The aim of this book is to provide clear guidelines to both the execution of specific statistical tests and the interpretation of the findings by
(1) explaining clearly the purpose of specific tests and the research designs for which they are relevant,
(2) demonstrating clearly the instructions for executing univariate and multivariate statistical tests, and
(3) explaining how obtained results should be interpreted.
1 Inferential Statistics and Test Selection...................................... 111.3.4.3 Identifying Independent Relationship .................201
12 Factor Analysis ........................................................................... 203
12.1 Aim .............................................................................................................203
12.1.1 Computation of the Correlation Matrix ...............................204
12.1.2 Extraction of Initial Factors ....................................................204
12.1.2.1 Method of Extraction ..............................................204
12.1.2.2 Determining the Number of Factors to Be
Extracted ...................................................................204
12.1.3 Rotation of Extracted Factors .................................................205
12.1.4 Rotation Methods .....................................................................205
12.1.5 Orthogonal vs. Oblique Rotation...........................................206
12.1.6 Number of Factor Analysis Runs ..........................................206
12.1.7 Interpreting Factors..................................................................207
12.2 Checklist of Requirements ......................................................................207
12.3 Assumptions..............................................................................................208
12.3.1 Statistical Assumptions............................................................208
12.3.2 Conceptual Assumptions ........................................................208
12.4 Factor Analysis: Example 1.....................................................................208
12.4.1 Data Entry Format....................................................................209
12.4.2 Windows Method.....................................................................210
12.4.3 SPSS Syntax Method................................................................214
12.4.4 SPSS Output ..............................................................................214
12.4.5 Results and Interpretation ......................................................218
12.4.5.1 Correlation Matrix ...................................................218
12.4.5.2 Factor Analysis Output...........................................219
12.5 Factor Analysis: Example 2.....................................................................221
12.5.1 Data Entry Format....................................................................222
12.5.2 Windows Method (First Run) ................................................222
12.5.3 SPSS Syntax Method (First Run) ...........................................226
12.5.4 SPSS Output ..............................................................................226
12.5.5 Results and Interpretation ......................................................232
12.5.5.1 Correlation Matrix ...................................................232
12.5.5.2 Factor Analysis Output...........................................232
12.5.6 Windows Method (Second Run)............................................233
12.5.7 SPSS Syntax Method (Second Run).......................................236
12.5.8 SPSS Output ..............................................................................236
12.5.9 Results and Interpretation ......................................................238
13 Reliability.................................................................................... 239
13.1 Aim .............................................................................................................239
13.1.1 External Consistency Procedures...........................................239
13.1.2 Internal Consistency Procedures ...........................................239
13.2 Example — Reliability .............................................................................240
13.2.1 Windows Method.....................................................................240
13.2.2 SPSS Syntax Method................................................................242
13.2.3 SPSS Output ..............................................................................243
13.2.4 Results and Interpretation ......................................................243
14 Multiple Regression................................................................... 245
14.1 Aim .............................................................................................................245
14.2 Types of Multiple Regression Method..................................................245
14.2.1 Standard Multiple Regression................................................245
14.2.2 Hierarchical Multiple Regression ..........................................246
14.2.3 Statistical (Stepwise) Regression............................................246
14.3 Checklist of Requirements ......................................................................247
14.4 Assumptions..............................................................................................248
14.5 Multicollinearity .......................................................................................248
14.6 Example 1 — Prediction Equation and Identification of
Independent Relationships (Forward Entry of Predictor
Variables)....................................................................................................249
14.6.1 Windows Method.....................................................................250
14.6.2 SPSS Syntax Method................................................................254
14.6.3 SPSS Output ..............................................................................255
14.6.4 Results and Interpretation ......................................................257
14.6.4.1 Prediction Equation (Predicting the Level
of Responsibility from the Three Defense
Strategies of PROVOKE, SELFDEF, and
INSANITY) ...............................................................257
14.6.4.2 Evaluating the Strength of the Prediction
Equation ....................................................................258
14.6.4.3 Identifying Multicollinearity .................................258
14.6.4.4 Identifying Independent Relationships ...............258
14.7 Example 2 — Hierarchical Regression..................................................259
14.7.1 Windows Method.....................................................................260
14.7.2 SPSS Syntax Method................................................................263
14.7.3 SPSS Output ..............................................................................264
14.7.4 Results and Interpretation ......................................................266
14.8 Example 3 — Path Analysis ...................................................................267
14.8.1 Windows Method.....................................................................268
14.8.2 SPSS Syntax Method................................................................272
14.8.3 SPSS Output ..............................................................................273
14.8.4 Results and Interpretation ......................................................278
15 Structural Equation Modeling .................................................. 281
15.1 What Is Structural Equation Modeling?...............................................281
15.2 The Role of Theory in SEM ....................................................................283
15.3 The Structural Equation Model..............................................................283
15.4 Goodness-of-Fit Criteria ..........................................................................284
15.4.1 Absolute Fit Measures .............................................................284
15.4.2 Incremental Fit Measures........................................................285
15.4.3 Parsimonious Fit Measures.....................................................286
