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Contents Preface Acknowledgements Chapter 1. Review of Basic Concepts 1.1 Introduction 1.2 A Simple Example of a Research Problem 1.3 Discrepancies between Real versus Ideal Research Situations 1.4 Samples and Populations 1.5 Descriptive versus Inferential Uses of Statistics 1.6 Levels of Measurement and Types of Variables 1.7 The Normal Distribution 1.8 Design Terminology 1.9 Parametric versus Nonparametric Statistics 1.10 Additional Implicit Assumptions 1.11 Selection of an Appropriate Bivariate Analysis 1.12 Summary Chapter 2. Review of Basic Statistics, Sampling Error, and Confidence Intervals 2.1 Introduction 2.2 Research Example: Description of a Sample of Heart Rate Scores 2.3 Sample Mean (M) 2.4 Sum of Squared Deviations (SS) and the Sample Variance (s2) 2.5 Degrees of Freedom (df) for a Sample Variance 2.6 Why is there Variance? 2.7 Sample Standard Deviation (s) 2.8 Assessment of Location of a Single X Score Relative to a Distribution of Scores 2.9 A Shift in Level of Analysis: The Distribution of Values of M Across Many Samples from the Same Population 2.10 An Index of Amount of Sampling Error: The Standard Error of the Mean (?M) 2.11 Effect of Sample Size (N) on the Magnitude of the Standard Error (?M ) 2.12 Sample Estimate of Standard Error of the Mean (SEM) 2.13 The Family of t Distributions 2.14 Confidence Intervals for Estimation of a Population Mean from a Sample Mean 2.14.1 The General Form of a Confidence Interval(CI) 2.14.2 Setting up a CI for M when ? is known 2.14.3 Setting up a CI for or M when? ? is not known 2.14. Reporting Confidence Intervals 2.15 Summary Chapter 3. Statistical Significance Testing 3.1 The Logic of Null Hypothesis Significance Tests (NHST) 3.2 Type I versus Type II error 3.3 Formal NHST Procedures: The z test for a Null Hypothesis about One Population Mean 3.3.1 Obtaining a Random Sample from the Population of Interest 3.3.2 Formulating a Null Hypothesis (Ho) 3.3.3 Formulating an Alternative Hypothesis (H1) 3.3.4 Choosing a nominal ???level 3.3.5 Determining the range of z scores used to reject Ho 3.3.6 Determining the range of values of M used to reject Ho 3.3.7 Reporting an exact p value 3.4 Common Research Practices Inconsistent with Assumptions and Rules for NHST 3.4.1 Use of Convenience Samples 3.4.2 Modification of Decision Rules After Initial Decision 3.4.3 Conducting Large Numbers of Significance Tests 3.4.4 Impact of Violations of Assumptions on Risk of Type I error 3.5 Strategies to Limit Risk of Type I error 3.5.1 Use of Random and Representative Samples 3.5.2 Adherence to the Rules for NHST 3.5.3 Limit the Number of Significance Tests 3.5.4 Bonferroni Corrected Per Comparison ? 3.5.5 Replication of Outcome in New Samples 3.5.6 Cross Validation 3.6 Interpretation of Results 3.6.1 Interpretation of Null Results 3.6.2 Interpretation of Statistically Significant Results 3.7 When Is a t test Used Instead of a z Test? 3.8 Effect Size 3.8.1. Evaluation of ?Practical? (versus Statistical) significance 3.8.2 Unit Free Index of Magnitude of Difference: Cohen?s d 3.9 Statistical Power Analysis 3.10 Numerical Results for a One Sample t test Obtained from SPSS 3.11 Guidelines for Reporting Results 3.12 Summary 3.12.1 Logical Problems with NHST 3.12.2 Other Applications of the t Ratio 3.12.3 What does it mean to say ?p < .05?? Chapter 4. Preliminary Data Screening 4.1 Introduction: Problems in Real Data 4.2 Quality Control during Data