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Building On The Foundations Of Statistics

This Pearson Original is published for Swinburne University
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Table of Contents

INTRODUCTION 1 SECTION 1 EXTENDING BEYOND THE BASICS OF HYPOTHESIS TESTING 1 Topic 1.1 Review of Concepts 1 Populations and Samples 1 Hypothesis Testing - The Mechanics 2 The 95% Confidence Interval 6 Observational versus Experimental Studies - Confounding and Causation 7 Experimental Design 8 Choosing the Appropriate Analysis 11 Topic 1.2 Entering Your Own Data in SPSS 15 Defining the Variables 16 Entering the Data 17 Saving the data file 18 Deleting cases and variables. 18 Topic 1.3 Correlation and Regression Revisited 20 Scatterplots 20 Pearson's r and the Regression Line 22 Linear Regression 27 Writing Reports 30 Checking the Direction of the Relationship 33 Topic 1.4 Limitations of Hypothesis Testing 36 Significance versus Importance 36 Not Significant versus No Relationship 39 Power Analysis 40 Topic 1.5 Using Dichotomous Variables in Regression 45 Topic 1.6 The Concept of Interaction 47 SECTION 2 MULTIPLE REGRESSION 53 Topic 2.1 The Basics of Multiple Regression 53 Using SPSS to Perform a Multiple Regression 53 Interpreting the SPSS Output 56 Review Exercises for Topic 2.1 Solutions on page 331 62 Topic 2.2 Understanding Part and Partial Correlation Coefficients 64 Partial Correlation Coefficients 64 Part Correlation Coefficients 69 Terminology - Mediating Variables 72 Review Exercises for Topic 2.2 Solutions on page 333 75 Topic 2.3 Presentation of Results 78 Identifying Hypotheses or Research Questions 78 Exploring the Output 78 Writing the Report 80 Topic 2.4 Testing Assumptions for Regression 84 The Regression Assumptions 84 Testing the Assumptions 84 Producing the Graphs for Assumption Testing 91 Topic 2.5 Other Practical Issues 92 Multicollinearity 92 Limitations on Predictions 92 Have I got Sufficient Data? 92 Topic 2.6 Testing for Interactions 93 Interactions Involving one Dichotomous and one Continuous Variable 93 Interactions Involving Two Continuous Variables 96 Topic 2.7 Different Regression Strategies 100 The Major Uses of Regression 100 Different Analytical Strategies 100 Section 2 Revision Exercises Solutions on page 341 102 SECTION 3 THE ANALYSIS OF VARIANCE 107 Topic 3.1 t-tests Revisited 107 Checking the Direction of the Difference 109 Assumptions underlying the independent samples t-test 112 Non-significant t-tests - Power 120 Some terminology 120 Type I and Type II Errors 121 Topic 3.2 Revision of Variance 122 Topic 3.3 Introduction to the Analysis of Variance - The Single Factor Independent Groups Design 123 Understanding the Basis of the Analysis of Variance 123 Calculating the F-Ratio 127 The Sampling Distribution of F 131 Special Case - Two Treatment Conditions 132 Effect Size 132 Review Exercises for Topic 3.3 Solutions on page 348 133 Topic 3.4 Producing and Reporting a One-Way Analysis of Variance Using SPSS for Windows 135 Using SPSS to Produce ANOVA Tables 135 Power Analysis for One-way ANOVA 139 Presenting Results 141 Assumptions 147 A Complete Worked Example 148 Review Exercises for Topic 3.4 Solutions on page 353 153 Topic 3.5 Analytical Comparisons in the Single Factor Independent Groups Design 155 Introduction 155 Specifying Comparisons in SPSS 157 Experimentwise Versus Comparisonwise Errors 159 Planned Versus Unplanned Comparisons 160 Performing Post Hoc Tests Using SPSS 163 Presentation of Results 165 A Review Example 168 Review Exercises for Topic 3.5 Solutions on page 358 173 Topic 3.6 Completely Randomised Factorial Design ANOVA 177 Advantages of Factorial Designs 178 Main Effects and Interaction 178 Using SPSS to Produce the ANOVA Table for Factorial Designs 182 Interpreting the SPSS Output 187 Reporting Results from a Factorial ANOVA (No Significant Interaction) 188 Reporting Results from a Factorial ANOVA (Significant Interaction) 190 Analytical Comparisons in Factorial Designs 196 Assumptions 204 A Review Example - Significant Interaction 205 A Review Example - No Significant Interaction 209 Review Exercises for Topic 3.6 215 Topic 3.7 Analysis of Variance for the Single Factor Within Subjects Design 218 Techniques for Controlling Nuisance Variables 218 Practice Effects in the Repeated Measures Design 219 Theory Behind the Analysis of Variance for Related Samples Designs 221 Calculating the F-ratio by Hand - A Worked Example 223 Effect Size and Power Analysis 225 The Assumptions for a Within-Subjects Analysis of Variance 226 Using SPSS to Obtain the ANOVA Table 226 Analytical Comparisons for the Single Factor Within Subjects Design 234 A Review Example 238 Review Exercises Solutions on page 379 245 Topic 3.8 Mixed Factorial Design ANOVA 248 Using SPSS to Produce the ANOVA Table for a Mixed Design 248 Interpreting the SPSS Output 252 Report on a Mixed Design ANOVA 253 Further Analyses for Mixed Design ANOVA 254 A Review Example 262 Longitudinal studies involving a Control Group 280 Review Exercises for Topic 3.8 Solutions on page 391 293 Section 3 Revision Exercises Solutions on page 393 297 APPENDIX A: Solutions to Exercises 317 APPENDIX B: Power Analysis Tables for Correlation 405 APPENDIX C: Power Analysis Tables for ANOVA 407 APPENDIX D: SPSS Revision Instructions 415 Index 423

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