Psychology Statistics For Dummies®
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Table of Contents
About This BookWhat You’re Not to ReadFoolish AssumptionsHow this Book is OrganisedIcons Used in This BookWhere to Go from Here
Chapter 1: Statistics? I Thought This Was Psychology!Know Your VariablesWhat is SPSS?Descriptive StatisticsCentral tendencyDispersionGraphsStandardised scoresInferential StatisticsHypothesesParametric and non-parametric variablesResearch DesignsCorrelational designExperimental designIndependent groups designRepeated measures designGetting StartedChapter 2: What Type of Data Are We Dealing With?Understanding Discrete and Continuous VariablesLooking at Levels of MeasurementMeasurement propertiesTypes of measurement levelDetermining the Role of VariablesIndependent variablesDependent variablesCovariatesChapter 3: Inputting Data, Labelling and Coding in SPSSVariable View WindowCreating variable namesDeciding on variable typeDisplaying the data: The width, decimals, columns and align headingsUsing labelsUsing valuesDealing with missing dataAssigning the level of measurementData View WindowEntering new dataCreating new variablesSorting casesRecoding variablesOutput WindowUsing the output windowSaving your outputChapter 4: Measures of Central TendencyDefining Central TendencyThe ModeDetermining the modeKnowing the advantages and disadvantages of using the modeObtaining the mode in SPSSThe MedianDetermining the medianKnowing the advantages and disadvantages to using the medianObtaining the median in SPSSThe MeanDetermining the meanKnowing the advantages and disadvantages to using the meanObtaining the mean in SPSSChoosing between the Mode, Median and MeanChapter 5: Measures of DispersionDefining DispersionThe RangeDetermining the rangeKnowing the advantages and disadvantages of using the rangeObtaining the range in SPSSThe Interquartile RangeDetermining the interquartile rangeKnowing the advantages and disadvantages of using the interquartile rangeObtaining the interquartile range in SPSSThe Standard DeviationDefining the standard deviationKnowing the advantages and disadvantages of using the standard deviationObtaining the standard deviation in SPSSChoosing between the Range, Interquartile Range and Standard DeviationChapter 6: Generating Graphs and ChartsThe HistogramUnderstanding the histogramObtaining a histogram in SPSSThe Bar ChartUnderstanding the bar chartObtaining a bar chart in SPSSThe Pie ChartUnderstanding the pie chartObtaining a pie chart in SPSSThe Box and Whisker PlotUnderstanding the box and whisker plotObtaining a box and whisker plot in SPSS
Chapter 7: Understanding Probability and InferenceExamining Statistical InferenceLooking at the population and the sampleKnowing the limitations of descriptive statisticsAiming to be 95 per cent confidentMaking Sense of ProbabilityDefining probabilityConsidering mutually exclusive and independent eventsUnderstanding conditional probabilityKnowing about oddsChapter 8: Testing HypothesesUnderstanding Null and Alternative HypothesesTesting the null hypothesisDefining the alternative hypothesisDeciding whether to accept or reject the null hypothesisTaking On Board Statistical Inference ErrorsKnowing about the Type I errorConsidering the Type II errorGetting it right sometimesLooking at One- and Two-Tailed HypothesesUsing a one-tailed hypothesisApplying a two-tailed hypothesisConfidence IntervalsDefining a 95 per cent confidence intervalCalculating a 95 per cent confidence intervalObtaining a 95 per cent confidence interval in SPSSChapter 9: What’s Normal about the Normal Distribution?Understanding the Normal DistributionDefining the normal distributionDetermining whether a distribution is approximately normalDetermining SkewnessDefining skewnessAssessing skewness graphicallyObtaining the skewness statistic in SPSSLooking at the Normal Distribution and Inferential StatisticsMaking inferences about individual scoresConsidering the sampling distributionMaking inferences about group scoresChapter 10: Standardised ScoresKnowing the Basics of Standardised ScoresDefining standardised scoresCalculating standardised scoresUsing Z Scores in Statistical AnalysesConnecting Z scores and the normal distributionUsing Z scores in inferential statisticsChapter 11: Effect Sizes and PowerDistinguishing between Effect Size and Statistical SignificanceExploring Effect Size for CorrelationsConsidering Effect Size When Comparing Differences Between Two Sets of ScoresObtaining an effect size for comparing differences between two sets of scoresInterpreting an effect size for differences between two sets of scoresLooking at Effect Size When Comparing Differences between More Than Two Sets of ScoresObtaining an effect size for comparing differences between more than two sets of scoresInterpreting an effect size for differences between more than two sets of scoresUnderstanding Statistical PowerSeeing which factors influence powerConsidering power and sample size