Collection 4.3 Example of an SPSS Data Worksheet 4.4 Identification of Errors and Inconsistencies 4.5 Missing Values 4.6 Empirical Examples of Data Screening for Individual Variables 4.6.1 Frequency Distribution Tables 4.6.2 Removal of Impossible or Extreme Scores 4.6.3 Bar Chart for a Categorical Variable 4.6.4 Histogram for a Quantitative Variable 4.7 Identification and Handling of Outliers 4.8 Screening Data for Bivariate Analyses 4.8.1 Bivariate Data Screening for Two Categorical Variables 4.8.2 Bivariate Data Screening for One Categorical and One Quantitative Variable 4.8.3 Bivariate Data Screening for Two Quantitative Variables 4.9 Nonlinear Relations 4.10 Data Transformations 4.11 Verifying that Remedies had Desired Effects 4.12 Multivariate Data Screening 4.13 Reporting Preliminary Data Screening 4.14 Summary and Checklist for Data Screening Chapter 5. Comparing Group Means Using the Independent Samples t Test 5.1 Research Situations where the Independent Samples t Test is Used 5.2 A Hypothetical Research Example 5.3 Assumptions about Scores on the Dependent Variable 5.3.1 Quantitative, Approximately Normally Distributed 5.3.2 Equal Variances of Scores Across Groups 5.3.3 Independent Observations both Between and Within Groups 5.3.4 Consequences of Violations of Assumptions 5.4 Preliminary Data Screening 5.5 Issues in Designing a Study 5.6 Formulas for the Independent Samples t Test 5.6.1 The Pooled Variances t Test 5.6.2 Computation of the Separate Variances t test and Adjusted df 5.6.3 Evaluation of Statistical Significance of a t Ratio 5.6.4 Confidence Interval around M1?M2 5.7 Conceptual Basis: Factors that Affect the Size of the t Ratio 5.7.1 Design Decisions that Affect Difference between Group Means, M1?M2 5.7.2 Design Decisions that Affect Within Group Variance, sp2 5.7.3 Design Decisions about Sample Sizes, n1 and n2 5.7.4 Summary: Factors that Influence the Size of t 5.8 Effect Size Indexes for t 5.8.1 Eta Squared (?2) 5.8.2 Cohen?s d 5.8.3 Point Biserial r (rpb) 5.9 Statistical Power and Decisions about Sample Size for the Independent Samples t Test 5.10 Describing the Nature of the Outcome 5.11 SPSS Output and Model Results Section 5.12 Summary Chapter 6. One Way Between S Analysis of Variance 6.1 Research Situations Where One Way Between S ANOVA is Used 6.2 Hypothetical Research Example 6.3 Assumptions about Scores on Dependent Variable for One Way Between S ANOVA 6.4 Issues in Planning a Study 6.5 Data Screening 6.6 Partition of Scores into Components 6.7 Computations for One Way Between S ANOVA 6.7.1 Comparison between Independent Samples t Test and One Way Between S ANOVA 6.7.2 Summarizing Information about Distances Between Group Means: Computing MSbetween 6.7.3 Summarizing Information about Variability of Scores Within Groups: Computing MSwithin 6.7.4 The F Ratio: Comparing MSbetween to MSwithin 6.7.5 Patterns of Scores Related to the Magnitudes of MSbetween and MSwithin 6.7.6 Expected Value of F When Ho is True 6.7.7 Confidence Intervals for Group Means 6.8 Effect Size Index for One Way Between S ANOVA 6.9 Statistical Power Analysis for One Way Between S ANOVA 6.10 Nature of Differences Among Group Means 6.10.1 Planned Contrasts 6.10.2 Post Hoc or ?Protected? Tests 6.11 SPSS Output and Model Results Section 6.12 Summary Chapter 7. Bivariate Pearson Correlation 7.1 Research Situations where Pearson r is Used 7.2 Hypothetical Research Example 7.3 Assumptions for Pearson r 7.4 Preliminary Data Screening 7.5 Design