# Psychology Statistics For Dummies®

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Introduction
Foolish Assumptions
How this Book is Organised
Icons Used in This Book
Where to Go from Here
Part I: Describing Data
Chapter 1: Statistics? I Thought This Was Psychology!
What is SPSS?
Descriptive Statistics
Central tendency
Dispersion
Graphs
Standardised scores
Inferential Statistics
Hypotheses
Parametric and non-parametric variables
Research Designs
Correlational design
Experimental design
Independent groups design
Repeated measures design
Getting Started
Chapter 2: What Type of Data Are We Dealing With?
Understanding Discrete and Continuous Variables
Looking at Levels of Measurement
Measurement properties
Types of measurement level
Determining the Role of Variables
Independent variables
Dependent variables
Covariates
Chapter 3: Inputting Data, Labelling and Coding in SPSS
Variable View Window
Creating variable names
Deciding on variable type
Displaying the data: The width, decimals, columns and align headings
Using labels
Using values
Dealing with missing data
Assigning the level of measurement
Data View Window
Entering new data
Creating new variables
Sorting cases
Recoding variables
Output Window
Using the output window
Chapter 4: Measures of Central Tendency
Defining Central Tendency
The Mode
Determining the mode
Obtaining the mode in SPSS
The Median
Determining the median
Obtaining the median in SPSS
The Mean
Determining the mean
Obtaining the mean in SPSS
Choosing between the Mode, Median and Mean
Chapter 5: Measures of Dispersion
Defining Dispersion
The Range
Determining the range
Obtaining the range in SPSS
The Interquartile Range
Determining the interquartile range
Obtaining the interquartile range in SPSS
The Standard Deviation
Defining the standard deviation
Obtaining the standard deviation in SPSS
Choosing between the Range, Interquartile Range and Standard Deviation
Chapter 6: Generating Graphs and Charts
The Histogram
Understanding the histogram
Obtaining a histogram in SPSS
The Bar Chart
Understanding the bar chart
Obtaining a bar chart in SPSS
The Pie Chart
Understanding the pie chart
Obtaining a pie chart in SPSS
The Box and Whisker Plot
Understanding the box and whisker plot
Obtaining a box and whisker plot in SPSS
Part II: Statistical Significance
Chapter 7: Understanding Probability and Inference
Examining Statistical Inference
Looking at the population and the sample
Knowing the limitations of descriptive statistics
Aiming to be 95 per cent confident
Making Sense of Probability
Defining probability
Considering mutually exclusive and independent events
Understanding conditional probability
Chapter 8: Testing Hypotheses
Understanding Null and Alternative Hypotheses
Testing the null hypothesis
Defining the alternative hypothesis
Deciding whether to accept or reject the null hypothesis
Taking On Board Statistical Inference Errors
Knowing about the Type I error
Considering the Type II error
Getting it right sometimes
Looking at One- and Two-Tailed Hypotheses
Using a one-tailed hypothesis
Applying a two-tailed hypothesis
Confidence Intervals
Defining a 95 per cent confidence interval
Calculating a 95 per cent confidence interval
Obtaining a 95 per cent confidence interval in SPSS
Chapter 9: What’s Normal about the Normal Distribution?
Understanding the Normal Distribution
Defining the normal distribution
Determining whether a distribution is approximately normal
Determining Skewness
Defining skewness
Assessing skewness graphically
Obtaining the skewness statistic in SPSS
Looking at the Normal Distribution and Inferential Statistics
Considering the sampling distribution
Chapter 10: Standardised Scores
Knowing the Basics of Standardised Scores
Defining standardised scores
Calculating standardised scores
Using Z Scores in Statistical Analyses
Connecting Z scores and the normal distribution
Using Z scores in inferential statistics
Chapter 11: Effect Sizes and Power
Distinguishing between Effect Size and Statistical Significance
Exploring Effect Size for Correlations
Considering Effect Size When Comparing Differences Between Two Sets of Scores