Chapter 12: CorrelationsUsing Scatterplots to Assess RelationshipsInspecting a scatterplotDrawing a scatterplot in SPSSUnderstanding the Correlation CoefficientExamining Shared VarianceUsing Pearson’s CorrelationKnowing when to use Pearson’s correlationPerforming Pearson’s correlation in SPSSInterpreting the outputWriting up the resultsUsing Spearman’s CorrelationKnowing when to use Spearman’s correlationPerforming Spearman’s correlation in SPSSInterpreting the outputWriting up the resultsUsing Kendall’s CorrelationPerforming Kendall’s correlation in SPSSInterpreting the outputWriting up the resultsUsing Partial CorrelationPerforming partial correlation in SPSSInterpreting the outputWriting up the resultsChapter 13: Linear RegressionGetting to Grips with the Basics of RegressionAdding a regression lineWorking out residualsUsing the regression equationUsing Simple RegressionPerforming simple regression in SPSSInterpreting the outputWriting up the resultsWorking with Multiple Variables: Multiple RegressionPerforming multiple regression in SPSSInterpreting the outputWriting up the resultsChecking Assumptions of RegressionNormally distributed residualsLinearityOutliersMulticollinearityHomoscedasticityType of dataChapter 14: Associations between Discrete VariablesSummarising Results in a Contingency TableObserved frequencies in contingency tablesPercentaging a contingency tableObtaining contingency tables in SPSSCalculating Chi-SquareExpected frequenciesCalculating chi-squareObtaining chi-square in SPSSInterpreting the output from chi-square in SPSSWriting up the results of a chi-square analysisUnderstanding the assumptions of chi-square analysisMeasuring the Strength of Association between Two VariablesLooking at the odds ratioPhi and Cramer’s V CoefficientsObtaining odds ratio, phi coefficient and Cramer’s V in SPSSUsing the McNemar TestCalculating the McNemar testObtaining a McNemar test in SPSS
Chapter 15: Independent t-tests and Mann–Whitney TestsUnderstanding Independent Groups DesignThe Independent t-testPerforming the independent t-test in SPSSInterpreting the outputWriting up the resultsConsidering assumptionsMann–Whitney testPerforming the Mann–Whitney test in SPSSInterpreting the outputWriting up the resultsConsidering assumptionsChapter 16: Between-Groups ANOVAOne-Way Between-Groups ANOVASeeing how ANOVA worksCalculating a one-way between-groups ANOVAObtaining a one-way between-groups ANOVA in SPSSInterpreting the SPSS output for a one-way between-groups ANOVAWriting up the results of a one-way between-groups ANOVAConsidering assumptions of a one-way between-groups ANOVATwo-Way Between-Groups ANOVAUnderstanding main effects and interactionsObtaining a two-way between-groups ANOVA in SPSSInterpreting the SPSS output for a two-way between-groups ANOVAWriting up the results of a two-way between-groups ANOVAConsidering assumptions of a two-way between-groups ANOVAKruskal–Wallis TestObtaining a Kruskal–Wallis test in SPSSInterpreting the SPSS output for a Kruskal–Wallis testWriting up the results of a Kruskal–Wallis testConsidering assumptions of a Kruskal–Wallis testChapter 17: Post Hoc Tests and Planned Comparisons for Independent Groups DesignsPost Hoc Tests for Independent Groups DesignsMultiplicityChoosing a post hoc testObtaining a Tukey HSD post hoc test in SPSSInterpreting the SPSS output for a Tukey HSD post hoc testWriting up the results of a post hoc Tukey HSD testPlanned Comparisons for Independent Groups DesignsChoosing a planned comparisonObtaining a Dunnett test in SPSSInterpreting the SPSS output for a Dunnett testWriting up the results of a Dunnett test
Chapter 18: Paired t-tests and Wilcoxon TestsUnderstanding Repeated Measures DesignPaired t-testPerforming a paired t-test in SPSSInterpreting the outputWriting up the resultsAssumptionsThe Wilcoxon TestPerforming the Wilcoxon test in SPSSInterpreting the outputWriting up the resultsChapter 19: Within-Groups ANOVAOne-Way Within-Groups ANOVAKnowing how ANOVA worksThe exampleObtaining a one-way within-groups ANOVA in SPSSInterpreting the SPSS output for a one-way within-groups ANOVAWriting up the results of a one-way within-groups ANOVAAssumptions of a one-way within-groups ANOVATwo-Way Within-Groups ANOVAMain effects and interactionsObtaining a two-way within-groups ANOVA in SPSSInterpreting the SPSS output for a two-way within-groups ANOVAInterpreting the interaction plot from a two-way within-groups ANOVAWriting up the results of a two-way within-groups ANOVAAssumptions of a two-way within-groups ANOVAThe Friedman TestObtaining a Friedman test in SPSSInterpreting the SPSS output for a Friedman testWriting up the results of a Friedman testAssumptions of the Friedman testChapter 20: Post Hoc Tests and Planned Comparisons for Repeated Measures DesignsWhy do you need to use post hoc tests and planned comparisons?Why should you not use t-tests?What is the difference between post hoc tests and planned comparisons?Post Hoc Tests for Repeated Measures DesignsThe exampleChoosing a post hoc testObtaining a post-hoc test for a within-groups ANOVA in SPSSInterpreting the SPSS output for a post-hoc testWriting up the results of a post hoc testPlanned Comparisons for Within Groups DesignsThe exampleChoosing a planned comparisonObtaining a simple planned contrast in SPSSInterpreting the SPSS output for planned comparison testsWriting up the results of planned contrastsExamining Differences between Conditions: The Bonferroni Correction
