Applying Statistics in Behavioural Research (2nd edition)
Applying Statistics in Behavioural Research is written for undergraduate students in the behavioural sciences, such as Psychology, Pedagogy, Sociology and Ethology. The topics range from basic techniques, like correlation and t-tests, to moderately advanced analyses, like multiple regression and MANOV A. The focus is on practical application and reporting, as well as on the correct interpretation of what is being reported. For example, why is interaction so important? What does it mean when the null hypothesis is retained? And why do we need effect sizes?
A characteristic feature of Applying Statistics in Behavioural Research is that it uses the same ‘basic report’ structure over and over in order to introduce the reader to new analyses. This enables students to study the subject matter very efficiently, as one needs less time to discover the structure. Another characteristic of the book is its systematic attention to reading and interpreting graphs in connection with the statistics.
Many statistics books use graphical explanations, but ignore the fact that some students are simply not visually oriented. For these students, graphical explanations make things harder, not easier. Here, understanding the visualizations is addressed in separate chapters. The book is also available online through www.boomstudent.nl.
Contents
Preface for students xv
Part I-A Descriptive Statistics: Univariate 1
1 Introduction of the examples 3
1.1 Example 1: Clinical psychology (depression prevention) 3
1.2 Example 2: Education (arithmetic lesson) 7
1.3 Example 3: Human-computer interaction (mind reading) 8
1.4 Example 4: Criminology (reconviction) 10
1.5 Example 5: Developmental psychology (bullying) 11
1.6 Example 6: Social psychology (food consumption) 12
1.7 Example 7: Sociology (spirituality) 15
1.8 Example 8: Ethology (the gaze of dogs) 17
1.9 Exercises 18
2 Basic report of one variable 19
2.1 Learning goals 19
2.2 Definition of a basic report of one variable 19
2.3 Design 19
2.4 Degree of control 21
2.5 Name of the analysis 21
2.6 Frequency distribution 22
2.7 Number of observations 23
2.8 Histogram 24
2.9 Five-number summary 27
2.10 Outliers 29
2.11 Modified boxplot 31
2.12 Mean and standard deviation 32
2.13 Indication of normality 34
2.14 Exercises 36
3 Visualising statistics of one variable 43
3.1 Learning goals 43
3.2 Some rules for visualising 43
3.3 Exercises 46
4 Relative scores 49
4.1 Learning goals 49
4.2 Target subject and reference group 49
4.3 Percentile scores 49
4.4 Standard scores 51
4.5 Computing probabilities in a normal distribution 52
4.6 Normal scores 55
4.7 Histograms of relative scores 56
4.8 Exercises 57
Part I-B Descriptive Statistics: Bivariate 65
5 Basic report of association between two quantitative variables 67
5.1 Learning goals 67
5.2 Definition of a basic report of association between two quantitative variables 67
5.3 Design 67
5.4 Degree of control 68
5.5 Name of the analysis 68
5.6 Scatter plot 69
5.7 Regression coefficients and correlation 70
5.8 Regression line 71
5.9 Influential observations 73
5.10 Linearity 74
5.11 Exercises 76
6 Predicted scores and residuals 81
6.1 Learning goals 81
6.2 Predicted scores and residuals 81
6.3 Mean and variance of predicted scores and residuals 82
6.4 Proportion explained variance 84
6.5 Relation between coefficients 85
6.6 Correlation and causality 88
6.7 Exercises 88
7 Visualising statistics of two variables 95
7.1 Learning goals 95
7.2 Some rules for visualising 95
7.3 Exercises 97
8 Basic report of association between two qualitative variables 103
8.1 Learning goals 103
