13Standardised scores ............................................................................ 13
Inferential Statistics ....................................................................................... 13Hypotheses ........................................................................................... 14Parametric and non-parametric variables ........................................ 14
Research Designs ........................................................................................... 15Correlational design ............................................................................ 15Experimental design ............................................................................ 16Independent groups design ................................................................ 16Repeated measures design ................................................................. 17
Getting Started ............................................................................................... 18
Chapter 2: What Type of Data Are We Dealing With? . . . . . . . . . . . . . .19Understanding Discrete and Continuous Variables .................................. 20Looking at Levels of Measurement .............................................................. 21
Measurement properties .................................................................... 21Types of measurement level .............................................................. 23
Determining the Role of Variables ............................................................... 24Independent variables ......................................................................... 25Dependent variables ............................................................................ 25Covariates ............................................................................................. 26
Psychology Statistics For Dummies xChapter 3: Inputting Data, Labelling and Coding in SPSS . . . . . . . . . .27
Variable View Window .................................................................................. 28Creating variable names ..................................................................... 29Deciding on variable type ................................................................... 30Displaying the data: The width, decimals,
columns and align headings .......................................................... 32Using labels ........................................................................................... 33Using values .......................................................................................... 34Dealing with missing data ................................................................... 36Assigning the level of measurement .................................................. 37
Data View Window ......................................................................................... 39Entering new data ................................................................................ 40Creating new variables ........................................................................ 42Sorting cases ........................................................................................ 43Recoding variables .............................................................................. 45
Output Window .............................................................................................. 48Using the output window .................................................................... 48Saving your output .............................................................................. 51
Chapter 4: Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . .53Defining Central Tendency ........................................................................... 54The Mode ........................................................................................................ 55
Determining the mode ......................................................................... 55Knowing the advantages and disadvantages
of using the mode ............................................................................. 58Obtaining the mode in SPSS ............................................................... 59
The Median ..................................................................................................... 64Determining the median...................................................................... 64Knowing the advantages and disadvantages
to using the median ......................................................................... 66Obtaining the median in SPSS ............................................................ 67
The Mean ........................................................................................................ 68Determining the mean ......................................................................... 68Knowing the advantages and disadvantages
to using the mean ............................................................................. 69Obtaining the mean in SPSS ................................................................ 69
Choosing between the Mode, Median and Mean ....................................... 71
Chapter 5: Measures of Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73Defining Dispersion ....................................................................................... 73The Range ....................................................................................................... 74
Determining the range ......................................................................... 74Knowing the advantages and disadvantages
of using the range ............................................................................. 75Obtaining the range in SPSS ............................................................... 76
xi Table of Contents
The Interquartile Range ................................................................................ 78Determining the interquartile range .................................................. 78Knowing the advantages and disadvantages
of using the interquartile range ...................................................... 81Obtaining the interquartile range in SPSS ........................................ 82
The Standard Deviation ................................................................................ 83Defining the standard deviation ......................................................... 83Knowing the advantages and disadvantages
of using the standard deviation ..................................................... 87Obtaining the standard deviation in SPSS ........................................ 87
Choosing between the Range, Interquartile Range and Standard Deviation ..................................................................................................... 89
Chapter 6: Generating Graphs and Charts . . . . . . . . . . . . . . . . . . . . . . . .91The Histogram ............................................................................................... 91
Understanding the histogram ............................................................ 92Obtaining a histogram in SPSS ........................................................... 96
The Bar Chart ................................................................................................. 98Understanding the bar chart .............................................................. 98Obtaining a bar chart in SPSS ........................................................... 100
The Pie Chart ............................................................................................... 101Understanding the pie chart ............................................................ 101Obtaining a pie chart in SPSS ........................................................... 103
