Psychology Statistics for Dummies

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**Introduction 1**

About This Book 2

What You’re Not to Read 2

Foolish Assumptions 3

How this Book is Organised 3

Icons Used in This Book 4

Where to Go from Here 5

**Part I: Describing Data 7**

**Chapter 1: Statistics? I Thought This Was Psychology!
9**

Know Your Variables 10

What is SPSS? 11

Descriptive Statistics 12

Central tendency 12

Dispersion 12

Graphs 13

Standardised scores 13

Inferential Statistics 13

Hypotheses 14

Parametric and non-parametric variables 14

Research Designs 15

Correlational design 15

Experimental design 16

Independent groups design 16

Repeated measures design 17

Getting Started 18

**Chapter 2: What Type of Data Are We Dealing With? 19**

Understanding Discrete and Continuous Variables 20

Looking at Levels of Measurement 21

Measurement properties 21

Types of measurement level 23

Determining the Role of Variables 24

Independent variables 25

Dependent variables 25

Covariates 26

**Chapter 3: Inputting Data, Labelling and Coding in SPSS
27**

Variable View Window 28

Creating variable names 29

Deciding on variable type 30

Displaying the data: The width, decimals, columns and align headings 32

Using labels 33

Using values 34

Dealing with missing data 36

Assigning the level of measurement 37

Data View Window 39

Entering new data 40

Creating new variables 42

Sorting cases 43

Recoding variables 45

Output Window 48

Using the output window 48

Saving your output 51

**Chapter 4: Measures of Central Tendency 53**

Defining Central Tendency 54

The Mode 55

Determining the mode 55

Knowing the advantages and disadvantages of using the mode 58

Obtaining the mode in SPSS 59

The Median 64

Determining the median 64

Knowing the advantages and disadvantages to using the median 66

Obtaining the median in SPSS 67

The Mean 68

Determining the mean 68

Knowing the advantages and disadvantages to using the mean 69

Obtaining the mean in SPSS 69

Choosing between the Mode, Median and Mean 71

**Chapter 5: Measures of Dispersion 73**

Defining Dispersion 73

The Range 74

Determining the range 74

Knowing the advantages and disadvantages of using the range 75

Obtaining the range in SPSS 76

The Interquartile Range 78

Determining the interquartile range 78

Knowing the advantages and disadvantages of using the interquartile range 81

Obtaining the interquartile range in SPSS 82

The Standard Deviation 83

Defining the standard deviation 83

Knowing the advantages and disadvantages of using the standard deviation 87

Obtaining the standard deviation in SPSS 87

Choosing between the Range, Interquartile Range and Standard Deviation 89

**Chapter 6: Generating Graphs and Charts 91**

The Histogram 91

Understanding the histogram 92

Obtaining a histogram in SPSS 96

The Bar Chart 98

Understanding the bar chart 98

Obtaining a bar chart in SPSS 100

The Pie Chart 101

Understanding the pie chart 101

Obtaining a pie chart in SPSS 103

The Box and Whisker Plot 103

Understanding the box and whisker plot 104

Obtaining a box and whisker plot in SPSS 107

**Part II: Statistical Significance 111**

**Chapter 7: Understanding Probability and Inference
113**

Examining Statistical Inference 113

Looking at the population and the sample 114

Knowing the limitations of descriptive statistics 115

Aiming to be 95 per cent confident 116

Making Sense of Probability 117

Defining probability 118

Considering mutually exclusive and independent events 118

Understanding conditional probability 121

Knowing about odds 122

**Chapter 8: Testing Hypotheses 123**

Understanding Null and Alternative Hypotheses 123

Testing the null hypothesis 124

Defining the alternative hypothesis 124

Deciding whether to accept or reject the null hypothesis 125

Taking On Board Statistical Inference Errors 127

Knowing about the Type I error 128

Considering the Type II error 128

Getting it right sometimes 129

Looking at One- and Two-Tailed Hypotheses 130

Using a one-tailed hypothesis 131

Applying a two-tailed hypothesis 131

Confidence Intervals 132

Defining a 95 per cent confidence interval 132

Calculating a 95 per cent confidence interval 133

Obtaining a 95 per cent confidence interval in SPSS 135

**Chapter 9: What’s Normal about the Normal Distribution?
139**

Understanding the Normal Distribution 140

Defining the normal distribution 140

Determining whether a distribution is approximately normal 141

Determining Skewness 144

Defining skewness 144

Assessing skewness graphically 145

Obtaining the skewness statistic in SPSS 147

Looking at the Normal Distribution and Inferential Statistics 150

Making inferences about individual scores 151

Considering the sampling distribution 152

Making inferences about group scores 153

**Chapter 10: Standardised Scores 155**

Knowing the Basics of Standardised Scores 155

Defining standardised scores 156

Calculating standardised scores 156

Using Z Scores in Statistical Analyses 159

Connecting Z scores and the normal distribution 160

Using Z scores in inferential statistics 161

**Chapter 11: Effect Sizes and Power 165**

Distinguishing between Effect Size and Statistical Significance 165

Exploring Effect Size for Correlations 166

Considering Effect Size When Comparing Differences Between Two Sets of Scores 167

Obtaining an effect size for comparing differences between two sets of scores 167

