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Analysis of Variance and Interaction


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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 5 Observational versus Experimental Studies - Confounding and Causation 6 Experimental Design 7 Choosing the Appropriate Analysis 10 Topic 1.2 Entering Your Own Data in SPSS 14 Defining the Variables 15 Entering the Data 16 Saving the data file 17 Deleting cases and variables. 17 Topic 1.3 Correlation and Regression Revisited 19 Scatterplots 19 Pearson's r and the regression line 21 Significance Testing and the Report 23 Checking the Direction of the Relationship 27 Topic 1.4 Limitations of Hypothesis Testing 30 Significance versus Importance 30 Not Significant versus No Relationship 33 Power Analysis 34 Topic 1.5 The concept of Interaction 39 Topic 1.6 t-tests Revisited 45 Revision 45 Checking the Direction of the Difference 47 Assumptions underlying the independent samples t-test 50 Non-significant t-tests - Power 58 Some terminology 58 Type I and Type II Errors 59 Interaction revisited 60 SECTION 2 THE ANALYSIS OF VARIANCE 64 Topic 2.1 Introduction to the Analysis of Variance - The Single Factor Independent Groups Design 65 Understanding the Basis of the Analysis of Variance 65 Calculating the F-Ratio 69 The Sampling Distribution of F 73 Special Case - Two Treatment Conditions 74 Effect Size 74 Review Exercises for Topic 2.1 75 Topic 2.2 Producing and Reporting a One-Way Analysis of Variance Using SPSS for Windows 77 Using SPSS to Produce ANOVA Tables 77 Power Analysis for Oneway ANOVA 81 Presenting Results 83 Assumptions 89 A Complete Worked Example 90 Review Exercises for Topic 2.2 95 Topic 2.3 Analytical Comparisons in the Single Factor Independent Groups Design 97 Introduction 97 Specifying Comparisons in SPSS 99 Experimentwise Versus Comparisonwise Errors 101 Planned Versus Unplanned Comparisons 102 Performing Post Hoc Tests Using SPSS 105 Presentation of Results 107 A Review Example 110 Review Exercises for Topic 2.3 114 Topic 2.4 The Completely Randomised Factorial Design 117 Advantages of Factorial Designs 118 Main Effects and Interaction 118 Using SPSS to Produce the ANOVA Table for Factorial Designs 122 Interpreting the SPSS Output 127 Reporting Results from a Factorial ANOVA (No Significant Interaction) 128 Reporting Results from a Factorial ANOVA (Significant Interaction) 130 Analytical Comparisons in Factorial Designs 136 Assumptions 144 A Review Example - Significant Interaction 145 A Review Example - No Significant Interaction 149 Review Exercises for Topic 2.4 154 Topic 2.5 Analysis of Variance for the Single Factor Within Subjects Design 156 Techniques for Controlling Nuisance Variables 156 Practice Effects in the Repeated Measures Design 157 Theory Behind the Analysis of Variance for Related Samples Designs 159 Calculating the F-ratio by Hand - A Worked Example 161 Effect Size and Power Analysis 163 The Assumptions for a Within-Subjects Analysis of Variance 164 Using SPSS To Obtain The ANOVA Table 164 Analytical Comparisons for the Single Factor Within Subjects Design 172 A Review Example 176 Review Exercises 183 Topic 2.6 The Mixed Factorial Design 186 Using SPSS to Produce the ANOVA Table for a Mixed Design 186 Interpreting the SPSS Output 190 Report on a Mixed Design ANOVA 191 Further Analyses for Mixed Design ANOVA 192 A Review Example 200 Longitudinal studies involving a Control Group 215 Review Exercises 228 REVISION EXERCISES 232

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