## Table of contents for Applied statistics : from bivariate through multivariate techniques / Rebecca M. Warner.

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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 �r1y, 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
17.15 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
18.8 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
18.15.3 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