The Box and Whisker Plot .......................................................................... 103Understanding the box and whisker plot ....................................... 104Obtaining a box and whisker plot in SPSS ...................................... 107
Part II: Statistical Significance ................................. 111
Chapter 7: Understanding Probability and Inference . . . . . . . . . . . . .113Examining Statistical Inference .................................................................. 113
Looking at the population and the sample .................................... 114Knowing the limitations of descriptive statistics .......................... 115Aiming to be 95 per cent confident ................................................. 116
Making Sense of Probability ....................................................................... 117Defining probability ........................................................................... 118Considering mutually exclusive and independent events ............ 118Understanding conditional probability........................................... 121Knowing about odds .......................................................................... 122
Chapter 8: Testing Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123Understanding Null and Alternative Hypotheses .................................... 123
Testing the null hypothesis .............................................................. 124Defining the alternative hypothesis ................................................ 124Deciding whether to accept or reject the null hypothesis ........... 125
Psychology Statistics For Dummies xiiTaking On Board Statistical Inference Errors .......................................... 127
Knowing about the Type I error ....................................................... 128Considering the Type II error ........................................................... 128Getting it right sometimes ............................................................... 129
Looking at One- and Two-Tailed Hypotheses .......................................... 130Using a one-tailed hypothesis .......................................................... 131Applying a two-tailed hypothesis .................................................... 131
Confidence Intervals ................................................................................... 132Defining a 95 per cent confidence interval ..................................... 132Calculating a 95 per cent confidence interval ................................ 133Obtaining a 95 per cent confidence interval in SPSS ..................... 135
Chapter 9: What’s Normal about the Normal Distribution? . . . . . . . .139Understanding the Normal Distribution ................................................... 140
Defining the normal distribution ..................................................... 140Determining whether a distribution is approximately normal .... 141
Determining Skewness ................................................................................ 144Defining skewness .............................................................................. 144Assessing skewness graphically ...................................................... 145Obtaining the skewness statistic in SPSS........................................ 147
Looking at the Normal Distribution and Inferential Statistics ............... 150Making inferences about individual scores .................................... 151Considering the sampling distribution ........................................... 152Making inferences about group scores ........................................... 153
Chapter 10: Standardised Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155Knowing the Basics of Standardised Scores ............................................ 155
Defining standardised scores ........................................................... 156Calculating standardised scores ...................................................... 156
Using Z Scores in Statistical Analyses ....................................................... 159Connecting Z scores and the normal distribution ......................... 160Using Z scores in inferential statistics ............................................ 161
Chapter 11: Effect Sizes and Power . . . . . . . . . . . . . . . . . . . . . . . . . . . .165Distinguishing between Effect Size and Statistical Significance ............ 165Exploring Effect Size for Correlations ....................................................... 166Considering Effect Size When Comparing Differences
Between Two Sets of Scores ................................................................... 167Obtaining an effect size for comparing differences
between two sets of scores ........................................................... 167Interpreting an effect size for differences
between two sets of scores ........................................................... 170
xiii Table of Contents
Looking at Effect Size When Comparing Differences between More Than Two Sets of Scores ............................................... 171
Obtaining an effect size for comparing differences between more than two sets of scores ........................................ 171
Interpreting an effect size for differences between more than two sets of scores ........................................ 177
Understanding Statistical Power ............................................................... 178Seeing which factors influence power............................................. 179Considering power and sample size ................................................ 180
Part III: Relationships between Variables ................... 183
Chapter 12: Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185Using Scatterplots to Assess Relationships ............................................. 185
Inspecting a scatterplot .................................................................... 186Drawing a scatterplot in SPSS .......................................................... 189
Understanding the Correlation Coefficient .............................................. 190Examining Shared Variance ........................................................................ 191Using Pearson’s Correlation ....................................................................... 192
Knowing when to use Pearson’s correlation .................................. 192Performing Pearson’s correlation in SPSS ...................................... 193Interpreting the output ..................................................................... 195Writing up the results........................................................................ 197
Using Spearman’s Correlation ................................................................... 198Knowing when to use Spearman’s correlation............................... 198Performing Spearman’s correlation in SPSS ................................... 199Interpreting the output ..................................................................... 201Writing up the results........................................................................ 201
Using Kendall’s Correlation ........................................................................ 202Performing Kendall’s correlation in SPSS ....................................... 203Interpreting the output ..................................................................... 204Writing up the results........................................................................ 205
Using Partial Correlation ............................................................................ 206Performing partial correlation in SPSS ........................................... 206Interpreting the output ..................................................................... 208Writing up the results........................................................................ 208
