Dane szczegółowe książki
Discovering statistics using SPSS: and sex and drugs and rock 'n' roll / Field, Andy
Autorzy
Tytuł
Discovering statistics using SPSS: and sex and drugs and rock 'n' roll
Tytuł oryginału
Discovering statistics using SPSS : and sex and drugs and rock 'n' roll
Wydawnictwo
Los Angeles-London-New Delhi-Singapore-Washington DC: Sage Publications, 2011
Numer wydania
3
ISBN
9781847879066; 9781847879073
Hasła przedmiotowe
Spis treści
pokaż spis treści
Preface … xix
How to use this book … xxiv
Acknowledgements … xxviii
Dedication … xxx
Symbols used in this book … xxxi
Some maths revision … xxxiii
1. Why is my evil lecturer forcing me to learn statistics? 1
1.1. What will this chapter tell me? (1) … 1
1.2. What the hell am I doing here? I don't belong here (1) … 2
1.2.1. The research process (1) … 3
1.3. Initial observation: finding something that needs explaining (1) … 3
1.4. Generating theories and testing them (1) … 4
1.5. Data collection 1: what to measure (1) … 7
1.5.1. Variables (1) … 7
1.5.2. Measurement error (1) … 10
1.5.3. Validity and reliability (1) … 11
1.6. Data collection 2: how to measure (1) … 12
1.6.1. Correlational research methods (1) … 12
1.6.2. Experimental research methods (1) … 13
1.6.3. Randomization (1) … 17
1.7. Analyzing data (1) … 18
1.7.1. Frequency distributions (1) … 18
1.7.2. The centre of a distribution (1) … 20
1.7.3. The dispersion in a distribution (1) … 23
1.7.4. Using a frequency distribution to go beyond the data (1) … 24
1.7.5. Fitting statistical models to the data (1) … 26
What have I discovered about statistics? (1) … 28
Key terms that I've discovered … 28
Smart Alex's stats quiz … 29
Further reading … 29
Interesting real research … 30
2. Everything you ever wanted to know about statistics (well, sort of) … 31
2.1. What will this chapter tell me? (1) … 31
2.2. Building statistical models (1) … 32
2.3. Populations and samples (1) … 34
2.4. Simple statistical models (1) … 35
2.4.1. The mean: a very simple statistical model (1) … 35
2.4.2. Assessing the fit of the mean: sums of squares, variance and standard deviations (1) … 35
2.4.3. Expressing the mean as a model (2) … 38
2.5. Going beyond the data (1) … 40
2.5.1. The standard error (1) … 40
2.5.2. Confidence intervals (2) … 43
2.6. Using statistical models to test research questions (1) … 48
2.6.1. Test statistics (1) … 52
2.6.2. One- and two-tailed tests (1) … 54
2.6.3. Type I and Type II errors (1) … 55
2.6.4. Effect sizes (2) … 56
2.6.5. Statistical power (2) … 58
What have I discovered about statistics? (1) … 59
Key terms that I've discovered … 59
Smart Alex's stats quiz … 59
Further reading … 60
Interesting real research … 60
3. The SPSS environment … 61
3.1. What will this chapter tell me? (1) … 61
3.2. Versions of SPSS (1) … 62
3.3. Getting started (1) … 62
3.4. The data editor (1) … 63
3.4.1. Entering data into the data editor (1) … 69
3.4.2. The 'Variable View' (1) … 70
3.4.3. Missing values (1) … 77
3.5. The SPSS viewer (1) … 78
3.6. The SPSS SmartViewer (1) … 81
3.7. The syntax window (3) … 82
3.8.saving files (1) … 83
3.9. Retrieving a file (1) … 84
What have I discovered about statistics? (1) … 85
Key terms that I've discovered … 85
Smart Alex's tasks … 85
Further reading … 86
Online tutorials … 86
4. Exploring data with graphs … 87
4.1. What will this chapter tell me? (1) … 87
4.2. The art of presenting data (1) … 88
4.2.1. What makes a good graph? (1) … 88
4.2.2. Lies, damned lies, and … erm … graphs (1) … 90
4.3. The SPSS Chart Builder (1) … 91
4.4. Histograms: a good way to spot obvious problems (1) … 93
4.5. Boxplots (box-whisker diagrams) (1) … 99
4.6. Graphing means: bar charts and error bars (1) … 103
4.6.1. Simple bar charts for independent means (1) … 105
4.6.2. Clustered bar charts for independent means (1) … 107
4.6.3. Simple bar charts for related means (1) … 109
4.6.4. Clustered bar charts for related means (1) … 111
4.6.5. Clustered bar charts for 'mixed' designs (1) … 113
4.7. Line charts (1) … 115
4.8. Graphing relationships: the scatterplot (1) … 116
4.8.1. Simple scatterplot (1) … 117
4.8.2. Grouped scatterplot (1) … 119
4.8.3. Simple and grouped 3-D scatterplots (1) … 121
4.8.4. Matrix scatterplot (1) … 123
4.8.5. Simple dot plot or density plot (1) … 125
4.8.6. Drop-line graph (1) … 126
4.9. Editing graphs (1) … 126
What have I discovered about statistics? (1) … 129
Key terms that I've discovered … 130
Smart Alex's tasks … 130
Further reading … 130
Online tutorial … 130
Interesting real research … 130
5. Exploring assumptions … 131
5.1. What will this chapter tell me? (1) … 131
5.2. What are assumptions? (1) … 132
5.3. Assumptions of parametric data (1) … 132
5.4. The assumption of normality (1) … 133
5.4.1. Oh no, it's that pesky frequency distribution again: checking normality visually (1) … 134
5.4.2. Quantifying normality with numbers (1) … 136
5.4.3. Exploring groups of data (1) … 140
5.5. Testing whether a distribution is normal (1) … 144
5.5.1. Doing the Kolmogorov-Smirnov test on SPSS (1) … 145
5.5.2. Output from the explore procedure (1) … 146
5.5.3. Reporting the K-S test (1) … 148
5.6. Testing for homogeneity of variance (1) … 149
5.6.1. Levene's test (1) … 150
5.6.2. Reporting Levene's test (1) … 152
5.7. Correcting problems in the data (2) … 153
5.7.1. Dealing with outliers (2) … 153
5.7.2. Dealing with non-normality and unequal variances (2) … 153
5.7.3. Transforming the data using SPSS (2) … 156
5.7.4. When it all goes horribly wrong (3) … 162
What have I discovered about statistics? (1) … 164
Key terms that I've discovered … 164
Smart Alex's tasks … 165
Online tutorial … 165
Further reading … 165
6. Correlation … 166
6.1. What will this chapter tell me? (1) … 166
6.2. Looking at relationships (1) … 167
6.3. How do we measure relationships? (1) … 167
6.3.1. A detour into the murky world of covariance (1) … 167
6.3.2. Standardization and the correlation coefficient (1) … 169
6.3.3. The significance of the correlation coefficient (3) … 171
6.3.4. Confidence intervals for r (3) … 172
6.3.5. A word of warning about interpretation: causality (1) … 173
6.4. Data entry for correlation analysis using SPSS (1) … 174
6.5. Bivariate correlation (1) … 175
6.5.1. General procedure for running correlations on SPSS (1) … 175
6.5.2. Pearson's correlation coefficient (1) … 177
6.5.3. Spearman's correlation coefficient (1) … 179
6.5.4. Kendall's tau (non-parametric) (1) … 181
6.5.5. Biserial and point-biserial correlations (3) … 182
6.6. Partial correlation (2) … 186
6.6.1. The theory behind part and partial correlation (2) … 186
6.6.2. Partial correlation using SPSS (2) … 188
6.6.3. Semi-partial (or part) correlations (2) … 190
6.7. Comparing correlations (3) … 191
6.7.1. Comparing independent rs (3) … 191
6.7.2. Comparing dependent rs (3) … 191
6.8. Calculating the effect size (1) … 192
6.9. How to report correlation coefficents (1) … 193
What have I discovered about statistics? (1) … 195
Key terms that I've discovered … 195
Smart Alex's tasks … 195
Further reading … 196
Online tutorial … 196
Interesting real research … 196
7. Regression 197