Issues in Planning Correlation Research 7.6 Computation of Pearson r 7.7 Statistical Significance Tests for Pearson r 7.7.1 Testing the Hypothesis that ?xy = 0 7.7.2 Testing Other Hypotheses about ?xy 7.7.3 Assessing Differences Between Correlations 7.7.4 Reporting Many Correlations: Need to Control Inflated Risk of Type I error 7.8 Setting up Confidence Intervals for Correlations 7.9 Factors that Influence the Magnitude and Sign of Pearson r 7.9.1 Pattern of X, Y Scores in Scatter Plot 7.9.2 Biased Sample Selection: Restricted Range or Extreme Groups. 7.9.3 Correlations for Samples that Combine Groups 7.9.4 Control of Extraneous Variables 7.9.5 Disproportionate Influence by Bivariate Outliers. 7.9.6 Shapes of Distributions of X and Y 7.9.7 Curvilinear Relations 7.9.8 Transformations of Data 7.9.9 Attenuation of Correlation due to Unreliability of Measurement 7.9.10 Part-whole Correlations 7.9.11 Aggregated Data 7.10 Pearson r and r2 as Effect Size Indexes 7.11 Statistical Power and Decisions about Sample Size in Correlation Studies 7.12 Interpreting Outcomes for Pearson r 7.12.1 ?Correlation does not necessarily imply causation? 7.12.2 Interpretation of Significant Pearson r Values 7.12.3 Interpretation of Non Significant Pearson r Values 7.13 SPSS Output and Model Results Write-up 7.14 Summary Chapter 8. Alternative Correlation Coefficients 8.1 Correlations for Different Types of Variables 8.2 Two Research Examples 8.3 Correlations for Rank or Ordinal Scores 8.4 Correlations for True Dichotomies 8.4.1 Point biserial r (rpb) 8.4.2 Phi coefficient (?) 8.5 Correlations for Artificially Dichotomized Variables 8.5.1 Biserial r (rbis) 8.5.2 Tetrachoric r (rtet) 8.6 Assumptions and Data Screening for Dichotomous Variables 8.7 Analysis of Data: Dog Ownership and Survival After a Heart Attack 8.8 Chi Squared Test of Association (Computational Methods for Tables of Any Size) 8.9 Other Measures of Association for Contingency Tables 8.10 SPSS Output and Model Results Write-up 8.11 Summary Chapter 9. Bivariate Regression 9.1 Research Situations Where Bivariate Regression is Used 9.2 A Research Example: Prediction of Salary from Years of Job Experience 9.3 Assumptions and Data Screening 9.4 Issues in Planning a Bivariate Regression Study 9.5 Formulas for Regression Coefficients 9.6 Statistical Significance Tests for Bivariate Regression 9.7 Setting Up Confidence Intervals around Regression Coefficients 9.8 Factors That Influence the Magnitude and Sign of b 9.9 Effect Size 9.10 Statistical Power 9.11 Raw Score Versus Standard Score Versions of Regression Equation 9.12 Removing Influence of X from the Y Variable by Looking at Residuals from Bivariate Regression 9.13 SPSS Example 9.14 Summary Chapter 10. Adding a Third Variable: Preliminary Exploratory Analyses 10.1 Three Variable Research Situations 10.2 First Research Example 10.3 Exploratory Statistical Analyses for Three Variable Research Situations 10.4 Separate Analysis of X1, Y Relationship for each Level of the X2 Control Variable 10.5 Partial Correlation Between X1 and Y Controlling for X2 10.6 Understanding Partial Correlation as Use of Bivariate Regression to Remove Variance Predictable by X2 from both X1 and Y 10.7 Computation of Partial r from Bivariate Pearson Correlations 10.8 Intuitive Approach to Understanding Partial r 10.9 Significance Tests, Confidence Intervals and Statistical Power for Partial Correlation 10.10 Interpretation of Various Outcomes for ry1.2 and ry1 10.11 Two