isc ove ring i Statistics sing SPSS

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1 isc ove ring i Statistics sing SPSS S E C O N D! E D I T I O N (and sex, drugs and rock V roll) A N D Y F I E L D Publications London o Thousand Oaks New Delhi

2 CONTENTS Preface How To Use This Book Acknowledgements Dedication Symbols Used in This Book Praise for the First Edition xxi xxv xxix xxxi xxxiii xxxiv 1 Everything You Ever Wanted To Know About Statistics (Well, Sort Of) What Will This Chapter Tell Us? Building Statistical Models Populations and Samples Simple Statistical Models The Mean, Sums of Squares, Variance and Standard Deviations Frequency Distributions Properties of Frequency Distributions The Standard Deviation and the Shape of the Distribution What is The Standard Normal Distribution? Is my Sample Representative of the Population? The Standard Error Confidence Intervals Linear Models How Can We Tell if Our Model Represents the Real World? Test Statistics One- and Two-Tailed Tests Type I and Type II Errors Effect Sizes Statistical Power 33

3 vi Discovering Statistics Using SPSS 1.9. Some Concluding Advice What Have We Discovered about Statistics? Key Terms That We've Discovered Smart Alex's Stats Quiz Further Reading 36 The SPSS Environment What will This Chapter Tell Us? Versions of SPSS Getting Started The Data Editor Entering Data into the Data Editor Creating a Variable The 'Variable View' Creating Coding Variables Types of Variables Missing Values Changing the Column Format Quick Test The Output Viewer The Syntax Window (D Saving Files Retrieving a File What Have We Discovered about Statistics? Key Terms That We've Discovered Smart Alex's Task Further Reading 62 Exploring Data What Will This Chapter Tell Us? Parametric Data Assumptions of Parametric Data Graphing and Screening Data Step 1: Spot the Obvious Mistakes Using Histograms Step 2: Descriptive Statistics and Boxplots Step 3: Correcting problems in the Data Step 4: Transforming the Data using SPSS Exploring Groups of Data Running the Analysis for all Data SPSS Output for all Data Running the Analysis for Different Groups Output for Different Groups Testing whether a Distribution is Normal Doing the Kolmogorov-Smirnov test on SPSS Output from the explore Procedure 94

4 Contents vii 3.6. Testing for Homogeneity of Variance Graphing Means What Have We Discovered about Statistics? Key Terms That We've Discovered Smart Alex's Tasks Further Reading Correlation What Will This Chapter tell Us? How do we Measure Relationships? A Detour into the World of Covariance Standardization and the Correlation Coefficient Data Entry for Correlation Analysis using SPSS Graphing Relationships: the Scatterplot Simple Scatterplot The 3-D Scatterplot Overlay Scatterplot Matrix Scatterplot Bivariate Correlation Pearson's Correlation Coefficient A Word of Warning about Interpretation: Causality Using R 2 for Interpretation Spearman's Correlation Coefficient Kendall's Tau (Non-Parametric) Biserial and Point-Biserial Correlations Partial Correlation The Theory behind Part and Partial Correlation Partial Correlation Using SPSS Semi-Partial (or Part) Correlations How to Report Correlation Coefficients What Have We Discovered about Statistics? Key Terms That We've Discovered Smart Alex's Tasks Further Reading Regression What Will This Chapter tell Us? An Introduction to Regression Some Important Information about Straight Lines The Method of Least Squares Assessing the Goodness-of-Fit: Sums of Squares, R and R Assessing Individual Predictors 150

5 viii Discovering Statistics Using SPSS 5.3. Doing Simple Regression on SPSS Interpreting a Simple Regression Overall Fit of the Model Model Parameters Using the Model Multiple Regression: The Basics An Example of a Multiple Regression Model Sums of Squares, R and R Methods of Regression Hierarchical (Blockwise Entry) Forced Entry Stepwise Methods Choosing a Method How Accurate is my Regression model? Assessing the Regression Model I: Diagnostics Outliers and Residuals Influential Cases A Final Comment on Diagnostic Statistics Assessing the Regression Model II: Generalization Checking Assumptions Cross-Validation of the Model (D Sample Size in Regression Multicollinearity How to Do Multiple Regression Using SPSS Main Options Statistics Regression Plots Saving Regression Diagnostics Further Options Interpreting Multiple Regression Descriptives 7S Summary of Model Model Parameters Excluded Variables Assessing the Assumption of No Multicollinearity Casewise Diagnostics Checking Assumptions How to Report Multiple Regression Categorical Predictors and Multiple Regression Dummy Coding SPSS Output for Dummy Variables What Have We Discovered about Statistics? 215