7.1. What will this chapter tell me? (1) … 197
7.2. An introduction to regression (1) … 198
7.2.1. Some important information about straight lines (1) … 199
7.2.2. The method of least squares (1) … 200
7.2.3. Assessing the goodness of fit: sums of squares, R and R^{2} (1) … 201
7.2.4. Assessing individual predictors (1) … 204
7.3. Doing simple regression on SPSS (1) … 205
7.4. Interpreting a simple regression (1) … 206
7.4.1. Overall fit of the model (1) … 206
7.4.2. Model parameters (1) … 207
7.4.3. Using the model (1) … 208
7.5. Multiple regression: the basics (2) … 209
7.5.1. An example of a multiple regression model (2) … 210
7.5.2. Sums of squares, R and R^{2} (2) … 211
7.5.3. Methods of regression (2) … 212
7.6. How accurate is my regression model? (2) … 214
7.6.1. Assessing the regression model I: diagnostics (2) … 214
7.6.2. Assessing the regression model II: generalization (2) … 220
7.7. How to do multiple regression using SPSS (2) … 225
7.7.1. Some things to think about before the analysis (2) … 225
7.7.2. Main options (2) … 225
7.7.3. Statistics (2) … 227
7.7.4. Regression plots (2) … 229
7.7.5.saving regression diagnostics (2) … 230
7.7.6. Further options (2) … 231
7.8. Interpreting multiple regression (2) … 233
7.8.1. Descriptives (2) … 233
7.8.2. Summary of model (2) … 234
7.8.3. Model parameters (2) … 237
7.8.4. Excluded variables (2) … 241
7.8.5. Assessing the assumption of no multicollinearity (2) … 241
7.8.6. Casewise diagnostics (2) … 244
7.8.7. Checking assumptions (2) … 247
7.9. What if I violate an assumption? (2) … 251
7.10. How to report multiple regression (2) … 252
7.11. Categorical predictors and multiple regression (3) … 253
7.11.1. Dummy coding (3) … 253
7.11.2. SPSS output for dummy variables (3) … 256
What have I discovered about statistics? (1) … 261
Key terms that I've discovered … 261
Smart Alex's tasks … 262
Further reading … 263
Online tutorial … 263
Interesting real research … 263
8. Logistic regression … 264
8.1. What will this chapter tell me? (1) … 264
8.2. Background to logistic regression (1) … 265
8.3. What are the principles behind logistic regression? (3) … 265
8.3.1. Assessing the model: the log-likelihood statistic (3) … 267
8.3.2. Assessing the model: ft and R^{2} (3) … 268
8.3.3. Assessing the contribution of predictors: the Wald statistic (2) … 269
8.3.4. The odds ratio: Exp(B) (3) … 270
8.3.5. Methods of logistic regression (2) … 271
8.4. Assumptions and things that can go wrong (4) … 273
8.4.1. Assumptions (2) … 273
8.4.2. Incomplete information from the predictors (4) … 273
8.4.3. Complete separation (4) … 274
8.4.4. Overdispersion (4) … 276
8.5. Binary logistic regression: an example that will make you feel eel (2) … 277
8.5.1. The main analysis (2) … 278
8.5.2. Method of regression (2) … 279
8.5.3. Categorical predictors (2) … 279
8.5.4. Obtaining residuals (2) … 280
8.5.5. Further options (2) … 281
8.6. Interpreting logistic regression (2) … 282
8.6.1. The initial model (2) … 282
8.6.2. Step 1: intervention (3) … 284
8.6.3. Listing predicted probabilities (2) … 291
8.6.4. Interpreting residuals (2) … 292
8.6.5. Calculating the effect size (2) … 294
8.7. How to report logistic regression (2) … 294
8.8. Testing assumptions: another example (2) … 294
8.8.1. Testing for linearity of the logit (3) … 296
8.8.2. Testing for multicollinearity (3) … 297
8.9. Predicting several categories: multinomial logistic regression (3) … 300
8.9.1. Running multinomial logistic regression in SPSS (3) … 301
8.9.2. Statistics (3) … 304
8.9.3. Other options (3) … 305
8.9.4. Interpreting the multinomial logistic regression output (3) … 306
8.9.5. Reporting the results … 312
What have I discovered about statistics? (1) … 313
Key terms that I've discovered … 313
Smart Alex's tasks … 313
Further reading … 315
Online tutorial … 315
Interesting real research … 315
9. Comparing two means … 316
9.1. What will this chapter tell me? (1) … 316
9.2. Looking at differences (1) … 317
9.2.1. A problem with error bar graphs of repeated-measures designs (1) … 317
9.2.2. Step 1: calculate the mean for each participant (2) … 320
9.2.3. Step 2: calculate the grand mean (2) … 320
9.2.4. Step 3: calculate the adjustment factor (2) … 322
9.2.5. Step 4: create adjusted values for each variable (2) … 323
9.3. The t-test (1) … 324
9.3.1. Rationale for the t-test (1) … 325
9.3.2. Assumptions of the t-test (1) … 326
9.4. The dependent t-test (1) … 326
9.4.1. Sampling distributions and the standard error (1) … 327
9.4.2. The dependent t-test equation explained (1) … 327
9.4.3. The dependent t-test and the assumption of normality (1) … 329
9.4.4. Dependent t-tests using SPSS (1) … 329
9.4.5. Output from the dependent t-test (1) … 330
9.4.6. Calculating the effect size (2) … 332
9.4.7. Reporting the dependent t-test (1) … 333
9.5. The independent t-test (1) … 334
9.5.1. The independent t-test equation explained (1) … 334
9.5.2. The independent t-test using SPSS (1) … 337
9.5.3. Output from the independent t-test (1) … 339
9.5.4. Calculating the effect size (2) … 341
9.5.5. Reporting the independent t-test (1) … 341
9.6. Between groups or repeated measures? (1) … 342
9.7. The t-test as a general linear model (2) … 342
9.8. What if my data are not normally distributed? (2) … 344
What have I discovered about statistics? (1) … 345
Key terms that I've discovered … 345
Smart Alex's task … 346
Further reading … 346
Online tutorial … 346
Interesting real research … 346
10. Comparing several means: ANOVA (GLM 1) … 347
10.1. What will this chapter tell me? (1) … 347
10.2. The theory behind ANOVA (2) … 348
10.2.1. Inflated error rates (2) … 348
10.2.2. Interpreting F (2) … 349
10.2.3. ANOVA as regression (2) … 349
10.2.4. Logic of the F-ratio (2) … 354
10.2.5. Total sum of squares (SS_{T}) (2) … 356
10.2.6. Model sum of squares (SS_{M}) (2) … 356
10.2.7. Residual sum of squares (SS_{R}) (2) … 357
10.2.8. Mean squares (2) … 358
10.2.9. The F-ratio (2) … 358
10.2.10. Assumptions of ANOVA (3) … 359
10.2.11. Planned contrasts (2) … 360
10.2.12. Post hoc procedures (2) … 372
10.3. Running one-way ANOVA on SPSS (2) … 375
10.3.1. Planned comparisons using SPSS (2) … 376
10.3.2. Post hoc tests in SPSS (2) … 378
10.3.3. Options (2) … 379
10.4. Output from one-way ANOVA (2) … 381
10.4.1. Output for the main analysis (2) … 381
10.4.2. Output for planned comparisons (2) … 384
10.4.3. Output for post hoc tests (2) … 385
10.5. Calculating the effect size (2) … 389
10.6. Reporting results from one-way independent ANOVA (2) … 390
10.7. Violations of assumptions in one-way independent ANOVA (2) … 391
What have I discovered about statistics? (1) … 392
Key terms that I've discovered … 392
Smart Alex's tasks … 393
Further reading … 394
Online tutorials … 394
Interesting real research … 394
11. Analysis of covariance, ANC0VA (GLM 2) … 395
11.1. What will this chapter tell me? (2) … 395
11.2. What is ANCOVA? (2) … 396
11.3. Assumptions and issues in ANCOVA (3) … 397
11.3.1. Independence of the covariate and treatment effect (3) … 397
11.3.2. Homogeneity of regression slopes (3) … 399
11.4. Conducting ANCOVA on SPSS (2) … 399
11.4.1. Inputting data (1) … 399