Obtaining an effect size for comparing differences between two sets of scores
Interpreting an effect size for differences between two sets of scores
Looking at Effect Size When Comparing Differences between More Than Two Sets of Scores
Obtaining an effect size for comparing differences between more than two sets of scores
Interpreting an effect size for differences between more than two sets of scores
Understanding Statistical Power
Seeing which factors influence power
Considering power and sample size
Part III: Relationships between Variables
Chapter 12: Correlations
Using Scatterplots to Assess Relationships
Inspecting a scatterplot
Drawing a scatterplot in SPSS
Understanding the Correlation Coefficient
Examining Shared Variance
Using Pearson’s Correlation
Knowing when to use Pearson’s correlation
Performing Pearson’s correlation in SPSS
Interpreting the output
Writing up the results
Using Spearman’s Correlation
Knowing when to use Spearman’s correlation
Performing Spearman’s correlation in SPSS
Interpreting the output
Writing up the results
Using Kendall’s Correlation
Performing Kendall’s correlation in SPSS
Interpreting the output
Writing up the results
Using Partial Correlation
Performing partial correlation in SPSS
Interpreting the output
Writing up the results
Chapter 13: Linear Regression
Getting to Grips with the Basics of Regression
Working out residuals
Using the regression equation
Using Simple Regression
Performing simple regression in SPSS
Interpreting the output
Writing up the results
Working with Multiple Variables: Multiple Regression
Performing multiple regression in SPSS
Interpreting the output
Writing up the results
Checking Assumptions of Regression
Normally distributed residuals
Linearity
Outliers
Multicollinearity
Homoscedasticity
Type of data
Chapter 14: Associations between Discrete Variables
Summarising Results in a Contingency Table
Observed frequencies in contingency tables
Percentaging a contingency table
Obtaining contingency tables in SPSS
Calculating Chi-Square
Expected frequencies
Calculating chi-square
Obtaining chi-square in SPSS
Interpreting the output from chi-square in SPSS
Writing up the results of a chi-square analysis
Understanding the assumptions of chi-square analysis
Measuring the Strength of Association between Two Variables
Looking at the odds ratio
Phi and Cramer’s V Coefficients
Obtaining odds ratio, phi coefficient and Cramer’s V in SPSS
Using the McNemar Test
Calculating the McNemar test
Obtaining a McNemar test in SPSS
Part IV: Analysing Independent Groups Research Designs
Chapter 15: Independent t-tests and Mann–Whitney Tests
Understanding Independent Groups Design
The Independent t-test
Performing the independent t-test in SPSS
Interpreting the output
Writing up the results
Considering assumptions
Mann–Whitney test
Performing the Mann–Whitney test in SPSS
Interpreting the output
Writing up the results
Considering assumptions
Chapter 16: Between-Groups ANOVA
One-Way Between-Groups ANOVA
Seeing how ANOVA works
Calculating a one-way between-groups ANOVA
Obtaining a one-way between-groups ANOVA in SPSS
Interpreting the SPSS output for a one-way between-groups ANOVA
Writing up the results of a one-way between-groups ANOVA
Considering assumptions of a one-way between-groups ANOVA
Two-Way Between-Groups ANOVA
Understanding main effects and interactions
Obtaining a two-way between-groups ANOVA in SPSS
Interpreting the SPSS output for a two-way between-groups ANOVA
Writing up the results of a two-way between-groups ANOVA
Considering assumptions of a two-way between-groups ANOVA
Kruskal–Wallis Test
Obtaining a Kruskal–Wallis test in SPSS
Interpreting the SPSS output for a Kruskal–Wallis test
Writing up the results of a Kruskal–Wallis test
Considering assumptions of a Kruskal–Wallis test
Chapter 17: Post Hoc Tests and Planned Comparisons for Independent Groups Designs
Post Hoc Tests for Independent Groups Designs
Multiplicity
Choosing a post hoc test
Obtaining a Tukey HSD post hoc test in SPSS
Interpreting the SPSS output for a Tukey HSD post hoc test
Writing up the results of a post hoc Tukey HSD test
Planned Comparisons for Independent Groups Designs
Choosing a planned comparison