6 Contents ix Key Terms That We've Discovered Smart Alex's Tasks Further Reading Logistic Regression What Will This Chapter tell Us? Background to Logistic Regression What Are the Principles behind Logistic Regression? J.7. Assessing the Model: The Log-Likelihood Statistic Assessing the Model: R and R Assessing the Contribution of Predictors: The Wald Statistic Exp b Methods of Logistic Regression The Forced Entry Method Stepwise Methods How do We Select a Method? Running the Analysis: A Research Example The Main Analysis Method of Regression Categorical Predictors Obtaining Residuals Further Options Interpreting Logistic Regression The Initial Model Step 1: False Belief Understanding Listing Predicted Probabilities Interpreting Residuals Calculating the Effect Size How to Report Logistic Regression Another Example /. Running the Analysis: Block Entry Regression Interpreting Output Testing for Multicollinearity Things that can go wrong Incomplete Information from the Predictors Complete Separation What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading Comparing Two Means What Will This Chapter tell Us? Revision of Experimental Research 270

7 x Discovering Statistics Using SPSS Two Methods of Data Collection Two Types of Variation Randomization Inputting Data and Displaying Means with Error Bar Charts J.7. Error Bar Graphs for Between-Group Designs Error Bar Graphs for Repeated-Measures Designs Step 1: Calculate the Mean for each Participant Step 2: Calculate the Grand Mean Step 3: Calculate the Adjustment Factor Step 4: Create Adjusted Values for each Variable Drawing the Error Bar Graph Testing Differences between Means: The /-Test Rationale for the t-test Assumptions of the t-test The Dependent f-test Sampling Distributions and the Standard Error The Dependent t-test Equation Explained Dependent t-tests Using SPSS Output from the Dependent t-test Calculating the Effect Size Reporting the Dependent t-test The Independent f-test The Independent t-test Equation Explained The Independent t-test Using SPSS Output from the Independent t-test Calculating the Effect Size Reporting the Independent t-test Between Groups or Repeated Measures? The f-test as a General Linear Model What If Our Data Are Not Normally Distributed? What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading 308 Comparing Several Means: ANOVA (GLM 1) What Will This Chapter Tell Us? The Theory Behind ANOVA Inflated Error Rates ANOVA as Regression Logic of the F-Ratio Total Sum of Squares (SS T ) Model Sum of Squares (SS M ) 320

8 Contents xi Residual Sum of Squares (SS R ) Mean Squares The F-Ratio Assumptions of ANOVA Planned Contrasts Choosing which Contrasts to Do Defining Contrasts Using Weights Non-Orthogonal Comparisons Standard Contrasts Polynomial Contrasts: Trend Analysis Post Hoc Procedures Post Hoc Procedures and Type I (a) and Type II Error Rates Post Hoc procedures and Violations of Test Assumptions Summary of Post Hoc Procedures Running One-Way ANOVA on SPSS Planned Comparisons Using SPSS Post Hoc Tests in SPSS Options Output from One-Way ANOVA Output for the Main Analysis Output for Planned Comparisons Output for Post Hoc Tests Calculating the Effect Size Reporting Results from One-Way Independent ANOVA Violations of Assumptions in One-Way Independent ANOVA What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading 362 Analysis of Covariance, ANCOVA (GLM 2) What Will This Chapter Tell Us? What is ANCOVA? Conducting ANCOVA on SPSS J.7. Inputting Data Main Analysis Contrasts and Other Options Interpreting the Output from ANCOVA Main Analysis Contrasts Interpreting the Covariate ANCOVA Run as a Multiple Regression 375

9 xii Discovering Statistics Using SPSS 9.6. Additional Assumptions in ANCOVA Homogeneity of Regression Slopes Testing for Homogeneity of Regression Slopes in SPSS Calculating the Effect Size Reporting Results What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading Factorial ANOVA (GLM 3) What Will This Chapter Tell Us? Theory of Factorial ANOVA (Between Groups) Factorial Designs An Example with Two Independent Variables Total Sum of Squares (SS T ) The Model Sum of Squares (SSJ The Main Effect of Gender (SS A ) The Main Effect of Alcohol (SS B ) The Interaction Effect (SS AxB )@ The Residual Sum of Squares (SS R ) The F-ratios Factorial ANOVA Using SPSS Entering the Data and Accessing the Main Dialog Box Custom Models J Graphing Interactions Contrasts Post Hoc Tests Options Output from Factorial ANOVA Output for the Preliminary Analysis Levene'sTest The Main ANOVA Table Contrasts Post Hoc Analysis Interpreting Interaction Graphs Calculating Effect Sizes Reporting the Results of Two-Way ANOVA Factorial ANOVA as Regression What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading 426