8.2 Definition of a basic report of association between two qualitative variables 103
8.3 Design 103
8.4 Degree of control 104
8.5 Name of the analysis 104
8.6 Contingency table 104
8.7 Conditional distributions 105
8.8 Stacked bar chart 105
8.9 Indication of strength of association 107
8.10 Exercises 108
9 Simpson’s paradox 111
9.1 Learning goals 111
9.2 Definition of Simpson’s paradox 111
9.3 An example of Simpson’s paradox 112
9.4 Exercises 117
Part II-A: Applying t-tests 119
10 Experiments and hypotheses 121
10.1 Learning goals 121
10.2 Within-subject designs versus between-subject designs 121
10.3 Dependent and independent variables 124
10.4 Degree of control in within-subject and between-subject designs 125
10.5 Hypotheses 129
10.6 Name of the analysis 132
10.7 Exercises 132
11 The t-test for paired observations 139
11.1 Learning goals 139
11.2 Definition of a basic report of a t-test for paired observations 139
11.3 Design 139
11.4 Degree of control 140
11.5 Name of the analysis 141
11.6 Scatter plot 141
11.7 Aggregated data 142
11.8 Hypotheses 144
11.9 Effect sizes 145
11.10 Test statistic 146
11.11 The p-value 147
11.12 Decision 149
11.13 Causal interpretation 153
11.14 Beyond the basic report: Check of assumptions 159
11.15 Beyond the basic report: A short report 161
11.16 Exercises 162
12 The t-test for independent samples 167
12.1 Learning goals 167
12.2 Definition of a basic report of a t-test for independent samples 167
12.3 Design 167
12.4 Degree of control 168
12.5 Name of the analysis 168
12.6 Scatter plot 168
12.7 Aggregated data 169
12.8 Hypotheses 171
12.9 Effect sizes 171
12.10 Test statistic 172
12.11 The p-value 172
12.12 Decision 173
12.13 Causal interpretation 175
12.14 Beyond the basic report: Check of assumptions 176
12.15 Beyond the basic report: A short report 178
12.16 Exercises 178
13 Visualising statistics of the t-test for independent samples 183
13.1 Learning goals 183
13.2 Some rules for visualising 183
13.3 Exercises 185
14 t-Tests in a mixed design 187
14.1 Learning goals 187
14.2 Description of data 187
14.3 Design and analysis 187
14.4 Exercises 189
Part II-B: Basic theory of statistical testing 191
15 Testing by enumeration 193
15.1 Learning goals 193
15.2 Definition of a basic report of enumeration 194
15.3 Population and sample 194
15.4 Aggregated data 195
15.5 Enumerated samples table 196
15.6 All possible sample means 197
15.7 Distribution of sample means and standard error 197
15.8 The p-value 198
15.9 Exactness of the p-value 199
15.10 Exercises 200
16 Testing by simulation 203
16.1 Learning goals 203
16.2 Definition of a basic report of simulation 204
16.3 Population and sample 204
16.4 Aggregated data 205
16.5 Simulation table 206
16.6 All simulated sample means 208
16.7 Distribution of sample means and standard error 208
16.8 The p-value 209
16.9 Exactness of the p-value 210
16.10 Exercises 211
17 Testing by reasoning: the z-test 213
17.1 Learning goals 213
17.2 Definition of a basic report of reasoning for the z-test 213
17.3 Population and sample 214
17.4 Aggregated data 214
17.5 Theoretical arguments 215
17.6 Distribution of sample means and standard error 217
17.7 The p-value 219
17.8 Exactness of the p-value 220
17.9 Exercises 220
18 Confidence interval of the mean based on the z-test 223
18.1 Learning goals 223
18.2 Formula of the confidence interval 223
18.3 Interpretation of a confidence interval 224
18.4 Exercises 226
19 Testing by reasoning: the t-test 227
19.1 Learning goals 227
19.2 Definition of a basic report of reasoning for the t-test 227
19.3 Population and sample 227
19.4 Aggregated data 228
19.5 Theoretical arguments 228
19.6 Distribution of sample means and standard error 230