Variable ?Causal? Models 10.11.1 Causal and Non Causal Paths 10.11.2 Interpreting Correlations as Evidence Consistent or Inconsistent with the Existence of a Path Between X1 and Y 10.12 Three Variable Models Consistent with Various outcomes for r1y and r1y.2 10.12.1 r1y ,and r1y.2 are both close to 0 (area a) 10.12.2 r1y.2 śr1y, and neither correlation is close to zero (area b) 10.12.3 ry1.2 is approximately zero, but ry1 was not equal to zero (area c) 10.12.4 ry1.2 becomes smaller than ry1 (but ry1.2 does not drop to zero and ry1.2 has the same sign as ry1) (area d) 10.12.5 ry1.2 is larger than r1y or ry1.2 is opposite in sign relative to r1y (area e) 10.13 Mediation versus Moderation 10.13.1 How to Recognize Possible Moderation in Preliminary Analyses 10.13.2 How to Recognize Possible Mediation in Preliminary Analyses 10.14 Model Results Section 10.15 Summary Chapter 11. Regression With Two Predictor Variables 11.1 Research Situations Involving Regression with Two Predictor Variables 11.2 Hypothetical Research Example 11.3 Graphic Representation of Regression Plane 11.4 Semipartial (or ?Part?) Correlation 11.5 Graphic Representation of Partition of Variance in Regression with Two Predictors 11.6 Assumptions for Regression with Two Predictors 11.7 Formulas for Regression Coefficients, Significance tests, and Confidence Intervals 11.7.1 Formulas for Standard Score ? Coefficients 11.7.2 Formulas for Raw Score (b) Coefficients 11.7.3 Formula for Multiple R and Multiple R2 11.7.4 Test of Significance for Overall Regression: Overall F test for Ho: R = 0 11.7.5 Test of Significance for each Individual Predictor: t test for Ho: bi = 0 11.7.6 Confidence Interval for each b Slope Coefficient 11.8 SPSS Regression Results 11.9 Conceptual Basis: Factors that Affect the Magnitude and Sign of ? and b Coefficients in MR with Two Predictors 11.10 Tracing Rules for ?Causal Model? Path Diagrams 11.11 Comparison of Equations for ?, b, pr, and sr 11.12 Nature of Predictive Relationships 11.13 Effect Size Information in Regression with Two Predictors 11.14 Statistical Power 11.15 Issues in Planning a Study 11.15.1 Sample Size 11.15.2 Selection of Predictor Variables 11.15.3 Multicollinearity among Predictors 11.15.4 Range of Scores 11.16 Use of Regression with Two Predictors to Test Mediated ?Causal? Models 11.17 Model Results Section 11.18 Summary Chapter 12. Dummy Predictor Variables and Interaction Terms in Multiple Regression 12.1 Research Situations Where Dummy Predictor Variables Can Be Used 12.2 Empirical Example 12.3 Screening for Violations of Assumptions 12.4 Issues in Planning a Study 12.5 Parameter Estimates and Significance Tests for Regression with Dummy Variables 12.6 Group Mean Comparisons Using One Way Between S ANOVA 12.6.1 Gender Differences in Mean Salary 12.6.2 College Differences in Mean Salary 12.7 Three Different Methods of Coding for Dummy Variables 12.7.1 Regression with Dummy Coded Dummy Predictor Variables 12.7.1.1 Two Group Example with a Dummy Coded Dummy Variable 12.7.1.2 Multiple Group Example with Dummy Coded Dummy Variables 12.7.2 Regression with Effect Coded Dummy Predictor Variables 12.7.2.1 Two Group Example Using an Effect Coded Dummy Variable 12.7.2.2 Multiple Group Example with Effect Coded Dummy Variables 12.7.3 Regression with Orthogonal Coding of Dummy Predictor Variables 12.8 Regression Models that Include Both Dummy and Quantitative Predictor Variables 12.9 Tests for Interaction (or Moderation) Involving Dummy