10 Contents xiii 11 Repeated-Measures Designs (GLM 4) What Will This Chapter Tell Us? Introduction to Repeated-Measures Designs The Assumption of Sphericity How is Sphericity Measured? Assessing the Severity of Departures from Sphericity What is the Effect of Violating the Assumption of Sphericity? What Do We Do If We Violate Sphericity? Theory of One-Way Repeated-Measures ANOVA The Total Sum of Squares (SS T ) The Within-Participant (SS W ) The Model Sum of Squares (SSJ The Residual Sum of Squares (SS R ) The Mean Squares The F-Ratio One-Way Repeated-Measures ANOVA Using SPSS The Main Analysis Defining Contrasts for Repeated Measures Post Hoc Tests and Additional Options Output for One-Way Repeated-Measures ANOVA Descriptives and other Diagnostics Assessing and Correcting for Sphericity The Main ANOVA Contrasts Post Hoc Tests Effect Sizes for Repeated-Measures ANOVA Reporting One-Way Repeated-Measures ANOVA Repeated Measures with Several Independent Variables The Main Analysis Contrasts Graphing Interactions Other Options Output for Factorial Repeated-Measures ANOVA Descriptives and Main Analysis The Effect of Drink The Effect of Imagery The Interaction Effect (Drink X Imagery) Contrasts for Repeated-Measures Variables Beer vs. Water, Positive vs. Neutral Imagery Beer vs. Water, Negative vs. Neutral Imagery Wine vs. Water, Positive vs. Neutral Imagery Wine vs. Water, Negative vs. Neutral Imagery Limitations of These Contrasts 478

11 xiv Discovering Statistics Using SPSS Effect Sizes for Factorial Repeated-Measures ANOVA Reporting the Results from Factorial Repeated- Measures ANOVA What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading Mixed Design ANOVA (GLM 5) What Will This Chapter Tell Us? What do Men and Women Look for in a Partner? Mixed ANOVA on SPSS The Main Analysis Other Options Output for Mixed Factorial ANOVA: Main Analysis The Effect of Gender The Effect of Looks The Effect of Charisma The Interaction between Gender and Looks Looks x Gender Interaction 1: Attractive vs. Average, Male vs. Female Looks x Gender Interaction 2: Ugly vs. Average, Male vs. Female The Interaction between Gender and Charisma Charisma X Gender Interaction 1: High vs. Some Charisma, Male vs. Female Charisma x Gender Interaction 2: Dullard vs. Some Charisma, Male vs. Female The Interaction between Attractiveness and Charisma Looks x Charisma Interaction 1: Attractive vs. Average, High Charisma vs. Some Charisma Looks x Charisma Interaction 2: Attractive vs. Average, Dullard vs. Some Looks x Charisma Interaction 3: Ugly vs. Average, High Charisma vs. Some Charisma Looks x Charisma Interaction 4: Ugly vs. Average, Dullard vs. Some Charisma The Interaction between Looks, Charisma and Gender Looks x Charisma x Gender Interaction 1: Attractive vs. Average, High Charisma vs. Some Charisma, Male vs. Female Looks x Charisma x Gender Interaction 2: Attractive vs. Average, Dullard vs. Some Charisma, Male vs. Female 510

12 Contents xv Looks x Charisma x Gender Interaction 3: Ugly vs. Average, High Charisma vs. Some Charisma, Males vs. Females Looks x Charisma x Gender Interaction 4: Ugly vs. Average, Dullard vs. Some Charisma, Male vs. Female Conclusions Calculating Effect Sizes Reporting the Results of Mixed ANOVA What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading Non-parametric Tests What Will This Chapter Tell Us? Comparing Two Independent Conditions: The Wilcoxon Rank-Sum Test and Mann-Whitney Test Theory Inputting Data and Provisional Analysis Running the Analysis Output from the Mann-Whitney Test Calculating an Effect Size Writing the Results Comparing Two Related Conditions: The Wilcoxon Signed-Rank Test Theory of Wilcoxon's Signed-Rank Test Running the Analysis Output for the Ecstasy Group Output for the Alcohol Group Calculating an Effect Size Writing and Interpreting the Results Differences between Several Independent Groups: The Kruskal-Wallis Test Theory of the Kruskal-Wallis Test Inputting Data and Provisional Analysis Doing the Kruskal-Wallis Test on SPSS Output from the Kruskal-Wallis Test Post Hoc Tests for the Kruskal-Wallis Test Testing for Trends: The Jonckheere-Terpstra Test Calculating an Effect Size Writing and Interpreting the Results Differences between Several Related Groups: Friedman's ANOVA Theory of Friedman's ANOVA Inputting Data and Provisional Analysis 560