19.7 The p-value 230
19.8 Exactness of the p-value 231
19.9 The distribution of t if the null hypothesis is false 232
19.10 Exercises 232
20 Confidence interval of the mean based on the t-test 235
20.1 Learning goals 235
20.2 Formula of the confidence interval 235
20.3 Interpretation of a confidence interval 236
20.4 Exercises 236
21 Power of a z-test 239
21.1 Learning goals 239
21.2 What is power? 239
21.3 Factors that influence power 239
21.4 Steps in computing the power 240
21.5 Power of a t-test 245
21.6 Exercises 246
22 Generalisation of the basic concepts in statistical testing 251
22.1 Learning goals 251
22.2 What is testing? 251
22.3 What is a statistical test? 252
22.4 Limitations of statistical tests 252
22.5 Type I and type II errors 252
22.6 Error probabilities 253
22.7 Classic requirements of statistical test 253
22.8 The steps in statistical significance tests 254
22.9 Exercises 258
23 The NHST controversy 261
23.1 Learning goals 261
23.2 What is a p-value? 261
23.3 Fisher versus Neyman-Pearson 266
23.4 Exercises 268
Part III: Simple forms of ANOVA 271
24 One-factor ANOVA 273
24.1 Learning goals 273
24.2 Definition of a basic report of a one-factor ANOVA 273
24.3 Design 273
24.4 Degree of control 274
24.5 Name of the analysis 274
24.6 Scatter plot 274
24.7 Aggregated data 275
24.8 Hypotheses 276
24.9 ANOVA table 277
24.10 Decision 288
24.11 Causal interpretation 289
24.12 Beyond the basic report: Post hoc tests 290
24.13 Beyond the basic report: Check of assumptions 291
24.14 Exercises 292
25 Visualising statistics of a one-factor ANOVA 297
25.1 Learning goals 297
25.2 Some rules for visualising 297
25.3 Exercises 300
26 Two-factor ANOVA 303
26.1 Learning goals 303
26.2 Definition of a basic report of a two-factor ANOVA 303
26.3 Design 303
26.4 Degree of control 304
26.5 Name of the analysis 304
26.6 Aggregated data 305
26.7 Interaction plot 306
26.8 Hypotheses 307
26.9 ANOVA table 308
26.10 Decisions 316
26.11 Causal interpretation 317
26.12 Check of assumptions 318
26.13 Exercises 318
27 Interaction 321
27.1 Learning goals 321
27.2 Interaction and the additive model 321
27.3 Interaction and consistency of effects 323
27.4 Interaction and the interaction plot 326
27.5 Interaction and causal models 328
27.6 Interaction and theory formation 331
27.7 Interaction and external validity 333
27.8 Interaction and follow-up analyses 333
27.9 Interaction versus correlation 334
27.10 Exercises 336
28 Visualising statistics of a two-factor ANOVA 341
28.1 Learning goals 341
28.2 Some rules for visualising 341
28.3 Exercises 345
29 Repeated measures ANOVA 347
29.1 Learning goals 347
29.2 Definition of a basic report of a repeated measures ANOVA 347
29.3 Design 347
29.4 Degree of control 348
29.5 Name of the analysis 349
29.6 Aggregated data 349
29.7 Hypotheses 350
29.8 ANOVA table 352
29.9 Decisions 358
29.10 Causal interpretation 359
29.11 Check of assumptions 359
29.12 The Efficiency of Within-Subject Designs 360
29.13 Exercises 361
30 Test reliability and Cronbach’s alpha 363
30.1 Learning goals 363
30.2 Situations in which Cronbach’s alpha can be relevant 363
30.3 Computation of Cronbach’s alpha 363
30.4 Interpretation of Cronbach’s alpha in classical test theory 365
30.5 Interpretation of Cronbach’s alpha in generalisability theory 368
30.6 Interpretations of Cronbach’s alpha 370
30.7 Exercises 371
Part IV: Introduction to GLM 375
31 Overview of designs and analyses 377
31.1 Introduction 377
31.2 Specification of designs 377
31.3 Concepts 378
31.4 Data layout and the arrangement of measurements 380
31.5 Elementary research questions 382
31.6 Choosing the analysis 385
31.7 Sources of variation 389
31.8 Exercises 389