Chapter 13: Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211Getting to Grips with the Basics of Regression ....................................... 212
Adding a regression line ................................................................... 212Working out residuals ....................................................................... 214Using the regression equation ......................................................... 215
Psychology Statistics For Dummies xivUsing Simple Regression ............................................................................. 217
Performing simple regression in SPSS ............................................ 217Interpreting the output ..................................................................... 218Writing up the results........................................................................ 222
Working with Multiple Variables: Multiple Regression .......................... 223Performing multiple regression in SPSS .......................................... 224Interpreting the output ..................................................................... 225Writing up the results........................................................................ 229
Checking Assumptions of Regression ....................................................... 230Normally distributed residuals ........................................................ 230Linearity .............................................................................................. 232Outliers ................................................................................................ 234Multicollinearity ................................................................................. 238Homoscedasticity .............................................................................. 240Type of data ........................................................................................ 242
Chapter 14: Associations between Discrete Variables . . . . . . . . . . .243Summarising Results in a Contingency Table .......................................... 244
Observed frequencies in contingency tables ................................. 244Percentaging a contingency table .................................................... 245Obtaining contingency tables in SPSS ............................................. 247
Calculating Chi-Square ................................................................................ 249Expected frequencies ........................................................................ 250Calculating chi-square ....................................................................... 251Obtaining chi-square in SPSS............................................................ 252Interpreting the output from chi-square in SPSS ........................... 253Writing up the results of a chi-square analysis .............................. 255Understanding the assumptions of chi-square analysis ............... 256
Measuring the Strength of Association between Two Variables ........... 257Looking at the odds ratio .................................................................. 257Phi and Cramer’s V Coefficients....................................................... 258Obtaining odds ratio, phi coefficient and Cramer’s V in SPSS ..... 259
Using the McNemar Test ............................................................................ 260Calculating the McNemar test .......................................................... 261Obtaining a McNemar test in SPSS .................................................. 262
Part IV: Analysing Independent Groups Research Designs ..................................................... 265
Chapter 15: Independent t- tests and Mann–Whitney Tests . . . . . . . .267Understanding Independent Groups Design ............................................ 268The Independent t-test ................................................................................ 268
Performing the independent t-test in SPSS ..................................... 269Interpreting the output ..................................................................... 272
xv Table of Contents
Writing up the results........................................................................ 275Considering assumptions ................................................................. 275
Mann-Whitney test ...................................................................................... 277Performing the Mann–Whitney test in SPSS ................................... 278Interpreting the output ..................................................................... 280Writing up the results........................................................................ 282Considering assumptions ................................................................. 283
Chapter 16: Between-Groups ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . .285One-Way Between-Groups ANOVA ............................................................ 286
Seeing how ANOVA works ................................................................ 287Calculating a one-way between-groups ANOVA ............................ 288Obtaining a one-way between-groups ANOVA in SPSS ................. 291Interpreting the SPSS output for a one-way
between-groups ANOVA ................................................................ 294Writing up the results of a one-way between-groups ANOVA ..... 296Considering assumptions of a one-way
between-groups ANOVA ................................................................ 296Two-Way Between-Groups ANOVA ........................................................... 298
Understanding main effects and interactions ................................ 299Obtaining a two-way between-groups ANOVA in SPSS ................. 300Interpreting the SPSS output for a two-way
between-groups ANOVA ................................................................ 301Writing up the results of a two-way
between-groups ANOVA ................................................................ 306Considering assumptions of a two-way
between-groups ANOVA ................................................................ 307Kruskal–Wallis Test ..................................................................................... 307
Obtaining a Kruskal–Wallis test in SPSS ......................................... 308Interpreting the SPSS output for a Kruskal–Wallis test................. 310Writing up the results of a Kruskal–Wallis test .............................. 311Considering assumptions of a Kruskal–Wallis test ....................... 311
Chapter 17: Post Hoc Tests and Planned Comparisons for Independent Groups Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313
Post Hoc Tests for Independent Groups Designs .................................... 314Multiplicity .......................................................................................... 315Choosing a post hoc test .................................................................. 316Obtaining a Tukey HSD post hoc test in SPSS ................................ 317Interpreting the SPSS output for a Tukey HSD post hoc test ....... 319Writing up the results of a post hoc Tukey HSD test .................... 322
Planned Comparisons for Independent Groups Designs ........................ 322Choosing a planned comparison ..................................................... 323Obtaining a Dunnett test in SPSS ..................................................... 323Interpreting the SPSS output for a Dunnett test ............................ 324Writing up the results of a Dunnett test ......................................... 326
Psychology Statistics For Dummies xvi
Part V: Analysing Repeated Measures Research Designs ..................................................... 327