11.4.2. Initial considerations: testing the independence of the independent variable and covariate (2) … 400
11.4.3. The main analysis (2) … 401
11.4.4. Contrasts and other options (2) … 401
11.5. Interpreting the output from ANCOVA (2) … 404
11.5.1. What happens when the covariate is excluded? (2) … 404
11.5.2. The main analysis (2) … 405
11.5.3. Contrasts (2) … 407
11.5.4. Interpreting the covariate (2) … 408
11.6. ANCOVA run as a multiple regression (2) … 408
11.7. Testing the assumption of homogeneity of regression slopes (3) … 413
11.8. Calculating the effect size (2) … 415
11.9. Reporting results (2) … 417
11.10. What to do when assumptions are violated in ANCOVA (3) … 418
What have I discovered about statistics? (2) … 418
Key terms that I've discovered … 419
Smart Alex's tasks … 419
Further reading … 420
Online tutorials … 420
Interesting real research … 420
12. Factorial ANOVA (GLM 3) … 421
12.1. What will this chapter tell me? (2) … 421
12.2. Theory of factorial ANOVA (between-groups) (2) … 422
12.2.1. Factorial designs (2) … 422
12.2.2. An example with two independent variables (2) … 423
12.2.3. Total sums of squares (SS_{T}) (2) … 424
12.2.4. The model sum of squares (SS_{M}) (2) … 426
12.2.5. The residual sum of squares (SS_{R}) (2) … 428
12.2.6. The F-ratios (2) … 429
12.3. Factorial ANOVA using SPSS (2) … 430
12.3.1. Entering the data and accessing the main dialog box (2) … 430
12.3.2. Graphing interactions (2) … 432
12.3.3. Contrasts (2) … 432
12.3.4. Post hoc tests (2) … 434
12.3.5. Options (2) … 434
12.4. Output from factorial ANOVA (2) … 435
12.4.1. Output for the preliminary analysis (2) … 435
12.4.2. Levene's test (2) … 436
12.4.3. The main ANOVA table (2) … 436
12.4.4. Contrasts (2) … 439
12.4.5. Simple effects analysis (3) … 440
12.4.6. Post hoc analysis (2) … 441
12.5. Interpreting interaction graphs (2) … 443
12.6. Calculating effect sizes (3) … 446
12.7. Reporting the results of two-way ANOVA (2) … 448
12.8. Factorial ANOVA as regression (3) … 450
12.9. What to do when assumptions are violated in factorial ANOVA (3) … 454
What have I discovered about statistics? (2) … 454
Key terms that I've discovered … 455
Smart Alex's tasks … 455
Further reading … 456
Online tutorials … 456
Interesting real research … 456
13. Repeated-measures designs (GLM 4) … 457
13.1. What will this chapter tell me? (2) … 457
13.2. Introduction to repeated-measures designs (2) … 458
13.2.1. The assumption of sphericity (2) … 459
13.2.2. How is sphericity measured? (2) … 459
13.2.3. Assessing the severity of departures from sphericity (2) … 460
13.2.4. What is the effect of violating the assumption of sphericity? (3) … 460
13.2.5. What do you do if you violate sphericity? (2) … 461
13.3. Theory of one-way repeated-measures ANOVA (2) … 462
13.3.1. The total sum of squares (SS_{T}) (2) … 464
13.3.2. The within-participant (SS_{W}) (2) … 465
13.3.3. The model sum of squares (SS_{M}) (2) … 466
13.3.4. The residual sum of squares (SS_{R}) (2) … 467
13.3.5. The mean squares (2) … 467
13.3.6. The F-ratio (2) … 467
13.3.7. The between-participant sum of squares (2) … 468
13.4. One-way repeated-measures ANOVA using SPSS (2) … 468
13.4.1. The main analysis (2) … 468
13.4.2. Defining contrasts for repeated-measures (2) … 471
13.4.3. Post hoc tests and additional options (3) … 471
13.5. Output for one-way repeated-measures ANOVA (2) … 474
13.5.1. Descriptives and other diagnostics (1) … 474
13.5.2. Assessing and correcting for sphericity: Mauchly's test (2) … 474
13.5.3. The main ANOVA (2) … 475
13.5.4. Contrasts (2) … 477
13.5.5. Post hoc tests (2) … 478
13.6. Effect sizes for repeated-measures ANOVA (3) … 479
13.7. Reporting one-way repeated-measures ANOVA (2) … 481
13.8. Repeated-measures with several independent variables (2) … 482
13.8.1. The main analysis (2) … 484
13.8.2. Contrasts (2) … 488
13.8.3. Simple effects analysis (3) … 488
13.8.4. Graphing interactions (2) … 490
13.8.5. Other options (2) … 491
13.9. Output for factorial repeated-measures ANOVA (2) … 492
13.9.1. Descriptives and main analysis (2) … 492
13.9.2. The effect of drink (2) … 493
13.9.3. The effect of imagery (2) … 495
13.9.4. The interaction effect (drink times imagery) (2) … 496
13.9.5. Contrasts for repeated-measures variables (2) … 498
13.10. Effect sizes for factorial repeated-measures ANOVA (3) … 501
13.11. Reporting the results from factorial repeated-measures ANOVA (2) … 502
13.12. What to do when assumptions are violated in repeated-measures ANOVA (3) … 503
What have I discovered about statistics? (2) … 503
Key terms that I've discovered … 504
Smart Alex's tasks … 504
Further reading … 505
Online tutorials … 505
Interesting real research … 505
14. Mixed design ANOVA (GLM 5) … 506
14.1. What will this chapter tell me? (1) … 506
14.2. Mixed designs (2) … 507
14.3. What do men and women look for in a partner? (2) … 508
14.4. Mixed ANOVA on SPSS (2) … 508
14.4.1. The main analysis (2) … 508
14.4.2. Other options (2) … 513
14.5. Output for mixed factorial ANOVA: main analysis (3) … 514
14.5.1. The main effect of gender (2) … 517
14.5.2. The main effect of looks (2) … 518
14.5.3. The main effect of charisma (2) … 520
14.5.4. The interaction between gender and looks (2) … 521
14.5.5. The interaction between gender and charisma (2) … 523
14.5.6. The interaction between attractiveness and charisma (2) … 524
14.5.7. The interaction between looks, charisma and gender (3) … 527
14.5.8. Conclusions (3) … 530
14.6. Calculating effect sizes (3) … 531
14.7. Reporting the results of mixed ANOVA (2) … 533
14.8. What to do when assumptions are violated in mixed ANOVA (3) … 536
What have I discovered about statistics? (2) … 536
Key terms that I've discovered … 537
Smart Alex's tasks … 537
Further reading … 538
Online tutorials … 538
Interesting real research … 538
15. Non-parametric tests 539
15.1. What will this chapter tell me? (1) … 539
15.2. When to use non-parametric tests (1) … 540
15.3. Comparing two independent conditions: the Wilcoxon rank-sum test and Mann-Whitney test (1) … 540
15.3.1. Theory (2) … 542
15.3.2. Inputting data and provisional analysis (1) … 545
15.3.3. Running the analysis (1) … 546
15.3.4. Output from the Mann-Whitney test (1) … 548
15.3.5. Calculating an effect size (2) … 550
15.3.6. Writing the results (1) … 550
15.4. Comparing two related conditions: the Wilcoxon signed-rank test (1) … 552
15.4.1. Theory of the Wilcoxon signed-rank test (2) … 552
15.4.2. Running the analysis (1) … 554
15.4.3. Output for the ecstasy group (1) … 556
15.4.4. Output for the alcohol group (1) … 557
15.4.5. Calculating an effect size (2) … 558
15.4.6. Writing the results (2) … 558
15.5. Differences between several independent groups: the Kruskal-Wallis test (1) … 559
15.5.1. Theory of the Kruskal-Wallis test (2) … 560
15.5.2. Inputting data and provisional analysis (1) … 562
15.5.3. Doing the Kruskal-Wallis test on SPSS (1) … 562
15.5.4. Output from the Kruskal-Wallis test (1) … 564
15.5.5. Post hoc tests for the Kruskal-Wallis test (2) … 565
15.5.6. Testing for trends: the Jonckheere-Terpstra test (2) … 568
15.5.7. Calculating an effect size (2) … 570