15.4.4 Note of Caution in the Use of Incremental Fit
Indices as “Rules of Thumb” .................................................286
15.5 Model Assessment....................................................................................287
15.6 Improving Model Fit................................................................................288
15.6.1 Modification Indices ................................................................288
15.6.2 Correlated Errors ......................................................................289
15.7 Checklist of Requirements ......................................................................289
15.8 Assumptions..............................................................................................291
15.9 Examples of Structural Equation Modeling.........................................291
15.10 Example 1: Linear Regression with Observed Variables...................292
15.10.1 Data Entry Format....................................................................293
15.10.2 Modeling in Amos Graphics ..................................................293
15.10.3 Results and Interpretation ......................................................296
15.10.3.1 Regression Weights, Standardized
Regression Weights, and Squared Multiple
Correlations ..............................................................297
15.11 Example 2: Regression with Unobserved (Latent) Variables............299
15.11.1 Results and Interpretation ......................................................300
15.11.1.1 Regression Weights, Standardized
Regression Weights, and Squared Multiple
Correlations ..............................................................301
15.11.1.2 Comparing the Latent-Construct Model
(Example 2) with the Observed-Measurement
Model (Example 1) ..................................................303
15.12 Example 3: Multimodel Path Analysis with Latent Variables..........303
15.12.1 Evaluation of the Measurement Model: Confirmatory
Factor Analysis (CFA)..............................................................304
15.12.2 Results and Interpretation ......................................................306
15.12.2.1 Regression Weights and Standardized
Regression Weights .................................................308
15.12.3 The Modified Model ................................................................310
15.12.4 Comparing the Original (Default) Model against the
Modified Model ........................................................................310
15.12.5 Multimodel Analysis: Evaluation of the Direct Path
Model vs. the Indirect Path Model........................................ 311
15.12.6 Defining the Direct and Indirect Models .............................314
15.12.7 Results and Interpretion..........................................................316
15.12.7.1 Goodness-of-Fit Comparison: Direct Model
vs. Indirect Model....................................................317
15.12.7.2 Regression Weights, Standardized
Regression Weights, and Squared Multiple
Correlations ..............................................................319
15.12.7.3 Explained Variances and Residual
Variances ...................................................................320
15.13 Example 4: Multigroup Analysis ...........................................................321
15.13.1 Multigroup Confirmatory Factor Analysis ..........................321
15.13.1.1 Conducting Multigroup Modeling for
Males and Females: The Measurement
Model.........................................................................321
15.13.1.2 Results and Interpretation......................................331
15.13.2 Multigroup Path Analysis.......................................................337
15.13.2.1 Conducting Multigroup Modeling for
Males and Females: The Path Model ...................338
15.13.2.2 Results and Interpretation......................................348
16 Nonpa rametric Tests .................................................................. 357
16.1 Aim .............................................................................................................357
16.2 Chi-Sq uare (χ2) Test for Single-Variable Experiments........................358
16.2.1 Assumptions..............................................................................358
16.2.2 Example 1 — Equal Expected Frequencies..........................358
16.2.2.1 Data Entry Format...................................................358
16.2.2.2 Windows Method ....................................................359
16.2.2.3 SPSS Syntax Method ...............................................360
16.2.2.4 SPSS Output .............................................................360
16.2.2.5 Results and Interpretation......................................360
16.2.3 Example 2 — Unequal Expected Frequencies.....................360
16.2.3.1 Windows Method ....................................................361
16.2.3.2 SPSS Syntax Method ...............................................362
16.2.3.3 SPSS Output .............................................................362
16.2.3.4 Results and Interpretation......................................363
16.3 Chi-Sq uare (χ2) Test of Independence between Two Variables ........363
16.3.1 Assumptions..............................................................................363
16.3.2 Windows Method.....................................................................363
16.3.3 SPSS Syntax Method................................................................366
16.3.4 SPSS Output .............................................................................367
16.3.5 Results and Interpretation ......................................................367
16.4 Mann– Whitney U Test for Two Independent Samples......................368
16.4.1 Assumptions..............................................................................368
16.4.2 Data Entry Format....................................................................369
16.4.3 Windows Method.....................................................................369
16.4.4 SPSS Syntax Method................................................................371
16.4.5 SPSS Output ..............................................................................371
16.4.6 Results and Interpretation ......................................................372
16.5 Kruska l–Wallis Test for Several Independent Samples......................372
16.5.1 Assumptions..............................................................................372
16.5.2 Data Entry Format....................................................................373
16.5.3 Windows Method.....................................................................373
16.5.4 SPSS Syntax Method................................................................375
16.5.5 SPSS Output ..............................................................................375
16.5.6 Results and Interpretation ......................................................375
16.6 Wilcoxon Signed Ranks Test for Two Related Samples.....................375
16.6.1 Assumptions..............................................................................376
16.6.2 Data Entry Format....................................................................376
16.6.3 Windows Method.....................................................................376
16.6.4 SPSS Syntax Method................................................................377
16.6.5 SPSS Output .............................................................................378
16.6.6 Results and Interpretation ......................................................378
16.7 Friedman Test for Several Related Samples.........................................378
16.7.1 Assumptions..............................................................................379
16.7.2 Data Entry Format....................................................................379
16.7.3 Windows Method.....................................................................379
16.7.4 SPSS Syntax Method................................................................380
16.7.5 SPSS Output ..............................................................................381
16.7.6 Results and Interpretation ......................................................381
(END)