Table of Contents

CONTENTS SECTION 1: Investigating the Relationship Between Two Metric Variables 1 1.1 Introduction 2 1.2 Graphing the Relationship 2 1.2.1 Checking for Bivariate Outliers 2 1.2.2 Describing the Relationship 3 1.2.3 Using SPSS to Produce Scatterplots 7 1.2.4 Further Exercise for Section 1.2 9 1.3 Summarising the Relationship 10 1.3.1 Pearson's Correlation Coefficient - A Measure of Strength 10 1.3.2 The Regression Equation - Summarising the Form of the Relationship 15 1.3.3 Using SPSS to Obtain Regression and Correlation Statistics 19 1.3.4 The Regression Procedure 20 1.3.5 Predictions and Residuals 25 1.3.6 Further Exercises for Section 1.3 26 1.4 Significance Testing and Power Analysis 30 1.4.1 Testing the Significance of Pearson's r 30 1.4.2 Power Analysis 31 1.4.3 Testing for Significance Using the Regression Output 33 1.4.4 Confidence Intervals for the Regression Coefficients 35 1.4.5 Prediction Intervals 37 1.4.6 Further Exercises for Section 1.4 39 1.5 The Theory Behind Simple Linear Regression 44 1.5.1 Sources of Variance 44 1.5.2 The Analysis of Variance Table 49 1.5.3 The Line of "Best Fit" 49 1.5.4 Further Exercises for Section 1.5 50 1.6 Investigating the Assumptions of Regression 52 1.6.1 The Assumptions Underlying Linear Regression 52 1.6.2 Metric Scales and Independence 52 1.6.3 Linearity 52 1.6.4 Equality of Variance 59 1.6.5 Normality 61 1.6.6 Using SPSS to Test the Assumptions 64 1.6.7 Further Examples 65 1.6.8 Further Exercises for Section 1.6 68 1.7 Cautionary Tales 71 1.7.1 Influential Points 71 1.7.2 Range of Independent Variable 73 1.7.3 Effects of Sub-populations 76 1.8 Using Dichotomous Variables in Regression 83 1.9 Summary of Section 1 86 1.10 Revision Exercises for Section 1 86 SECTION 2: Data Screening and Data Transformation 93 2.1 Introduction 94 2.2 Data Selection Techniques 94 2.2.1 Sorting Cases and Deleting Cases 94 2.2.2 Selecting Specific Subgroups 96 2.2.3 Using the Split File Procedure 99 2.3 Data Modification 100 2.3.1 Creating New Variables 100 2.3.2 Recoding Variables 103 2.4 Data Screening 108 2.4.1 Identifying Out of Range Values for Categorical Variables 108 2.4.2 Identifying Out of Range Values for Metric Variables 109 2.4.3 Identifying Outliers 109 2.4.4 Dealing With Out Of Range Values 111 2.4.5 Dealing With Outliers 112 2.4.6 A Step by Step Approach to Data Screening 113 2.5 Transforming Variables 115 2.5.1 Introduction 115 2.5.2 Transforming Variables 115 2.6 Summary of Section 2 130 2.7 Revision Exercises for Section 2 130 SECTION 3: Multiple Regression 131 3.1 Introduction 132 3.2 The Basics of Multiple Regression 132 3.2.1 Using SPSS to Perform a Multiple Regression. 132 3.2.2 Interpreting the SPSS Output 135 3.2.3 Exercises for Section 3.2 138 3.3 Understanding Partial and Part Correlation Coefficients 143 3.3.1 Partial Correlation Coefficients 143 3.3.2 Part Correlation Coefficients 149 3.3.3 Further Exercises for Section 3.3 151 3.4 Selecting and Using Different Regression Strategies 153 3.4.1 The Major Uses of Regression 153 3.4.2 Different Analytical Strategies 153 3.4.3 Producing and Interpreting a Hierarchical Regression 156 3.4.4 Producing and Interpreting a Stepwise Regression 162 3.4.5 Terminology -Mediating Variables 166 3.5 Presentation of Results 169 3.5.1 Identify Hypotheses or Research Questions 169 3.5.2 Exploring the Hypotheses 169 3.5.3 Writing the Report 170 3.5.4 A Further Example 172 3.5.5 Exercises for Section 3.5 176 3.6 Testing Assumptions 178 3.6.1 The Regression Assumptions 178 3.6.2 Testing the Regression Assumptions 179 3.6.3 Exercises for Section 3.6 180 3.7 Other Practical Issues 181 3.7.1 Multicollinearity 181 3.7.2 Limitations on Predictions 181 3.7.3 Have I got Sufficient Data? 181 3.7.4 Screening for Influential Points 181 3.8 Testing for Interactions 182 3.8.1 Interactions Involving One Dichotomous and One Continuous Variable 182 3.8.2 Interactions Involving Two Continuous Variables 187 3.8.3 Cautionary Tales 190 3.9 Summary of Section 3 190 3.10 Revision Exercises for Section 3 191 SECTION 4: Factor Analysis 203 4.1 Some Background Ideas 204 4.2 Steps Involved in a Factor Analysis 210 4.2.1 STEP 1 Evaluate the Data - Is it Suitable for a Factor Analysis? 210 4.2.2 STEP 2 Extract the Factors 211 4.2.3 STEP 3 Decide How Many Factors to Keep 213 4.2.4 STEP 4 The Rotation Phase 216 4.2.5 STEP 5 Interpret The Factors. 221 4.2.6 Oblique Rotations 223 4.3 Using SPSS to Perform a Factor Analysis 227 4.3.1 Using the Menus 227 3.3.2 Using Syntax 230 4.4 Constructing Scales 233 4.4.1 Running the Factor Analysis 233 4.4.2 Interpreting the Factors 238 4.4.3 Creating Factor Scores 240 4.4.4 Revisiting Eigenvalues and Communalities 245 4.5 Refining Your Factor Analysis 249 4.5.1 Methods of Extraction 249 4.5.2 Assessing a Factor Analysis 254 4.5.3 Looking for a Good Factor Solution 255 4.5.4 Factor Analysis Process 264 4.5.5 Interpreting the Factors - Revisited 266 4.5.6 Writing a Report 270 4.6 Review Exercises 275 SECTION 5: Multivariate Analysis of Variance MANOVA 299 5.1 Introduction and Review of ANOVA 300 5.1.1 Introduction 300 5.1.2 General Review of ANOVA 300 5.1.3 Single Factor Between Subjects ANOVA 301 5.1.4 Single Factor Within Subjects ANOVA 304 5.1.5 Summary of Section 5.1 308 5.2 Multivariate Analysis of Variance - Overview 309 5.3 Single Factor Between Subjects MANOVA 310 5.3.1 Introduction 310 5.3.2 Examples 310 5.3.3 Exercises 322 5.4 Practical Issues in MANOVA 331 5.4.1 Assumptions Underlying MANOVA 331 5.4.2 More Detail on the Homogeneity Assumption 331 5.4.3 Screening Your Data 335 5.4.4 Do You Have Sufficient Data? 335 5.5 Single Factor Within Subjects MANOVA 336 5.5.1 Introduction 336 5.5.2 Examples 336 5.5.3 Exercises 345 5.6 Section 5 Review Exercises 357 Solutions to Exercises 371 Appendix A: Sampling Variation in Correlation 459 Appendix B: Power Analysis Tables for Correlation 461 Appendix C: Alternative Follow-up Analyses in MANOVA 462 Index 463