13 xvi Discovering Statistics Using SPSS Doing Friedman's ANOVA on SPSS Output from Friedman's ANOVA Post Hoc Tests for Friedman's ANOVA Calculating an Effect Size Writing and Interpreting the Results What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading Multivariate Analysis of Variance (MANOVA) What Will This Chapter tell Us? Introduction: Similarities and Differences to ANOVA Words of Warning Current Controversies The Example for this Chapter Theory of MANOVA Introduction to Matrices Some Important Matrices and their Functions Calculating MANOVA by Hand: A Worked Example Univariate ANOVA for DV 1 (Actions) Univariate ANOVA for DV 2 (Thoughts) The Relationship between DVs: Cross-Products The Total SSCP Matrix (T) The Residual SSCP Matrix (E) The Model SSCP Matrix (H) Principle of the MANOVA Test Statistic Discriminant Function Variates Pillai-Bartlett Trace (V) Hotelling's T Wilks's Lambda (A) Roy's Largest Root Assumptions of MANOVA Checking Assumptions Choosing a Test Statistic Follow-Up Analysis MANOVA on SPSS The Main Analysis Multiple Comparisons in MANOVA Additional Options Output from MANOVA Preliminary Analysis and Testing Assumptions MANOVA Test Statistics Univariate Test Statistics 600

14 Contents xvii SSCP Matrices Contrasts Following Up MANOVA with Discriminant Analysis Output from the Discriminant Analysis Some Final Remarks The Final Interpretation Univariate ANOVA or Discriminant Analysis? What Have We discovered About Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading Exploratory Factor Analysis What Will This Chapter Tell Us? Factors Graphical Representation of Factors Mathematical Representation of Factors Factor Scores The Regression Method Other Methods Uses of Factor Scores Discovering Factors Choosing a Method Communality Factor Analysis vs. Principal Component Analysis Theory behind Principal Component Analysis Factor Extraction: Eigenvalues and the Scree Plot Improving Interpretation: Factor Rotation Choosing a Method of Factor Rotation Substantive Importance of Factor Loadings Research Example Initial Considerations Sample Size Data Screening Running the Analysis Factor Extraction on SPSS Rotation Scores Options Interpreting Output from SPSS Preliminary Analysis Factor Extraction Factor Rotation 659

15 xviii Discovering Statistics Using SPSS Orthogonal Rotation (Varimax) Oblique Rotation Factor Scores Summary Reliability Analysis Measures of Reliability Interpreting Cronbach's a (some cautionary tales...) Reliability Analysis on SPSS Interpreting the Output What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Task Further Reading Categorical Data What Will This Chapter Tell Us? Theory of Analysing Categorical Data Pearson's Chi-Square Test The Likelihood Ratio Yates's Correction Assumptions of the Chi-Square Test Doing Chi-Square on SPSS Entering Data: Raw Scores Entering Data: Weight Cases Running the Analysis Output for the Chi-Square Test Calculating an Effect Size Reporting the Results of Chi-Square Several Categorical Variables: Log Linear Analysis Chi-Square as Regression LogLinear Analysis Assumptions in Loglinear Analysis Loglinear Analysis Using SPSS Initial Considerations The Loglinear Analysis Output from Loglinear Analysis Following up Loglinear Analysis Effect Sizes in Loglinear Analysis Reporting the Results of Loglinear Analysis What Have We Discovered about Statistics? Key Terms that We've Discovered Smart Alex's Tasks Further Reading 720

16 Contents xix 17 Epilogue 721 Glossary 723 Appendix 751 A. 1. Table of the Standard Normal Distribution 751 A.2. Critical Values of the r-distribution 755 A.3. Critical Values of the F-Distribution 756 A.4. Critical Values of the Chi-Square Distribution 760 A.5. The Welch F-Test 760 A.6. Calculating Simple Effects 760 A.7. Jonckheere's Trend Test 760 A.8. Chapter A.9. Calculation of Factor Score Coefficients 761 References 762 Index 771