15.5.8. Writing and interpreting the results (1) … 571
15.6. Differences between several related groups: Friedman's ANOVA (1) … 573
15.6.1. Theory of Friedman's ANOVA (2) … 573
15.6.2. Inputting data and provisional analysis (1) … 575
15.6.3. Doing Friedman's ANOVA on SPSS (1) … 575
15.6.4. Output from Friedman's ANOVA (1) … 576
15.6.5. Post hoc tests for Friedman's ANOVA (2) … 577
15.6.6. Calculating an effect size (2) … 579
15.6.7. Writing and interpreting the results (1) … 580
What have I discovered about statistics? (1) … 581
Key terms that I've discovered … 582
Smart Alex's tasks … 582
Further reading … 583
Online tutorial … 583
Interesting real research … 583
16. Multivariate analysis of variance (MANOVA) … 584
16.1. What will this chapter tell me? (2) … 584
16.2. When to use MANOVA (2) … 585
16.3. Introduction: similarities and differences to ANOVA (2) … 585
16.3.1. Words of warning (2) … 587
16.3.2. The example for this chapter (2) … 587
16.4. Theory of MANOVA (3) … 588
16.4.1. Introduction to matrices (3) … 588
16.4.2. Some important matrices and their functions (3) … 590
16.4.3. Calculating MANOVA by hand: a worked example (3) … 591
16.4.4. Principle of the MANOVA test statistic (4) … 598
16.5. Practical issues when conducting MANOVA (3) … 603
16.5.1. Assumptions and how to check them (3) … 603
16.5.2. Choosing a test statistic (3) … 604
16.5.3. Follow-up analysis (3) … 605
16.6. MANOVA on SPSS (2) … 605
16.6.1. The main analysis (2) … 606
16.6.2. Multiple comparisons in MANOVA (2) … 607
16.6.3. Additional options (3) … 607
16.7. Output from MANOVA (3) … 608
16.7.1. Preliminary analysis and testing assumptions (3) … 608
16.7.2. MANOVA test statistics (3) … 608
16.7.3. Univariate test statistics (2) … 609
16.7.4. SSCP Matrices (3) … 611
16.7.5. Contrast (3) … 613
16.8. Reporting results from MANOVA (2) … 614
16.9. Following up MANOVA with discriminant analysis (3) … 615
16.10. Output from the discriminant analysis (4) … 618
16.11. Reporting results from discriminant analysis (2) … 621
16.12. Some final remarks (4) … 622
16.12.1. The final interpretation (4) … 622
16.12.2. Univariate ANOVA or discriminant analysis? … 624
16.13. What to do when assumptions are violated in MANOVA (3) … 624
What have I discovered about statistics? (2) … 624
Key terms that I've discovered … 625
Smart Alex's tasks … 625
Further reading … 626
Online tutorials … 626
Interesting real research … 626
17. Exploratory factor analysis … 627
17.1. What will this chapter tell me? (1) … 627
17.2. When to use factor analysis (2) … 628
17.3. Factors (2) … 628
17.3.1. Graphical representation of factors (2) … 630
17.3.2. Mathematical representation of factors (2) … 631
17.3.3. Factor scores (2) … 633
17.4. Discovering factors (2) … 636
17.4.1. Choosing a method (2) … 636
17.4.2. Communality (2) … 637
17.4.3. Factor analysis vs. principal component analysis (2) … 638
17.4.4. Theory behind principal component analysis (3) … 638
17.4.5. Factor extraction: eigenvalues and the scree plot (2) … 639
17.4.6. Improving interpretation: factor rotation (3) … 642
17.5. Research example (2) … 645
17.5.1. Before you begin (2) … 645
17.6. Running the analysis (2) … 650
17.6.1. Factor extraction on SPSS (2) … 651
17.6.2. Rotation (2) … 653
17.6.3. Scores (2) … 654
17.6.4. Options (2) … 654
17.7. Interpreting output from SPSS (2) … 655
17.7.1. Preliminary analysis (2) … 656
17.7.2. Factor extraction (2) … 660
17.7.3. Factor rotation (2) … 664
17.7.4. Factor scores (2) … 669
17.7.5. Summary (2) … 671
17.8. How to report factor analysis (1) … 671
17.9. Reliability analysis (2) … 673
17.9.1. Measures of reliability (3) … 673
17.9.2. Interpreting Cronbach's alpha (some cautionary tales …) (2) … 675
17.9.3. Reliability analysis on SPSS (2) … 676
17.9.4. Interpreting the output (2) … 678
17.10. How to report reliability analysis (2) … 681
What have I discovered about statistics? (2) … 682
Key terms that I've discovered … 682
Smart Alex's tasks … 683
Further reading … 685
Online tutorial … 685
Interesting real research … 685
18. Categorical data … 686
18.1. What will this chapter tell me? (1) … 686
18.2. Analysing categorical data (1) … 687
18.3. Theory of analysing categorical data (1) … 687
18.3.1. Pearson's chi-square test (1) … 688
18.3.2. Fisher's exact test (1) … 690
18.3.3. The likelihood ratio (2) … 690
18.3.4. Yates' correction (2) … 691
18.4. Assumptions of the chi-square test (1) … 691
18.5. Doing chi-square on SPSS (1) … 692
18.5.1. Entering data: raw scores (1) … 692
18.5.2. Entering data: weight cases (1) … 692
18.5.3. Running the analysis (1) … 694
18.5.4. Output for the chi-square test (1) … 696
18.5.5. Breaking down a significant chi-square test with standardized residuals (2) … 698
18.5.6. Calculating an effect size (2) … 699
18.5.7. Reporting the results of chi-square (1) … 700
18.6. Several categorical variables: loglinear analysis (3) … 702
18.6.1. Chi-square as regression (4) … 702
18.6.2. Loglinear analysis (3) … 708
18.7. Assumptions in loglinear analysis (2) … 710
18.8. Loglinear analysis using SPSS (2) … 711
18.8.1. Initial considerations (2) … 711
18.8.2. The loglinear analysis (2) … 712
18.9. Output from loglinear analysis (3) … 714
18.10. Following up loglinear analysis (2) … 719
18.11. Effect sizes in loglinear analysis (2) … 720
18.12. Reporting the results of loglinear analysis (2) … 721
What have I discovered about statistics? (1) … 722
Key terms that I've discovered … 722
Smart Alex's tasks … 722
Further reading … 724
Online tutorial … 724
Interesting real research … 724
19. Multilevel linear models … 725
19.1. What will this chapter tell me? (1) … 725
19.2. Hierarchical data (2) … 726
19.2.1. The intraclass correlation (2) … 728
19.2.2. Benefits of multilevel models (2) … 729
19.3. Theory of multilevel linear models (3) … 730
19.3.1. An example (2) … 730
19.3.2. Fixed and random coefficients (3) … 732
19.4. The multilevel model (4) … 734
19.4.1. Assessing the fit and comparing multilevel models (4) … 737
19.4.2. Types of covariance structures (4) … 737
19.5. Some practical issues (3) … 739
19.5.1. Assumptions (3) … 739
19.5.2. Sample size and power (3) … 740
19.5.3. Centring variables (4) … 740
19.6. Multilevel modelling on SPSS (4) … 741
19.6.1. Entering the data (2) … 742
19.6.2. Ignoring the data structure: ANOVA (2) … 742
19.6.3. Ignoring the data structure: ANCOVA (2) … 746
19.6.4. Factoring in the data structure: random intercepts (3) … 749
19.6.5. Factoring in the data structure: random intercepts and slopes (4) … 752
19.6.6. Adding an interaction to the model (4) … 756
19.7. Growth models (4) … 761
19.7.1. Growth curves (polynomials) (4) … 761
19.7.2. An example: the honeymoon period (2) … 761
19.7.3. Restructuring the data (3) … 763
19.7.4. Running a growth model on SPSS (4) … 767
19.7.5. Further analysis (4) … 774
19.8. How to report a multilevel model (3) … 775
What have I discovered about statistics? (2) … 776
Key terms that I've discovered … 777
Smart Alex's tasks … 777
Further reading … 778
Online tutorial … 778
Interesting real research … 778
Epilogue … 779
Glossary … 781
Appendix … 797