Chapter 18: Paired t-tests and Wilcoxon Tests . . . . . . . . . . . . . . . . . .329Understanding Repeated Measures Design ............................................. 329Paired t-test .................................................................................................. 330
Performing a paired t-test in SPSS ................................................... 331Interpreting the output ..................................................................... 333Writing up the results........................................................................ 336Assumptions ....................................................................................... 336
The Wilcoxon Test ....................................................................................... 339Performing the Wilcoxon test in SPSS ............................................. 339Interpreting the output ..................................................................... 342Writing up the results........................................................................ 343
Chapter 19: Within-Groups ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . .347One-Way Within-Groups ANOVA ............................................................... 347
Knowing how ANOVA works ............................................................ 348The example ....................................................................................... 349Obtaining a one-way within-groups ANOVA in SPSS ..................... 353Interpreting the SPSS output for a one-way
within-groups ANOVA .................................................................... 356Writing up the results of a one-way within-groups ANOVA ......... 360Assumptions of a one-way within-groups ANOVA ......................... 360
Two-Way Within-Groups ANOVA ............................................................... 361Main effects and interactions ........................................................... 362Obtaining a two-way within-groups ANOVA in SPSS ..................... 363Interpreting the SPSS output for a two-way
within-groups ANOVA .................................................................... 367Interpreting the interaction plot from a two-way
within-groups ANOVA .................................................................... 371Writing up the results of a two-way within-groups ANOVA ......... 372Assumptions of a two-way within-groups ANOVA......................... 373
The Friedman Test ...................................................................................... 374Obtaining a Friedman test in SPSS ................................................... 375Interpreting the SPSS output for a Friedman test .......................... 376Writing up the results of a Friedman test ....................................... 377Assumptions of the Friedman test ................................................... 378
Chapter 20: Post Hoc Tests and Planned Comparisons for Repeated Measures Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .379
Why do you need to use post hoc tests and planned comparisons? ........................................................... 380
Why should you not use t-tests? ...................................................... 380What is the difference between post hoc tests
and planned comparisons? ........................................................... 381
xvii Table of Contents
Post Hoc Tests for Repeated Measures Designs ..................................... 381The example ....................................................................................... 382Choosing a post hoc test .................................................................. 382Obtaining a post-hoc test for a within-groups ANOVA in SPSS .... 383Interpreting the SPSS output for a post-hoc test ........................... 384Writing up the results of a post hoc test ........................................ 386
Planned Comparisons for Within Groups Designs .................................. 387The example ....................................................................................... 388Choosing a planned comparison ..................................................... 388Obtaining a simple planned contrast in SPSS ................................ 389Interpreting the SPSS output for planned comparison tests........ 391Writing up the results of planned contrasts .................................. 392
Examining Differences between Conditions: The Bonferroni Correction ..................................................................... 393
Chapter 21: Mixed ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .395Getting to Grips with Mixed ANOVA ......................................................... 395
The example ....................................................................................... 396Main Effects and Interactions .................................................................... 397Performing the ANOVA in SPSS ................................................................. 398
Interpreting the SPSS output for a two-way mixed ANOVA .......... 403Writing up the results of a two-way mixed ANOVA ....................... 410Assumptions ....................................................................................... 411
Part VI: The Part of Tens ........................................... 415
Chapter 22: Ten Pieces of Good Advice for Inferential Testing . . . . .417Statistical Significance Is Not the Same as Practical Significance ......... 417Fail to Prepare, Prepare to Fail .................................................................. 418Don’t Go Fishing for a Significant Result .................................................. 418Check Your Assumptions ........................................................................... 418My p Is Bigger Than Your p ........................................................................ 418Differences and Relationships Are Not Opposing Trends ...................... 419Where Did My Post-hoc Tests Go? ............................................................ 419Categorising Continuous Data ................................................................... 419Be Consistent ............................................................................................... 420Get Help! ....................................................................................................... 420
Chapter 23: Ten Tips for Writing Your Results Section . . . . . . . . . . . .421Reporting the p-value .................................................................................. 421Reporting Other Figures ............................................................................. 422Don’t Forget About the Descriptive Statistics ......................................... 422Do Not Overuse the Mean .......................................................................... 422
Psychology Statistics For Dummies xviiiReport Effect Sizes and Direction of Effects ............................................. 423The Case of the Missing Participants ........................................................ 423Be Careful With Your Language ................................................................. 424Beware Correlations and Causality ........................................................... 424Make Sure to Answer Your Own Question ............................................... 424Add Some Structure .................................................................................... 424
Index ....................................................................... 425
Introduction
W e recently collected data from psychology students across 31 univer-sities regarding their attitudes towards statistics; 51 per cent of the
students did not realise statistics would be a substantial component of their course and the majority had negative attitudes or anxiety towards the sub-ject. So if this sounds familiar take comfort in the fact you are not alone!