Interpreting an effect size for differences between two sets of scores 170

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 178

Seeing which factors influence power 179

Considering power and sample size 180

**Part III: Relationships between Variables 183**

**Chapter 12: Correlations 185**

Using Scatterplots to Assess Relationships 185

Inspecting a scatterplot 186

Drawing a scatterplot in SPSS 189

Understanding the Correlation Coefficient 190

Examining Shared Variance 191

Using Pearson’s Correlation 192

Knowing when to use Pearson’s correlation 192

Performing Pearson’s correlation in SPSS 193

Interpreting the output 195

Writing up the results 197

Using Spearman’s Correlation 198

Knowing when to use Spearman’s correlation 198

Performing Spearman’s correlation in SPSS 199

Interpreting the output 201

Writing up the results 201

Using Kendall’s Correlation 202

Performing Kendall’s correlation in SPSS 203

Interpreting the output 204

Writing up the results 205

Using Partial Correlation 206

Performing partial correlation in SPSS 206

Interpreting the output 208

Writing up the results 208

**Chapter 13: Linear Regression 211**

Getting to Grips with the Basics of Regression 212

Adding a regression line 212

Working out residuals 214

Using the regression equation 215

Using Simple Regression 217

Performing simple regression in SPSS 217

Interpreting the output 218

Writing up the results 222

Working with Multiple Variables: Multiple Regression 223

Performing multiple regression in SPSS 224

Interpreting the output 225

Writing up the results 229

Checking Assumptions of Regression 230

Normally distributed residuals 230

Linearity 232

Outliers 234

Multicollinearity 238

Homoscedasticity 240

Type of data 242

**Chapter 14: Associations between Discrete Variables
243**

Summarising Results in a Contingency Table 244

Observed frequencies in contingency tables 244

Percentaging a contingency table 245

Obtaining contingency tables in SPSS 247

Calculating Chi-Square 249

Expected frequencies 250

Calculating chi-square 251

Obtaining chi-square in SPSS 252

Interpreting the output from chi-square in SPSS 253

Writing up the results of a chi-square analysis 255

Understanding the assumptions of chi-square analysis 256

Measuring the Strength of Association between Two Variables 257

Looking at the odds ratio 257

Phi and Cramer’s V Coefficients 258

Obtaining odds ratio, phi coefficient and Cramer’s V in SPSS 259

Using the McNemar Test 260

Calculating the McNemar test 261

Obtaining a McNemar test in SPSS 262

**Part IV: Analysing Independent Groups Research Designs
265**

**Chapter 15: Independent t-tests and Mann–Whitney Tests
267**

Understanding Independent Groups Design 268

The Independent t-test 268

Performing the independent t-test in SPSS 269

Interpreting the output 272

Writing up the results 275

Considering assumptions 275

Mann-Whitney test 277

Performing the Mann–Whitney test in SPSS 278

Interpreting the output 280

Writing up the results 282

Considering assumptions 283

**Chapter 16: Between-Groups ANOVA 285**

One-Way Between-Groups ANOVA 286

Seeing how ANOVA works 287

Calculating a one-way between-groups ANOVA 288

Obtaining a one-way between-groups ANOVA in SPSS 291

Interpreting the SPSS output for a one-way

between-groups ANOVA 294

Writing up the results of a one-way between-groups ANOVA 296

Considering assumptions of a one-way

between-groups ANOVA 296

Two-Way Between-Groups ANOVA 298

Understanding main effects and interactions 299

Obtaining a two-way between-groups ANOVA in SPSS 300

Interpreting the SPSS output for a two-way

between-groups ANOVA 301

Writing up the results of a two-way

between-groups ANOVA 306

Considering assumptions of a two-way

between-groups ANOVA 307

Kruskal–Wallis Test 307

Obtaining a Kruskal–Wallis test in SPSS 308

Interpreting the SPSS output for a Kruskal–Wallis test 310

Writing up the results of a Kruskal–Wallis test 311

Considering 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 314

Multiplicity 315