A. 1. Table of the standard normal distribution … 797
A. 2. Critical values of the f-distribution … 803
A. 3. Critical values of the F-distribution … 804
A. 4. Critical values of the chi-square distribution … 808
References… 809
Index … 816
How to use this book … xxiv
Acknowledgements … xxviii
Dedication … xxx
Symbols used in this book … xxxi
Some maths revision … xxxiii
1. Why is my evil lecturer forcing me to learn statistics? 1
1.1. What will this chapter tell me? (1) … 1
1.2. What the hell am I doing here? I don't belong here (1) … 2
1.2.1. The research process (1) … 3
1.3. Initial observation: finding something that needs explaining (1) … 3
1.4. Generating theories and testing them (1) … 4
1.5. Data collection 1: what to measure (1) … 7
1.5.1. Variables (1) … 7
1.5.2. Measurement error (1) … 10
1.5.3. Validity and reliability (1) … 11
1.6. Data collection 2: how to measure (1) … 12
1.6.1. Correlational research methods (1) … 12
1.6.2. Experimental research methods (1) … 13
1.6.3. Randomization (1) … 17
1.7. Analyzing data (1) … 18
1.7.1. Frequency distributions (1) … 18
1.7.2. The centre of a distribution (1) … 20
1.7.3. The dispersion in a distribution (1) … 23
1.7.4. Using a frequency distribution to go beyond the data (1) … 24
1.7.5. Fitting statistical models to the data (1) … 26
What have I discovered about statistics? (1) … 28
Key terms that I've discovered … 28
Smart Alex's stats quiz … 29
Further reading … 29
Interesting real research … 30
2. Everything you ever wanted to know about statistics (well, sort of) … 31
2.1. What will this chapter tell me? (1) … 31
2.2. Building statistical models (1) … 32
2.3. Populations and samples (1) … 34
2.4. Simple statistical models (1) … 35
2.4.1. The mean: a very simple statistical model (1) … 35
2.4.2. Assessing the fit of the mean: sums of squares, variance and standard deviations (1) … 35
2.4.3. Expressing the mean as a model (2) … 38
2.5. Going beyond the data (1) … 40
2.5.1. The standard error (1) … 40
2.5.2. Confidence intervals (2) … 43
2.6. Using statistical models to test research questions (1) … 48
2.6.1. Test statistics (1) … 52
2.6.2. One- and two-tailed tests (1) … 54
2.6.3. Type I and Type II errors (1) … 55
2.6.4. Effect sizes (2) … 56
2.6.5. Statistical power (2) … 58
What have I discovered about statistics? (1) … 59
Key terms that I've discovered … 59
Smart Alex's stats quiz … 59
Further reading … 60
Interesting real research … 60
3. The SPSS environment … 61
3.1. What will this chapter tell me? (1) … 61
3.2. Versions of SPSS (1) … 62
3.3. Getting started (1) … 62
3.4. The data editor (1) … 63
3.4.1. Entering data into the data editor (1) … 69
3.4.2. The 'Variable View' (1) … 70
3.4.3. Missing values (1) … 77
3.5. The SPSS viewer (1) … 78
3.6. The SPSS SmartViewer (1) … 81
3.7. The syntax window (3) … 82
3.8.saving files (1) … 83
3.9. Retrieving a file (1) … 84
What have I discovered about statistics? (1) … 85
Key terms that I've discovered … 85
Smart Alex's tasks … 85
Further reading … 86
Online tutorials … 86
4. Exploring data with graphs … 87
4.1. What will this chapter tell me? (1) … 87
4.2. The art of presenting data (1) … 88
4.2.1. What makes a good graph? (1) … 88
4.2.2. Lies, damned lies, and … erm … graphs (1) … 90
4.3. The SPSS Chart Builder (1) … 91
4.4. Histograms: a good way to spot obvious problems (1) … 93
4.5. Boxplots (box-whisker diagrams) (1) … 99
4.6. Graphing means: bar charts and error bars (1) … 103
4.6.1. Simple bar charts for independent means (1) … 105
4.6.2. Clustered bar charts for independent means (1) … 107
4.6.3. Simple bar charts for related means (1) … 109
4.6.4. Clustered bar charts for related means (1) … 111
4.6.5. Clustered bar charts for 'mixed' designs (1) … 113
4.7. Line charts (1) … 115
4.8. Graphing relationships: the scatterplot (1) … 116
4.8.1. Simple scatterplot (1) … 117
4.8.2. Grouped scatterplot (1) … 119
4.8.3. Simple and grouped 3-D scatterplots (1) … 121
4.8.4. Matrix scatterplot (1) … 123
4.8.5. Simple dot plot or density plot (1) … 125
4.8.6. Drop-line graph (1) … 126
4.9. Editing graphs (1) … 126
What have I discovered about statistics? (1) … 129
Key terms that I've discovered … 130
Smart Alex's tasks … 130
Further reading … 130
Online tutorial … 130
Interesting real research … 130
5. Exploring assumptions … 131
5.1. What will this chapter tell me? (1) … 131
5.2. What are assumptions? (1) … 132
5.3. Assumptions of parametric data (1) … 132
5.4. The assumption of normality (1) … 133
5.4.1. Oh no, it's that pesky frequency distribution again: checking normality visually (1) … 134
5.4.2. Quantifying normality with numbers (1) … 136
5.4.3. Exploring groups of data (1) … 140
5.5. Testing whether a distribution is normal (1) … 144
5.5.1. Doing the Kolmogorov-Smirnov test on SPSS (1) … 145
5.5.2. Output from the explore procedure (1) … 146
5.5.3. Reporting the K-S test (1) … 148
5.6. Testing for homogeneity of variance (1) … 149
5.6.1. Levene's test (1) … 150
5.6.2. Reporting Levene's test (1) … 152
5.7. Correcting problems in the data (2) … 153
5.7.1. Dealing with outliers (2) … 153
5.7.2. Dealing with non-normality and unequal variances (2) … 153
5.7.3. Transforming the data using SPSS (2) … 156
5.7.4. When it all goes horribly wrong (3) … 162
What have I discovered about statistics? (1) … 164
Key terms that I've discovered … 164
Smart Alex's tasks … 165
Online tutorial … 165
Further reading … 165
6. Correlation … 166
6.1. What will this chapter tell me? (1) … 166
6.2. Looking at relationships (1) … 167
6.3. How do we measure relationships? (1) … 167
6.3.1. A detour into the murky world of covariance (1) … 167
6.3.2. Standardization and the correlation coefficient (1) … 169
6.3.3. The significance of the correlation coefficient (3) … 171
6.3.4. Confidence intervals for r (3) … 172
6.3.5. A word of warning about interpretation: causality (1) … 173
6.4. Data entry for correlation analysis using SPSS (1) … 174
6.5. Bivariate correlation (1) … 175
6.5.1. General procedure for running correlations on SPSS (1) … 175
6.5.2. Pearson's correlation coefficient (1) … 177
6.5.3. Spearman's correlation coefficient (1) … 179
6.5.4. Kendall's tau (non-parametric) (1) … 181
6.5.5. Biserial and point-biserial correlations (3) … 182
6.6. Partial correlation (2) … 186
6.6.1. The theory behind part and partial correlation (2) … 186
6.6.2. Partial correlation using SPSS (2) … 188
6.6.3. Semi-partial (or part) correlations (2) … 190
6.7. Comparing correlations (3) … 191
6.7.1. Comparing independent rs (3) … 191
6.7.2. Comparing dependent rs (3) … 191
6.8. Calculating the effect size (1) … 192
6.9. How to report correlation coefficents (1) … 193
What have I discovered about statistics? (1) … 195
Key terms that I've discovered … 195
Smart Alex's tasks … 195
Further reading … 196
Online tutorial … 196
Interesting real research … 196
7. Regression 197
7.1. What will this chapter tell me? (1) … 197
7.2. An introduction to regression (1) … 198
7.2.1. Some important information about straight lines (1) … 199
7.2.2. The method of least squares (1) … 200
7.2.3. Assessing the goodness of fit: sums of squares, R and R^{2} (1) … 201