Let’s get one thing out of the way right now. The statistics component you have to complete for your degree is not impossible and it shouldn’t be gru-elling. If you can cope with cognitive psychology theories and understand psycho-biological models you should have no difficulty. Remember this isn’t mathematics; the computer will run all the complex number crunching for you. This book has been written in a clear and concise manner that will help you through the course. We don’t assume any previous knowledge of statis-tics and in return we ask you relinquish any negative attitudes you may have!
The second point we need to address is why, when you have enrolled for psychology, are you being forced to study statistics? You need to know that statistics is an important and necessary part of all psychology courses. Psychology is an empirical discipline, which means we use evidence to decide between competing theories and approaches. Collecting quantitative information allows us to represent this data in an objective and easily com-parable format. This information must be summarised and analysed (after all, pages of numbers aren’t that meaningful) and this allows us to infer con-clusions and make decisions. Understanding statistics not only allows you to conduct and analyse your own research, but importantly it allows you to read and critically evaluate previous research.
Also, statistics are important in psychology because psychologists use their statistical knowledge in their day-to-day work. Consider a psychologist who is working with clients exhibiting depression, anxiety and self-harm. They must decide which therapy is most useful for particular conditions, whether anxiety is related to (or can predict) self harm, or whether clients who self harm differ in their levels of depression. Statistical knowledge is a crucial tool in any psychologist’s job.
2 Psychology Statistics For Dummies
About This BookThe aim of this book is to provide an easily accessible reference guide, written in plain English, that will allow students to readily understand, carry out, interpret and report all types of statistical procedures required for their course. While we have targeted this book at psychology undergradu-ate students we hope it will be useful to all social science and health science students.
The book is structured in a relatively linear way; starting with the more basic concepts and progressing through to more complex techniques. This is the order in which the statistics component of the psychology degree is normally taught. Note, though, that this doesn’t mean you are expected to start from page one and read the book from cover to cover. Instead each chapter (and each statistical technique) is designed to be self-contained and does not nec-essarily require any previous knowledge. For example, if you were to look up the technique ‘partial correlation’ you will find a clear, jargon-free explana-tion of the technique followed by an example (with step-by-step instructions demonstrating how to perform the technique on SPSS, how to interpret the output and, importantly, how to report the results appropriately). Each sta-tistical procedure in the book follows this same framework enabling you to quickly find the technique of interest, run the required analysis and write it up in an appropriate way.
As we know (both from research we have conducted and subjective experi-ence of teaching courses) statistics tends to be a psychology student’s least favourite subject and causes anxiety in the majority of psychology students. We therefore deliberately steer clear of complex mathematical formulae as well as superfluous and rarely-used techniques. Instead we have concen-trated on producing a clear and concise guide illustrated with visual aids and practical examples.
What You’re Not to ReadWe have deliberately tried to keep our explanations concise but there is still a lot of information contained in this book. Occasionally you will see the technical stuff icon; this, as the icon suggests, contains more technical information which we regard as valuable in understanding the technique but not crucial to conducting the analysis. You can skip these sections and still understand the topic in question.