Predictor Variables 12.10 Interaction Terms that Involve Two Quantitative Predictors 12.11 Effect Size and Statistical Power 12.12 Nature of the Relationship and/or Follow-up Tests 12.13 Results Section 12.14 Summary Chapter 13. Factorial Analysis of Variance 13.1 Research Situations and Research Questions 13.1.1 First Null Hypothesis: Test of Main Effect for Factor A 13.1.2 Second Null Hypothesis: Test of Main Effect for Factor B 13.1.3 Third Null Hypothesis: Test of the A x B Interaction 13.2 Screening for Violations of Assumptions 13.3 Issues in Planning a Study 13.4 Empirical Example: Description of Hypothetical Data 13.5 Computations for Between S Factorial ANOVA 13.5.1 Notation for Sample Statistics that Estimate Score Components in Factorial ANOVA 13.5.2 Notation for Theoretical Effect Terms (or Unknown Population Parameters) in Factorial ANOVA 13.5.3 Formulas for Sums of Squares and Degrees of Freedom 13.6 Conceptual Basis: Factors that Affect the Size of Sums of Squares and F Ratios in Factorial ANOVA 13.6.1 Distances Between Group Means (Magnitude of the ? and ? Effects) 13.6.2 Number of Scores (n) Within each Group or Cell 13.6.3 Variability of Scores Within Groups or Cells (Magnitude of MSwg) 13.7 Effect Size Estimates for Factorial ANOVA 13.8 Statistical Power 13.9 Nature of the Relationships, Follow-up Tests, and Information to include in Results 13.9.1 Nature of a Two-Way Interaction 13.9.2 Nature of Main Effect Differences 13.10 Factorial ANOVA Using SPSS GLM Procedure 13.11 Summary Chapter 14. Multiple Regression with More than Two Predictors 14.1 Research Questions 14.2 Empirical Example 14.3 Screening for Violations of Assumptions 14.4 Issues in Planning a Study 14.5 Computation of Regression Coefficients with k Predictor Variables 14.6 Methods of Entry for Predictor Variables 14.6.1 Standard or Simultaneous Method of Entry 14.6.2 Sequential or Hierarchical (User-Determined) Methods of Entry 14.6.3 Statistical (Data-Driven) Order of Entry 14.7 Variance Partitioning in Regression for Standard Regression Versus Regression Analyses that Involve a Series of Steps 14.8 Test of the Significance of the Overall Regression Equation 14.9 Tests of Significance of Individual Predictor Variables 14.10 Effect Size 14.10.1 Effect Size for Overall Regression 14.10.2 Effect sizes for Individual Predictor Variables 14.11 Changes in F and R as Additional Predictors are Added to a Model in Sequential or Statistical Regression 14.12 Statistical Power 14.13 Nature of the Relationship Between each X predictor and Y (Controlling for Other Predictors) 14.14 Assessment of Multivariate Outliers in Regression 14.15 Results Sections for All Three Methods of Entry 14.16 Summary Appendix A to Chapter 14: A Review of Matrix Algebra Notation and Operations and Application of Matrix Algebra to Estimation of Slope Coefficients for Regression with More than k Predictor Variables Appendix B to Chapter 14: Tables for Wilkinson & Dallal (1981) Procedures for the Test of Significance of Multiple R2 in Method = Forward Statistical Regression Chapter 15. Analysis of Covariance 15.1 Research Situations and Research 15.2 Empirical Example 15.3 Screening for Violations of Assumptions 15.4 Variance Partitioning in ANCOVA 15.5 Issues in Planning a Study 15.6 Formulas for ANCOVA 15.7 Computation of Adjusted Effects and Adjusted Y* Means 15.8 Conceptual Basis: Factors that Affect the Magnitude of SSAadj and SSresidual and the Pattern of Adjusted Group Means 15.9 