7.2.4. Assessing individual predictors (1) … 204
7.3. Doing simple regression on SPSS (1) … 205
7.4. Interpreting a simple regression (1) … 206
7.4.1. Overall fit of the model (1) … 206
7.4.2. Model parameters (1) … 207
7.4.3. Using the model (1) … 208
7.5. Multiple regression: the basics (2) … 209
7.5.1. An example of a multiple regression model (2) … 210
7.5.2. Sums of squares, R and R^{2} (2) … 211
7.5.3. Methods of regression (2) … 212
7.6. How accurate is my regression model? (2) … 214
7.6.1. Assessing the regression model I: diagnostics (2) … 214
7.6.2. Assessing the regression model II: generalization (2) … 220
7.7. How to do multiple regression using SPSS (2) … 225
7.7.1. Some things to think about before the analysis (2) … 225
7.7.2. Main options (2) … 225
7.7.3. Statistics (2) … 227
7.7.4. Regression plots (2) … 229
7.7.5.saving regression diagnostics (2) … 230
7.7.6. Further options (2) … 231
7.8. Interpreting multiple regression (2) … 233
7.8.1. Descriptives (2) … 233
7.8.2. Summary of model (2) … 234
7.8.3. Model parameters (2) … 237
7.8.4. Excluded variables (2) … 241
7.8.5. Assessing the assumption of no multicollinearity (2) … 241
7.8.6. Casewise diagnostics (2) … 244
7.8.7. Checking assumptions (2) … 247
7.9. What if I violate an assumption? (2) … 251
7.10. How to report multiple regression (2) … 252
7.11. Categorical predictors and multiple regression (3) … 253
7.11.1. Dummy coding (3) … 253
7.11.2. SPSS output for dummy variables (3) … 256
What have I discovered about statistics? (1) … 261
Key terms that I've discovered … 261
Smart Alex's tasks … 262
Further reading … 263
Online tutorial … 263
Interesting real research … 263
8. Logistic regression … 264
8.1. What will this chapter tell me? (1) … 264
8.2. Background to logistic regression (1) … 265
8.3. What are the principles behind logistic regression? (3) … 265
8.3.1. Assessing the model: the log-likelihood statistic (3) … 267
8.3.2. Assessing the model: ft and R^{2} (3) … 268
8.3.3. Assessing the contribution of predictors: the Wald statistic (2) … 269
8.3.4. The odds ratio: Exp(B) (3) … 270
8.3.5. Methods of logistic regression (2) … 271
8.4. Assumptions and things that can go wrong (4) … 273
8.4.1. Assumptions (2) … 273
8.4.2. Incomplete information from the predictors (4) … 273
8.4.3. Complete separation (4) … 274
8.4.4. Overdispersion (4) … 276
8.5. Binary logistic regression: an example that will make you feel eel (2) … 277
8.5.1. The main analysis (2) … 278
8.5.2. Method of regression (2) … 279
8.5.3. Categorical predictors (2) … 279
8.5.4. Obtaining residuals (2) … 280
8.5.5. Further options (2) … 281
8.6. Interpreting logistic regression (2) … 282
8.6.1. The initial model (2) … 282
8.6.2. Step 1: intervention (3) … 284
8.6.3. Listing predicted probabilities (2) … 291
8.6.4. Interpreting residuals (2) … 292
8.6.5. Calculating the effect size (2) … 294
8.7. How to report logistic regression (2) … 294
8.8. Testing assumptions: another example (2) … 294
8.8.1. Testing for linearity of the logit (3) … 296
8.8.2. Testing for multicollinearity (3) … 297
8.9. Predicting several categories: multinomial logistic regression (3) … 300
8.9.1. Running multinomial logistic regression in SPSS (3) … 301
8.9.2. Statistics (3) … 304
8.9.3. Other options (3) … 305
8.9.4. Interpreting the multinomial logistic regression output (3) … 306
8.9.5. Reporting the results … 312
What have I discovered about statistics? (1) … 313
Key terms that I've discovered … 313
Smart Alex's tasks … 313
Further reading … 315
Online tutorial … 315
Interesting real research … 315
9. Comparing two means … 316
9.1. What will this chapter tell me? (1) … 316
9.2. Looking at differences (1) … 317
9.2.1. A problem with error bar graphs of repeated-measures designs (1) … 317
9.2.2. Step 1: calculate the mean for each participant (2) … 320
9.2.3. Step 2: calculate the grand mean (2) … 320
9.2.4. Step 3: calculate the adjustment factor (2) … 322
9.2.5. Step 4: create adjusted values for each variable (2) … 323
9.3. The t-test (1) … 324
9.3.1. Rationale for the t-test (1) … 325
9.3.2. Assumptions of the t-test (1) … 326
9.4. The dependent t-test (1) … 326
9.4.1. Sampling distributions and the standard error (1) … 327
9.4.2. The dependent t-test equation explained (1) … 327
9.4.3. The dependent t-test and the assumption of normality (1) … 329
9.4.4. Dependent t-tests using SPSS (1) … 329
9.4.5. Output from the dependent t-test (1) … 330
9.4.6. Calculating the effect size (2) … 332
9.4.7. Reporting the dependent t-test (1) … 333
9.5. The independent t-test (1) … 334
9.5.1. The independent t-test equation explained (1) … 334
9.5.2. The independent t-test using SPSS (1) … 337
9.5.3. Output from the independent t-test (1) … 339
9.5.4. Calculating the effect size (2) … 341
9.5.5. Reporting the independent t-test (1) … 341
9.6. Between groups or repeated measures? (1) … 342
9.7. The t-test as a general linear model (2) … 342
9.8. What if my data are not normally distributed? (2) … 344
What have I discovered about statistics? (1) … 345
Key terms that I've discovered … 345
Smart Alex's task … 346
Further reading … 346
Online tutorial … 346
Interesting real research … 346
10. Comparing several means: ANOVA (GLM 1) … 347
10.1. What will this chapter tell me? (1) … 347
10.2. The theory behind ANOVA (2) … 348
10.2.1. Inflated error rates (2) … 348
10.2.2. Interpreting F (2) … 349
10.2.3. ANOVA as regression (2) … 349
10.2.4. Logic of the F-ratio (2) … 354
10.2.5. Total sum of squares (SS_{T}) (2) … 356
10.2.6. Model sum of squares (SS_{M}) (2) … 356
10.2.7. Residual sum of squares (SS_{R}) (2) … 357
10.2.8. Mean squares (2) … 358
10.2.9. The F-ratio (2) … 358
10.2.10. Assumptions of ANOVA (3) … 359
10.2.11. Planned contrasts (2) … 360
10.2.12. Post hoc procedures (2) … 372
10.3. Running one-way ANOVA on SPSS (2) … 375
10.3.1. Planned comparisons using SPSS (2) … 376
10.3.2. Post hoc tests in SPSS (2) … 378
10.3.3. Options (2) … 379
10.4. Output from one-way ANOVA (2) … 381
10.4.1. Output for the main analysis (2) … 381
10.4.2. Output for planned comparisons (2) … 384
10.4.3. Output for post hoc tests (2) … 385
10.5. Calculating the effect size (2) … 389
10.6. Reporting results from one-way independent ANOVA (2) … 390
10.7. Violations of assumptions in one-way independent ANOVA (2) … 391
What have I discovered about statistics? (1) … 392
Key terms that I've discovered … 392
Smart Alex's tasks … 393
Further reading … 394
Online tutorials … 394
Interesting real research … 394
11. Analysis of covariance, ANC0VA (GLM 2) … 395
11.1. What will this chapter tell me? (2) … 395
11.2. What is ANCOVA? (2) … 396
11.3. Assumptions and issues in ANCOVA (3) … 397
11.3.1. Independence of the covariate and treatment effect (3) … 397
11.3.2. Homogeneity of regression slopes (3) … 399
11.4. Conducting ANCOVA on SPSS (2) … 399
11.4.1. Inputting data (1) … 399
11.4.2. Initial considerations: testing the independence of the independent variable and covariate (2) … 400
11.4.3. The main analysis (2) … 401
11.4.4. Contrasts and other options (2) … 401
11.5. Interpreting the output from ANCOVA (2) … 404