3 Introduction
Likewise you may come across sidebars where we have elaborated on a topic. We think they are interesting, but we are biased! If you are in a hurry you can skip these sections.
Foolish AssumptionsRightly or wrongly we have made some assumptions when writing this book. We assume that:
✓ You have SPSS installed and you are familiar with using a computer. We do not outline how to install SPSS and we are assuming that you are familiar with using the mouse (pointing, clicking, etc.) and the keyboard to enter or manipulate information. We do not assume that you have used SPSS before; Chapter 3 gives an introduction to this programme and we provide you with step-by-step instructions for each procedure.
✓ You are not a mathematical genius but you do have some basic under-standing of using numbers. If you know what we mean by squaring a number (multiplying a number by itself; if we square 5 we get 25) or taking a square root – the opposite of squaring a number (the square root of a number is that value when squared gives the original number; the square root of 25 is 5) you will be fine. Remember the computer will be doing the calculations for you.
✓ You do not need to conduct complex multivariate statistics. This is an introductory book and we limit out discussion to the type of analyses commonly required by undergraduate syllabuses.
How this Book is OrganisedThis book has been organised into six parts:
✓ Part I of the book deals with describing and summarising data. It starts by explaining, with examples, the types of variables commonly used and level of measurement. These concepts are key in deciding how to treat your data and which statistics are most appropriate to analyse your data. We deal with the SPSS environment, so if you haven’t used SPSS before, or need a refresher, this a good place to start. We also cover the first descriptive statistics: the mean, mode and median. From there we go on to key ideas such as measures of dispersion and interpreting and producing the most commonly used graphs for displaying data.
4 Psychology Statistics For Dummies
✓ Part II of the book focuses on some of the concepts which are funda-mental for an understanding of statistics. If you don’t know the differ-ence between a null and alternative hypothesis, unsure why you have to report the p-value and an effect size or have never really been confident of what statistical inference actually means, then this part of the book is for you!
✓ Part III of the book deals with inferential statistics, the ones that exam-ine relationships or associations between variables, including cor-relations, regression and tests for categorical data. We explain each technique clearly – what it is used for and when you should use it, fol-lowed by instructions on how to perform the analysis in SPSS, how to interpret the subsequent output and how to write up the results in both the correct statistical format and in plain English.
✓ Part IV of the book deals with the inferential statistics that examine dif-ferences between two or more independent groups of data. In particular we address the Independent t-test, Mann-Whitney test and Analysis of Variance (ANOVA). For each technique we offer a clear explanation, show you how it works in SPSS, and how to interpret and write up the results.
✓ Part V of the book deals with the inferential statistics that examine differences between two or more repeated measurements. Here we cover the Paired t-test, the Wilcoxon test and Analysis of Variance (ANOVA). We also focus on analysis of research designs that include both independent groups and repeated measurements: the Mixed ANOVA.
✓ Part VI, the final part of the book, provides you with hints and tips on how to avoid mistakes and write up your results in the most appropriate way. We hope these pointers can save you from the pitfalls often made by inexperienced researchers and can contribute to you producing a better results section. We outline some of the common mistakes and misunderstandings students make when performing statistical analyses and how you can avoid them, and we provide quick and useful tips for writing your results section.
Icons Used in This BookAs with all For Dummies books, you will notice icons in the margin that sig-nify there is something special about that piece of information.
This points out a helpful hint designed to save you time or from thinking harder than you have to.
5 Introduction
This one is important! It indicates a piece of information that you should bear in mind even after the book has been closed.
This icon highlights a common misunderstanding or error that we don’t want you to make.
This contains a more detailed discussion or explanation of a topic; you can skip this material if you are in a rush.
Where to Go from HereYou could read this book cover to cover but we have designed it so you can easily find the topics you are interested in and get the information you want without having to read pages of mathematical formulae or find out what every single option in SPSS does. If you are completely new to this area we suggest you start with Chapter 1. Need some help navigating SPSS for the first time? Turn to Chapter 3. If you are not quite sure what a p-value or an effect size is, you’ll need to refer to Part II of the book. For any of the other techniques we suggest you use the table of contents or index to guide you to the right place.