Effect Size 15.10 Statistical Power 15.11 Nature of the Relationship and/or Follow-up Tests 15.12 SPSS Analysis and Model Results Section 15.13 Additional Discussion of ANCOVA Results 15.14 Summary Appendix to Chapter 15: Alternative Methods of Analysis for Pretest?Post test Data Chapter 16. Discriminant Analysis 16.1 Research Situations and Research Questions 16.2 Introduction of Empirical Example 16.3 Screening for Violations of Assumptions 16.4 Issues in Planning a Study 16.5 Equations for Discriminant Analysis 16.6 Conceptual Basis: Factors that Affect the Magnitude of Wilks?s ? 16.7 Effect Size 16.8 Statistical Power and Sample Size Recommendations 16.9 Follow-up Tests to Assess What Pattern of Scores Best Differentiates Groups 16.10 Results Section 16.11 One Way ANOVA on Discriminant Function Scores 16.12 Summary Chapter 17. Multivariate Analysis of Variance 17.1 Research Situations and Research Questions 17.2 Introduction of Initial Research Example: A One Way MANOVA 17.3 Why Include Multiple Outcome Measures? 17.4 Equivalence of MANOVA and DA 17.5 The General Linear Model (GLM) 17.6 Assumptions and Data Screening 17.7 Issues in Planning a Study 17.8 Conceptual Basis and Some Formulas for MANOVA 17.9 Multivariate Test Statistics 17.10 Factors that Influence the Magnitude of ? 17.11 Effect Size for MANOVA 17.12 Statistical Power and Sample Size Decisions 17.13 SPSS Output for a One Way MANOVA: Re-analysis of the Career Group Data from Chapter 16 17.14 A 2 x 3 Factorial MANOVA of the Career Group Data 17.14.1 Possible Follow Up Tests to Assess Nature of Main Effects 17.14.2 Possible Follow Up Tests to Assess the Nature of the Interaction 17.14.3 Additional Comments about Inconclusive Outcomes 17.15 A 3 x 6 Factorial MANOVA with a Statistically Significant Interaction 17.16 Comparison of Univariate and Multivariate Follow Up Analyses for MANOVA 17.17 Summary Chapter 18. Principal Components and Factor Analysis 18.1 Research Situations 18.2 Path Model for Factor Analysis 18.3 Factor Analysis as a Method of ?Data Reduction? 18.4 Introduction of Empirical Example 18.5 Screening for Violations of Assumptions 18.6 Issues in Planning a Factor Analytic Study 18.7 Computation of Loadings 18.8 Steps in Computation of Principal Components or Factor Analysis 18.8.1 Computation of the correlation matrix R 18.8.2 Computation of Initial Loading Matrix A 18.8.3 Limiting the Number of Components or Factors 18.8.4 Optional: Rotation of Factors 18.8.5 Naming or Labeling Components or Factors 18.9 Analysis 1: Principal Component Analysis of 3 Items Retaining All Three Components 18.9.1 Communality for Each Item based on all Three Components 18.9.2 Variance Reproduced by Each of the Three Components 18.9.3 Perfect Reproduction of Correlations from Three Components 18.10 Analysis 2: Principal Component Analysis of 3 Items Retaining only the First Component 18.10.1 Communality for each Item based on One Component2 18.10.2 Variance reproduced by the First Component 18.10.3 Partial Reproduction of Correlations from One Component 18.11 Principal Components Versus Principal Axis Factoring 18.12 Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation 18.12.1 Communality for Each Item Based on Two Retain4ed Factors 18.12.2 Variance Reproduced by Two Retained Factors 18.12.3 Partial Reproduction of Correlations from Loadings on Two Factors 18.13 Geometric Representation of Factor Analysis 18.13.1 Correlation Between Two Variables 18.13.2 Correlation