11.5.1. What happens when the covariate is excluded? (2) … 404
11.5.2. The main analysis (2) … 405
11.5.3. Contrasts (2) … 407
11.5.4. Interpreting the covariate (2) … 408
11.6. ANCOVA run as a multiple regression (2) … 408
11.7. Testing the assumption of homogeneity of regression slopes (3) … 413
11.8. Calculating the effect size (2) … 415
11.9. Reporting results (2) … 417
11.10. What to do when assumptions are violated in ANCOVA (3) … 418
What have I discovered about statistics? (2) … 418
Key terms that I've discovered … 419
Smart Alex's tasks … 419
Further reading … 420
Online tutorials … 420
Interesting real research … 420
12. Factorial ANOVA (GLM 3) … 421
12.1. What will this chapter tell me? (2) … 421
12.2. Theory of factorial ANOVA (between-groups) (2) … 422
12.2.1. Factorial designs (2) … 422
12.2.2. An example with two independent variables (2) … 423
12.2.3. Total sums of squares (SS_{T}) (2) … 424
12.2.4. The model sum of squares (SS_{M}) (2) … 426
12.2.5. The residual sum of squares (SS_{R}) (2) … 428
12.2.6. The F-ratios (2) … 429
12.3. Factorial ANOVA using SPSS (2) … 430
12.3.1. Entering the data and accessing the main dialog box (2) … 430
12.3.2. Graphing interactions (2) … 432
12.3.3. Contrasts (2) … 432
12.3.4. Post hoc tests (2) … 434
12.3.5. Options (2) … 434
12.4. Output from factorial ANOVA (2) … 435
12.4.1. Output for the preliminary analysis (2) … 435
12.4.2. Levene's test (2) … 436
12.4.3. The main ANOVA table (2) … 436
12.4.4. Contrasts (2) … 439
12.4.5. Simple effects analysis (3) … 440
12.4.6. Post hoc analysis (2) … 441
12.5. Interpreting interaction graphs (2) … 443
12.6. Calculating effect sizes (3) … 446
12.7. Reporting the results of two-way ANOVA (2) … 448
12.8. Factorial ANOVA as regression (3) … 450
12.9. What to do when assumptions are violated in factorial ANOVA (3) … 454
What have I discovered about statistics? (2) … 454
Key terms that I've discovered … 455
Smart Alex's tasks … 455
Further reading … 456
Online tutorials … 456
Interesting real research … 456
13. Repeated-measures designs (GLM 4) … 457
13.1. What will this chapter tell me? (2) … 457
13.2. Introduction to repeated-measures designs (2) … 458
13.2.1. The assumption of sphericity (2) … 459
13.2.2. How is sphericity measured? (2) … 459
13.2.3. Assessing the severity of departures from sphericity (2) … 460
13.2.4. What is the effect of violating the assumption of sphericity? (3) … 460
13.2.5. What do you do if you violate sphericity? (2) … 461
13.3. Theory of one-way repeated-measures ANOVA (2) … 462
13.3.1. The total sum of squares (SS_{T}) (2) … 464
13.3.2. The within-participant (SS_{W}) (2) … 465
13.3.3. The model sum of squares (SS_{M}) (2) … 466
13.3.4. The residual sum of squares (SS_{R}) (2) … 467
13.3.5. The mean squares (2) … 467
13.3.6. The F-ratio (2) … 467
13.3.7. The between-participant sum of squares (2) … 468
13.4. One-way repeated-measures ANOVA using SPSS (2) … 468
13.4.1. The main analysis (2) … 468
13.4.2. Defining contrasts for repeated-measures (2) … 471
13.4.3. Post hoc tests and additional options (3) … 471
13.5. Output for one-way repeated-measures ANOVA (2) … 474
13.5.1. Descriptives and other diagnostics (1) … 474
13.5.2. Assessing and correcting for sphericity: Mauchly's test (2) … 474
13.5.3. The main ANOVA (2) … 475
13.5.4. Contrasts (2) … 477
13.5.5. Post hoc tests (2) … 478
13.6. Effect sizes for repeated-measures ANOVA (3) … 479
13.7. Reporting one-way repeated-measures ANOVA (2) … 481
13.8. Repeated-measures with several independent variables (2) … 482
13.8.1. The main analysis (2) … 484
13.8.2. Contrasts (2) … 488
13.8.3. Simple effects analysis (3) … 488
13.8.4. Graphing interactions (2) … 490
13.8.5. Other options (2) … 491
13.9. Output for factorial repeated-measures ANOVA (2) … 492
13.9.1. Descriptives and main analysis (2) … 492
13.9.2. The effect of drink (2) … 493
13.9.3. The effect of imagery (2) … 495
13.9.4. The interaction effect (drink times imagery) (2) … 496
13.9.5. Contrasts for repeated-measures variables (2) … 498
13.10. Effect sizes for factorial repeated-measures ANOVA (3) … 501
13.11. Reporting the results from factorial repeated-measures ANOVA (2) … 502
13.12. What to do when assumptions are violated in repeated-measures ANOVA (3) … 503
What have I discovered about statistics? (2) … 503
Key terms that I've discovered … 504
Smart Alex's tasks … 504
Further reading … 505
Online tutorials … 505
Interesting real research … 505
14. Mixed design ANOVA (GLM 5) … 506
14.1. What will this chapter tell me? (1) … 506
14.2. Mixed designs (2) … 507
14.3. What do men and women look for in a partner? (2) … 508
14.4. Mixed ANOVA on SPSS (2) … 508
14.4.1. The main analysis (2) … 508
14.4.2. Other options (2) … 513
14.5. Output for mixed factorial ANOVA: main analysis (3) … 514
14.5.1. The main effect of gender (2) … 517
14.5.2. The main effect of looks (2) … 518
14.5.3. The main effect of charisma (2) … 520
14.5.4. The interaction between gender and looks (2) … 521
14.5.5. The interaction between gender and charisma (2) … 523
14.5.6. The interaction between attractiveness and charisma (2) … 524
14.5.7. The interaction between looks, charisma and gender (3) … 527
14.5.8. Conclusions (3) … 530
14.6. Calculating effect sizes (3) … 531
14.7. Reporting the results of mixed ANOVA (2) … 533
14.8. What to do when assumptions are violated in mixed ANOVA (3) … 536
What have I discovered about statistics? (2) … 536
Key terms that I've discovered … 537
Smart Alex's tasks … 537
Further reading … 538
Online tutorials … 538
Interesting real research … 538
15. Non-parametric tests 539
15.1. What will this chapter tell me? (1) … 539
15.2. When to use non-parametric tests (1) … 540
15.3. Comparing two independent conditions: the Wilcoxon rank-sum test and Mann-Whitney test (1) … 540
15.3.1. Theory (2) … 542
15.3.2. Inputting data and provisional analysis (1) … 545
15.3.3. Running the analysis (1) … 546
15.3.4. Output from the Mann-Whitney test (1) … 548
15.3.5. Calculating an effect size (2) … 550
15.3.6. Writing the results (1) … 550
15.4. Comparing two related conditions: the Wilcoxon signed-rank test (1) … 552
15.4.1. Theory of the Wilcoxon signed-rank test (2) … 552
15.4.2. Running the analysis (1) … 554
15.4.3. Output for the ecstasy group (1) … 556
15.4.4. Output for the alcohol group (1) … 557
15.4.5. Calculating an effect size (2) … 558
15.4.6. Writing the results (2) … 558
15.5. Differences between several independent groups: the Kruskal-Wallis test (1) … 559
15.5.1. Theory of the Kruskal-Wallis test (2) … 560
15.5.2. Inputting data and provisional analysis (1) … 562
15.5.3. Doing the Kruskal-Wallis test on SPSS (1) … 562
15.5.4. Output from the Kruskal-Wallis test (1) … 564
15.5.5. Post hoc tests for the Kruskal-Wallis test (2) … 565
15.5.6. Testing for trends: the Jonckheere-Terpstra test (2) … 568
15.5.7. Calculating an effect size (2) … 570
15.5.8. Writing and interpreting the results (1) … 571
15.6. Differences between several related groups: Friedman's ANOVA (1) … 573
15.6.1. Theory of Friedman's ANOVA (2) … 573
15.6.2. Inputting data and provisional analysis (1) … 575