Remember you can’t make the computer (or your head) explode so, with book in hand, it’s time to start analysing that data!
6 Psychology Statistics For Dummies
Part IDescribing Data
In this part . . .
W e know: you’re studying psychology, not statistics. You’re not a mathematician and never wanted to
be. Never fear, help is near. This part of the book covers the key concepts you need to grasp to describe statistical data accurately and successfully. We talk about the simplest descriptive statistics – mean, mode and median – and important ideas such as measures of dispersion and how to interpret and produce the graphs for displaying data.
We also introduce you to SPSS (Statistical Package for Social Sciences, to give it its full name) and walk you through the basics of using the program to produce straightforward statistics.
Chapter 1
Statistics? I Thought This Was Psychology!
In This Chapter▶ Understanding variables
▶ Introducing SPSS
▶ Outlining descriptive and inferential statistics
▶ Differentiating between parametric and non-parametric statistics
▶ Explaining research designs
W hen we tell our initially fresh-faced and enthusiastic first year students that statistics is a substantial component of their course approxi-
mately half of them are genuinely shocked. ‘We came to study psychology, not statistics’, they shout. Presumably they thought they would be spending the next three years ordering troubled individuals to ‘lie down on the couch and tell me about your mother’. We tell them there is no point running for the exits as they will quickly learn that statistics is part of all undergraduate psychology courses, and that if they plan to undertake post-graduate studies or work in this area they will be using these techniques for a long time to come (besides, we were expecting this reaction and have locked the exits). Then we hear the cry ‘But I’m not a mathematician. I am interested in people and behaviour’. We don’t expect students to be mathematicians. If you have a quick scan through this book you won’t be confronted with pages of scary looking equations. These days we use computer-based software packages such as SPSS to do all the complex calculations for us. We tell them that psychology is a scientific discipline. If they want to learn about people they have to objectively collect information, summarise it and analyse it. Summarising and analysing allows you to interpret the information and give it meaning in terms of theories and real world problems. Summarising and analysing information is statistics; it is a fundamental and integrated component of psychology.
The aim of this chapter is to give you a roadmap of the main statistical con-cepts you will encounter during your undergraduate psychology studies and to signpost you to relevant chapters on topics where you can learn how to become a statistics superhero (or at least scrape by).
10 Part I: Describing Data
Know Your VariablesAll quantitative research in psychology involves collecting information (called data) that can be represented by numbers. For example, levels of depression can be represented by depression scores obtained from a ques-tionnaire, or a person’s gender can be represented by a number (1 for male and 2 for female). The characteristics you are measuring are known as vari-ables because they vary! They can vary over time within the same person (depression scores can vary over a person’s life time) or vary between dif-ferent individuals (individuals can be classified as male or female, but once a person is classified this variable doesn’t tend to change!).
Several names and properties exist, associated with variables in any data set, which you must become familiar with. Variables can be continuous or discrete, have different levels of measurement and can be independent or dependent. We cover all this information in Chapter 2. Initially these terms may seem a little bamboozling, but it is important you ensure you have a good understanding of them, as they dictate the statistical analyses that are available and appropriate for your data. For example, it helps to report a mean depression score of 32.4 for a particular group of participants, but a mean gender score of 1.6 for the same group doesn’t much make sense (we discuss the mean in Chapter 4)!
Variables can be classified as discrete, where you specify discrete categories (for example, male and female), or continuous, where scores can lie any-where along a continuum (for example, depression scores may lie anywhere between 0 and 63 if measured by the Beck Depression Inventory).
Variables also differ in their measurement properties. Four levels of measure-ment exist:
✓ Nominal: This contains the least amount of information of the levels. At the nominal level, a numerical value is applied arbitrarily. Gender is an example of nominal level of measurement (for example, 1 for male and 2 for female), and it makes no sense to say one is greater or less than the other.
✓ Ordinal: Rankings on a class test are an example of an ordinal level of measurement; we can order participants from the highest to the lowest score but we don’t how much better the first person did compared to the second person (it could be 1 mark or it could be 20 marks!).
✓ Interval: IQ scores are measured at the interval level, which means we can order the scores but the difference between each point is equal. That is, the difference between 95 and 100 is the same as the difference between 115 and 120.