Obtaining a Dunnett test in SPSS
Interpreting the SPSS output for a Dunnett test
Writing up the results of a Dunnett test
Part V: Analysing Repeated Measures Research Designs
Chapter 18: Paired t-tests and Wilcoxon Tests
Understanding Repeated Measures Design
Paired t-test
Performing a paired t-test in SPSS
Interpreting the output
Writing up the results
Assumptions
The Wilcoxon Test
Performing the Wilcoxon test in SPSS
Interpreting the output
Writing up the results
Chapter 19: Within-Groups ANOVA
One-Way Within-Groups ANOVA
Knowing how ANOVA works
The example
Obtaining a one-way within-groups ANOVA in SPSS
Interpreting the SPSS output for a one-way within-groups ANOVA
Writing up the results of a one-way within-groups ANOVA
Assumptions of a one-way within-groups ANOVA
Two-Way Within-Groups ANOVA
Main effects and interactions
Obtaining a two-way within-groups ANOVA in SPSS
Interpreting the SPSS output for a two-way within-groups ANOVA
Interpreting the interaction plot from a two-way within-groups ANOVA
Writing up the results of a two-way within-groups ANOVA
Assumptions of a two-way within-groups ANOVA
The Friedman Test
Obtaining a Friedman test in SPSS
Interpreting the SPSS output for a Friedman test
Writing up the results of a Friedman test
Assumptions of the Friedman test
Chapter 20: Post Hoc Tests and Planned Comparisons for Repeated Measures Designs
Why 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 Designs
The example
Choosing a post hoc test
Obtaining a post-hoc test for a within-groups ANOVA in SPSS
Interpreting the SPSS output for a post-hoc test
Writing up the results of a post hoc test
Planned Comparisons for Within Groups Designs
The example
Choosing a planned comparison
Obtaining a simple planned contrast in SPSS
Interpreting the SPSS output for planned comparison tests
Writing up the results of planned contrasts
Examining Differences between Conditions: The Bonferroni Correction
Chapter 21: Mixed ANOVA
Getting to Grips with Mixed ANOVA
The example
Main Effects and Interactions
Performing the ANOVA in SPSS
Interpreting the SPSS output for a two-way mixed ANOVA
Writing up the results of a two-way mixed ANOVA
Assumptions
Part VI: The Part of Tens
Chapter 22: Ten Pieces of Good Advice for Inferential Testing
Statistical Significance Is Not the Same as Practical Significance
Fail to Prepare, Prepare to Fail
Don’t Go Fishing for a Significant Result
My p Is Bigger Than Your p
Differences and Relationships Are Not Opposing Trends
Where Did My Post-hoc Tests Go?
Categorising Continuous Data
Be Consistent
Get Help!
Chapter 23: Ten Tips for Writing Your Results Section
Reporting the p-value
Reporting Other Figures
Don’t Forget About the Descriptive Statistics
Do Not Overuse the Mean
Report Effect Sizes and Direction of Effects
The Case of the Missing Participants
Beware Correlations and Causality
Cheat Sheet

Psychology Statistics For Dummies®

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.

Publisher’s Acknowledgments

Some of the people who helped bring this book to market include the following:

Acquisitions, Editorial, and Vertical Websites

Project Editor: Simon Bell

Commissioning Editor: Mike Baker

Assistant Editor: Ben Kemble

Development Editor: Charlie Wilson

Copy Editor: Mary White

Technical Editor: Alix Godfrey

Production Manager: Daniel Mersey

Publisher: David Palmer

Cover Photos: © iStock / Blackie

Cartoons: Ed McLachlan

Composition Services

Project Coordinator: Kristie Rees

Layout and Graphics: Carrie A. Cesavice, Joyce Haughey, Christin Swinford

Indexer: Potomac Indexing, LLC

Publishing and Editorial for Consumer Dummies

Kathleen Nebenhaus, Vice President and Executive Publisher

Kristin Ferguson-Wagstaffe, Product Development Director

Ensley Eikenburg, Associate Publisher, Travel

Kelly Regan, Editorial Director, Travel

Publishing for Technology Dummies

Andy Cummings, Vice President and Publisher

Composition Services

Debbie Stailey, Director of Composition Services

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.

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.

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.