15.6.3. Doing Friedman's ANOVA on SPSS (1) … 575
15.6.4. Output from Friedman's ANOVA (1) … 576
15.6.5. Post hoc tests for Friedman's ANOVA (2) … 577
15.6.6. Calculating an effect size (2) … 579
15.6.7. Writing and interpreting the results (1) … 580
What have I discovered about statistics? (1) … 581
Key terms that I've discovered … 582
Smart Alex's tasks … 582
Further reading … 583
Online tutorial … 583
Interesting real research … 583
16. Multivariate analysis of variance (MANOVA) … 584
16.1. What will this chapter tell me? (2) … 584
16.2. When to use MANOVA (2) … 585
16.3. Introduction: similarities and differences to ANOVA (2) … 585
16.3.1. Words of warning (2) … 587
16.3.2. The example for this chapter (2) … 587
16.4. Theory of MANOVA (3) … 588
16.4.1. Introduction to matrices (3) … 588
16.4.2. Some important matrices and their functions (3) … 590
16.4.3. Calculating MANOVA by hand: a worked example (3) … 591
16.4.4. Principle of the MANOVA test statistic (4) … 598
16.5. Practical issues when conducting MANOVA (3) … 603
16.5.1. Assumptions and how to check them (3) … 603
16.5.2. Choosing a test statistic (3) … 604
16.5.3. Follow-up analysis (3) … 605
16.6. MANOVA on SPSS (2) … 605
16.6.1. The main analysis (2) … 606
16.6.2. Multiple comparisons in MANOVA (2) … 607
16.6.3. Additional options (3) … 607
16.7. Output from MANOVA (3) … 608
16.7.1. Preliminary analysis and testing assumptions (3) … 608
16.7.2. MANOVA test statistics (3) … 608
16.7.3. Univariate test statistics (2) … 609
16.7.4. SSCP Matrices (3) … 611
16.7.5. Contrast (3) … 613
16.8. Reporting results from MANOVA (2) … 614
16.9. Following up MANOVA with discriminant analysis (3) … 615
16.10. Output from the discriminant analysis (4) … 618
16.11. Reporting results from discriminant analysis (2) … 621
16.12. Some final remarks (4) … 622
16.12.1. The final interpretation (4) … 622
16.12.2. Univariate ANOVA or discriminant analysis? … 624
16.13. What to do when assumptions are violated in MANOVA (3) … 624
What have I discovered about statistics? (2) … 624
Key terms that I've discovered … 625
Smart Alex's tasks … 625
Further reading … 626
Online tutorials … 626
Interesting real research … 626
17. Exploratory factor analysis … 627
17.1. What will this chapter tell me? (1) … 627
17.2. When to use factor analysis (2) … 628
17.3. Factors (2) … 628
17.3.1. Graphical representation of factors (2) … 630
17.3.2. Mathematical representation of factors (2) … 631
17.3.3. Factor scores (2) … 633
17.4. Discovering factors (2) … 636
17.4.1. Choosing a method (2) … 636
17.4.2. Communality (2) … 637
17.4.3. Factor analysis vs. principal component analysis (2) … 638
17.4.4. Theory behind principal component analysis (3) … 638
17.4.5. Factor extraction: eigenvalues and the scree plot (2) … 639
17.4.6. Improving interpretation: factor rotation (3) … 642
17.5. Research example (2) … 645
17.5.1. Before you begin (2) … 645
17.6. Running the analysis (2) … 650
17.6.1. Factor extraction on SPSS (2) … 651
17.6.2. Rotation (2) … 653
17.6.3. Scores (2) … 654
17.6.4. Options (2) … 654
17.7. Interpreting output from SPSS (2) … 655
17.7.1. Preliminary analysis (2) … 656
17.7.2. Factor extraction (2) … 660
17.7.3. Factor rotation (2) … 664
17.7.4. Factor scores (2) … 669
17.7.5. Summary (2) … 671
17.8. How to report factor analysis (1) … 671
17.9. Reliability analysis (2) … 673
17.9.1. Measures of reliability (3) … 673
17.9.2. Interpreting Cronbach's alpha (some cautionary tales …) (2) … 675
17.9.3. Reliability analysis on SPSS (2) … 676
17.9.4. Interpreting the output (2) … 678
17.10. How to report reliability analysis (2) … 681
What have I discovered about statistics? (2) … 682
Key terms that I've discovered … 682
Smart Alex's tasks … 683
Further reading … 685
Online tutorial … 685
Interesting real research … 685
18. Categorical data … 686
18.1. What will this chapter tell me? (1) … 686
18.2. Analysing categorical data (1) … 687
18.3. Theory of analysing categorical data (1) … 687
18.3.1. Pearson's chi-square test (1) … 688
18.3.2. Fisher's exact test (1) … 690
18.3.3. The likelihood ratio (2) … 690
18.3.4. Yates' correction (2) … 691
18.4. Assumptions of the chi-square test (1) … 691
18.5. Doing chi-square on SPSS (1) … 692
18.5.1. Entering data: raw scores (1) … 692
18.5.2. Entering data: weight cases (1) … 692
18.5.3. Running the analysis (1) … 694
18.5.4. Output for the chi-square test (1) … 696
18.5.5. Breaking down a significant chi-square test with standardized residuals (2) … 698
18.5.6. Calculating an effect size (2) … 699
18.5.7. Reporting the results of chi-square (1) … 700
18.6. Several categorical variables: loglinear analysis (3) … 702
18.6.1. Chi-square as regression (4) … 702
18.6.2. Loglinear analysis (3) … 708
18.7. Assumptions in loglinear analysis (2) … 710
18.8. Loglinear analysis using SPSS (2) … 711
18.8.1. Initial considerations (2) … 711
18.8.2. The loglinear analysis (2) … 712
18.9. Output from loglinear analysis (3) … 714
18.10. Following up loglinear analysis (2) … 719
18.11. Effect sizes in loglinear analysis (2) … 720
18.12. Reporting the results of loglinear analysis (2) … 721
What have I discovered about statistics? (1) … 722
Key terms that I've discovered … 722
Smart Alex's tasks … 722
Further reading … 724
Online tutorial … 724
Interesting real research … 724
19. Multilevel linear models … 725
19.1. What will this chapter tell me? (1) … 725
19.2. Hierarchical data (2) … 726
19.2.1. The intraclass correlation (2) … 728
19.2.2. Benefits of multilevel models (2) … 729
19.3. Theory of multilevel linear models (3) … 730
19.3.1. An example (2) … 730
19.3.2. Fixed and random coefficients (3) … 732
19.4. The multilevel model (4) … 734
19.4.1. Assessing the fit and comparing multilevel models (4) … 737
19.4.2. Types of covariance structures (4) … 737
19.5. Some practical issues (3) … 739
19.5.1. Assumptions (3) … 739
19.5.2. Sample size and power (3) … 740
19.5.3. Centring variables (4) … 740
19.6. Multilevel modelling on SPSS (4) … 741
19.6.1. Entering the data (2) … 742
19.6.2. Ignoring the data structure: ANOVA (2) … 742
19.6.3. Ignoring the data structure: ANCOVA (2) … 746
19.6.4. Factoring in the data structure: random intercepts (3) … 749
19.6.5. Factoring in the data structure: random intercepts and slopes (4) … 752
19.6.6. Adding an interaction to the model (4) … 756
19.7. Growth models (4) … 761
19.7.1. Growth curves (polynomials) (4) … 761
19.7.2. An example: the honeymoon period (2) … 761
19.7.3. Restructuring the data (3) … 763
19.7.4. Running a growth model on SPSS (4) … 767
19.7.5. Further analysis (4) … 774
19.8. How to report a multilevel model (3) … 775
What have I discovered about statistics? (2) … 776
Key terms that I've discovered … 777
Smart Alex's tasks … 777
Further reading … 778
Online tutorial … 778
Interesting real research … 778
Epilogue … 779
Glossary … 781
Appendix … 797
A. 1. Table of the standard normal distribution … 797
A. 2. Critical values of the f-distribution … 803
A. 3. Critical values of the F-distribution … 804
A. 4. Critical values of the chi-square distribution … 808
References… 809
Index … 816