Getting to Grips with Mixed ANOVAThe exampleMain Effects and InteractionsPerforming the ANOVA in SPSSInterpreting the SPSS output for a two-way mixed ANOVAWriting up the results of a two-way mixed ANOVAAssumptions
Chapter 22: Ten Pieces of Good Advice for Inferential TestingStatistical Significance Is Not the Same as Practical SignificanceFail to Prepare, Prepare to FailDon’t Go Fishing for a Significant ResultCheck Your AssumptionsMy p Is Bigger Than Your pDifferences and Relationships Are Not Opposing TrendsWhere Did My Post-hoc Tests Go?Categorising Continuous DataBe ConsistentGet Help!Chapter 23: Ten Tips for Writing Your Results SectionReporting the p-valueReporting Other FiguresDon’t Forget About the Descriptive StatisticsDo Not Overuse the MeanReport Effect Sizes and Direction of EffectsThe Case of the Missing ParticipantsBe Careful with Your LanguageBeware Correlations and CausalityMake Sure to Answer Your Own QuestionAdd Some StructureCheat Sheet
Psychology Statistics For Dummies®
Psychology Statistics For Dummies®
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About the Authors
Donncha 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 dumbing 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.
Dedication
From Donncha: For my mother and father. Thank you for everything.
From Martin: For Tom, who joined the world half way through the development of this book and has been a glorious distraction ever since.
Author’s Acknowledgments
From 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 statistical 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 content 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 supported 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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Introduction
We recently collected data from psychology students across 31 universities 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 subject. 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 gruelling. 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 statistics 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 comparable format. This information must be summarised and analysed (after all, pages of numbers aren’t that meaningful) and this allows us to infer conclusions 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.
About This Book
The 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 undergraduate 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 necessarily require any previous knowledge. For example, if you were to look up the technique ‘partial correlation’ you will find a clear, jargon-free explanation 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 statistical 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 experience 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 concentrated on producing a clear and concise guide illustrated with visual aids and practical examples.
What You’re Not to Read
We 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.
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 Assumptions
Rightly 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 understanding 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 Organised
This 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.
Part II of the book focuses on some of the concepts which are fundamental for an understanding of statistics. If you don’t know the difference 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 examine relationships or associations between variables, including correlations, regression and tests for categorical data. We explain each technique clearly – what it is used for and when you should use it, followed 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 differences 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 Book
As with all For Dummies books, you will notice icons in the margin that signify 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.
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 Here
You 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!
Part I
Describing Data
In this part . . .
We 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.