Between a Variable and a Factor 18.13.3 Factor Rotation 18.14 The Two Multiple Regressions 18.14.1 Construction of Factor Scores (such as score on F1) from z scores 18.14.2 Prediction of Standard Scores on Variables (zxi) from a Limited Number of Factors (F1, F2) 18.15 Analysis 4: PAF with Varimax Rotation 18.15.1 Variance Reproduced by Each Factor at Three Stages in the Analysis 18.15.2 Rotated Factor Loadings 18.15.3 Example of Reverse Scored Item 18.16 Questions to Address in Interpretation of Factor Analysis or Principal Components 18.16.1. How many factors or components or latent variables are needed to account for (or reconstruct) the pattern of correlations among the measured variables? 18.16.2. How ?important? are the factors or components? How much variance does each factor or component explain? 18.16.3. What, if anything, do the retained factors or components mean? Can we label or name our factors? 18.16.4 How adequately do the retained components or factors reproduce the structure in the original data, that is, the correlation matrix? 18.17 Results Section for Analysis 4: PAF with Varimax Rotation, Two Factors Retained 18.18 Factor Scores Versus Unit Weighted Composite Scores As Follow Up to Factor Analysis 18.19 Summary of Issues in Factor Analysis 18.20 Optional: Brief Introduction to Concepts in Structural Equation Modeling Chapter 19. Reliability, Validity, and Multiple Item Scales 19.1 Assessment of Measurement Quality 19.1.1 Reliability 19.9.2 Validity 19.1.3 Sensitivity 19.1.4 Bias 19.2 Cost and Invasiveness of Measurements 19.2.1 Cost 19.2.2 Invasiveness 19.2.3 Reactivity of Measurement 19.3 Empirical Examples of Reliability Assessment 19.3.1 Definition of Reliability 19.3.2 Test Retest Reliability Assessment for a Quantitative Variable 19.3.3 Reliability Assessment for Scores on a Categorical Variable 19.4 Concepts from Classical Measurement Theory 19.5 Use of Multiple Item Measures to Improve Measurement Reliability 19.6 Three Methods for Computation of Summated Scales 19.6.1 Implicit Assumptions: All Items Measure Same Construct and are Scored in Same Direction 19.6.2 Reverse Worded Questions 19.6.3 Method One: Simple Unit Weighted Sum of Raw Scores 19.6.4 Method Two: Simple Unit Weighted Sum of z scores 19.6.5 Method Three: Optimally Weighted Linear Combination of Scores Based on Multivariate Analyses 19.6.6 Advantages and Disadvantages of Unit Weighted Composites Compared to Optimally Weighted Composites 19.7 Assessment of Internal Homogeneity Reliability for Total Score on Multiple Item Scale 19.7.1 Empirical Example: Factor Analysis of Five Items Selected from CES-D Depression Scale 19.7.2 Cronbach ? reliability: Conceptual Issues 19.7.3 Empirical Example: Cronbach ? Reliability for Five CES-D Items 19.7.4 Improving Cronbach ? by Dropping a ?Poor? Item 19.7.5 Improving Cronbach ? by Increasing the Number of Items 19.7.6 Other Methods of Reliability Assessment for Multiple Item Measures 19.7.6.1 Split Half Reliability 19.7.6.2 Parallel Forms Reliability 19.8 Correlations among Scores Obtained Using Different Methods of Summing Items 19.9 Validity Assessment 19.9.1 Content and Face Validity 19.9.2 Criterion Validity 19.9.2.1 Convergent Validity 19.9.2.2 Discriminant Validity 19.9.2.3 Concurrent Validity 19.9.2.4 Predictive Validity 19.9.3 Construct Validity: Summary 19.10 Typical Scale Development Study 19.10.1 Generate Initial List of Items or Measures 19.10.2 Administer Survey to Participants 19.10.3 Factor