Choosing a post hoc test 316

Obtaining a Tukey HSD post hoc test in SPSS 317

Interpreting the SPSS output for a Tukey HSD post hoc test 319

Writing up the results of a post hoc Tukey HSD test 322

Planned Comparisons for Independent Groups Designs 322

Choosing a planned comparison 323

Obtaining a Dunnett test in SPSS 323

Interpreting the SPSS output for a Dunnett test 324

Writing up the results of a Dunnett test 326

**Part V: Analysing Repeated Measures Research Designs
327**

**Chapter 18: Paired t-tests and Wilcoxon Tests 329**

Understanding Repeated Measures Design 329

Paired t-test 330

Performing a paired t-test in SPSS 331

Interpreting the output 333

Writing up the results 336

Assumptions 336

The Wilcoxon Test 339

Performing the Wilcoxon test in SPSS 339

Interpreting the output 342

Writing up the results 343

**Chapter 19: Within-Groups ANOVA 347**

One-Way Within-Groups ANOVA 347

Knowing how ANOVA works 348

The example 349

Obtaining a one-way within-groups ANOVA in SPSS 353

Interpreting the SPSS output for a one-way within-groups ANOVA 356

Writing up the results of a one-way within-groups ANOVA 360

Assumptions of a one-way within-groups ANOVA 360

Two-Way Within-Groups ANOVA 361

Main effects and interactions 362

Obtaining a two-way within-groups ANOVA in SPSS 363

Interpreting the SPSS output for a two-way within-groups ANOVA 367

Interpreting the interaction plot from a two-way within-groups ANOVA 371

Writing up the results of a two-way within-groups ANOVA 372

Assumptions of a two-way within-groups ANOVA 373

The Friedman Test 374

Obtaining a Friedman test in SPSS 375

Interpreting the SPSS output for a Friedman test 376

Writing up the results of a Friedman test 377

Assumptions 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? 380

What is the difference between post hoc tests and planned comparisons? 381

Post Hoc Tests for Repeated Measures Designs 381

The example 382

Choosing a post hoc test 382

Obtaining a post-hoc test for a within-groups ANOVA in SPSS 383

Interpreting the SPSS output for a post-hoc test 384

Writing up the results of a post hoc test 386

Planned Comparisons for Within Groups Designs 387

The example 388

Choosing a planned comparison 388

Obtaining a simple planned contrast in SPSS 389

Interpreting the SPSS output for planned comparison tests 391

Writing up the results of planned contrasts 392

Examining Differences between Conditions: The Bonferroni Correction 393

**Chapter 21: Mixed ANOVA 395**

Getting to Grips with Mixed ANOVA 395

The example 396

Main Effects and Interactions 397

Performing the ANOVA in SPSS 398

Interpreting the SPSS output for a two-way mixed ANOVA 403

Writing up the results of a two-way mixed ANOVA 410

Assumptions 411

**Part VI: The Part of Tens 415**

**Chapter 22: Ten Pieces of Good Advice for Inferential Testing
417**

Statistical Significance Is Not the Same as Practical Significance 417

Fail to Prepare, Prepare to Fail 418

Don’t Go Fishing for a Significant Result 418

Check Your Assumptions 418

My p Is Bigger Than Your p 418

Differences and Relationships Are Not Opposing Trends 419

Where Did My Post-hoc Tests Go? 419

Categorising Continuous Data 419

Be Consistent 420

Get Help! 420

**Chapter 23: Ten Tips for Writing Your Results Section
421**

Reporting the p-value 421

Reporting Other Figures 422

Don’t Forget About the Descriptive Statistics 422

Do Not Overuse the Mean 422

Report Effect Sizes and Direction of Effects 423

The Case of the Missing Participants 423

Be Careful With Your Language 424

Beware Correlations and Causality 424

Make Sure to Answer Your Own Question 424

Add Some Structure 424

Index 425

Donncha Hanna, PhD is a psychology lecturer at Queen's University Belfast whose primary teaching responsibilities include statistics and research methods. Martin Dempster, PhD is a health psychologist and the research coordinator for the Doctorate in Clinical Psychology programme at Queen's University Belfast.

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