32 Multiple Regression Analysis 391
32.1 Learning goals 391
32.2 Definition of a basic report of a multiple regression analysis 391
32.3 Design 391
32.4 Degree of control 393
32.5 Name of the analysis 393
32.6 Aggregated data 393
32.7 Hypotheses 394
32.8 ANOVA table 396
32.9 Regression weights 398
32.10 Decisions 400
32.11 Causal interpretation 401
32.12 Exercises 401
33 Extensions of multiple regression analysis 409
33.1 Learning goals 409
33.2 Standardised regression weights 409
33.3 Dummy coding of a single factor 412
33.4 Dummy coding of an interaction 413
33.5 Using dummy coding in multiple linear regression 414
33.6 Non-linear effects of covariates 416
33.7 Beyond the basic report: Checking assumptions 417
33.8 Beyond the basic report: A short report 418
33.9 Exercises 419
34 GLM-Univariate 421
34.1 Learning goals 421
34.2 Definition of a basic report of GLM-Univariate 421
34.3 Design 421
34.4 Degree of control 422
34.5 Name of the analysis 422
34.6 Aggregated data 423
34.7 Hypotheses 424
34.8 ANOVA table 426
34.9 Regression weights and corrected means 427
34.10 Decisions 432
34.11 Causal interpretation 432
34.12 Beyond the basic report: A short report 433
34.13 Exercises 434
35 GLM-Multivariate 441
35.1 Learning goals 441
35.2 Definition of a basic report of GLM-Multivariate 441
35.3 Design 441
35.4 Degree of control 442
35.5 Name of the analysis 443
35.6 Aggregated data 443
35.7 Hypotheses 444
35.8 Test table 446
35.9 Regression weights and corrected means 448
35.10 Decisions 449
35.11 Causal interpretation 451
35.12 Beyond the basic report: A short report 451
35.13 Beyond the basic report: Connecting the significance tests and means 452
35.14 Exercises 458
36 GLM-Repeated measures with a single dependent variable 463
36.1 Learning goals 463
36.2 Definition of a basic report of GLM-Repeated measures 463
36.3 Design 463
36.4 Degree of control 467
36.5 Name of the analysis 467
36.6 Aggregated data 467
36.7 Hypotheses 468
36.8 Test table 470
36.9 Regression weights and corrected means 473
36.10 Decisions 474
36.11 Causal interpretation 475
36.12 Checking assumptions 478
36.13 Beyond the basic report: A short report 479
36.14 Exercises 481
37 GLM-Repeated measures with several dependent variables 489
37.1 Learning goals 489
37.2 Definition of a basic report of GLM-Repeated Measures 489
37.3 Design 489
37.4 Degree of control 492
37.5 Name of the analysis 492
37.6 Aggregated data 492
37.7 Hypotheses 492
37.8 Test table 494
37.9 Regression weights and corrected means 497
37.10 Decisions 499
37.11 Causal interpretation 500
37.12 Exercises 501
Part V: Introduction to nonparametric tests 503
38 The Mann-Whitney test 505
38.1 Learning goals 505
38.2 Definition of a basic report of a MW test 505
38.3 Design 505
38.4 Degree of control 506
38.5 Name of the analysis 507
38.6 Aggregated data 508
38.7 Hypotheses 510
38.8 Test statistics 511
38.9 Standardised effect size 513
38.10 Decision 514
38.11 Causal interpretation 514
38.12 Beyond the basic report: A short report 514
38.13 Exercises 514
39 Chi-square test for independence 517
39.1 Learning goals 517
39.2 Definition of a basic report of Chi-square test for independence 519
39.3 Design 519
39.4 Degree of control 522
39.5 Name of the analysis 522
39.6 Aggregated data 522
39.7 Hypotheses 523
39.8 Test statistics 524
39.9 Standardised effect size 526
39.10 Decision 528
39.11 Causal interpretation 528
39.12 Beyond the basic report: A short report 529
39.13 Exercises 529
Appendix: Tables 530
Table A The standard normal distribution 530
Table B Critical values of Student’s distributions 533
Table C Random numbers 534
Table F Critical values of F-distributions 536
References 548
Index 559