Analyze Scores on Items 19.10.4 Develop Summated Scales 19.10.5 Assess Score Reliability 19.10.6 Assess Score Validity 19.10.7 Backtrack and Repeat Stages of Development as Necessary 19.10.8 Create ?Final? Version of Scale 19.11 Summary Chapter 20. Analysis of Repeated Measures 20.1 Introduction 20.2 Empirical Example: Experiment to Assess Effect of Stress on Heart Rate 20.2.1 Analysis of Data from the Stress/HR Study as a Between S or Independent Samples Design 20.2.2 Independent Samples t Test for the Stress/ HR Data 20.2.3 One Way Between S ANOVA for the Stress/ HR Data 20.3 Discussion of Sources of Within Group Error in Between S Versus Within S Data 20.4 The Conceptual Basis for the Paired Samples t Test and One Way Repeated Measures ANOVA 20.5 Computation of a Paired Samples t Test to Compare Mean HR Between Baseline and Pain Conditions 20.6 SPSS Example: Analysis of Stress/ HR Data Using a Paired Samples t Test 20.7 Comparison Between Independent Samples t Test and Paired Samples t Test 20.8 SPSS Example: Analysis of Stress/ HR Data Using a Univariate One Way Repeated Measures ANOVA 20.9 Using the SPSS GLM Procedure for Repeated Measures ANOVA 20.10 Screening for Violations of Assumptions in Univariate Repeated Measures 20.11 The Greenhouse-Geisser and Huynh Feldt ?? Correction Factors for df in Univariate Repeated Measures ANOVA 20.12 MANOVA Approach to Analysis of Repeated Measures 20.13 Effect Size 20.14 Statistical Power 20.15 Planned Contrasts 20.16 Results Section for Repeated Measures Study of Stress and Heart Rate 20.17 Design Problems in Repeated Measures Designs 20.18 More Complex Designs 20.19 Alternative Analyses for Pretest Posttest Scores 20.20 Summary Chapter 21. Binary Logistic Regression 21.1 Research Situations 21.1.1 Types of Variables 21.1.2 Research Questions 21.1.3 Assumptions Required for Linear Regression Versus Binary Logistic Regression 21.2 Simple Empirical Example: Dog Ownership and Odds of Death 21.3 Conceptual Basis For Binary Logistic Regression Analysis 21.3.1 Why Ordinary Linear Regression Is Inadequate 21.3.2 Modifying the Method of Analysis to Handle These Problems 21.4 Definition and Interpretation of Odds 21.5 A New Type of Dependent Variable: The Logit 21.6 Terms Involved in Binary Logistic Regression Analysis 21.6.1 Estimation of Coefficients for a Binary Logistic Regression Model 21.6.2 Assessment of Overall Goodness of Fit for a Binary Logistic Regression Model 21.6.3 Alternative Assessments of Overall Goodness of Fit 21.6.4 Information about Predictive Usefulness of Individual Predictor Variables 21.6.5 Evaluating Accuracy of Group Classification 21.7 Analysis of Data for First Empirical Example: Dog Ownership/ Death Study 21.7.1 SPSS Menu Selections and Dialogue Windows 21.7.2. Interpretation of SPSS Output 21.7.2.1 Null Model 21.7.2.2 Full Model 21.7.3 Results for the Dog Ownership/ Death Study 21.8 Issues in Planning and Conducting a Study 21.8.1 Preliminary Data Screening 21.8.2 Design Decisions 21.8.3 Coding Scores on Binary Variables 21.9 More Complex Models 21.10 Binary Logistic Regression for Second Empirical Analysis: Drug Dose and Gender as Predictors of Odds of Death 21.11 Comparison of Discriminant Analysis to Binary Logistic Regression 21.12 Summary Tables of Critical Values Glossary References Index About the Author

Library of Congress Subject Headings for this publication:

Social sciences -- Statistical methods.

Psychology -- Statistical methods.

Multivariate analysis.