Quantitative Research by Example

Ioan Gelu Ionas, MBA, Ph.D.

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Contents

  1. About this book
  2. 1. Foreword

Planning a Study

  1. 2. A Few Words About Causality
  2. 3. Variance and Error
  3. 4. Design
    Sections
    1. 4.1 Occam’s Razor
    2. 4.2 Experimental Versus Non-Experimental Research
    3. 4.3 Between-Subjects vs. Within-Subjects Designs
    4. 4.4 Variables
    5. 4.5 Descriptive vs. Inferential Designs
    6. 4.6 Research Questions
    7. 4.7 Hypotheses
    8. 4.8 Hypothesis Testing
    9. 4.9 The p-Value Controversy
    10. 4.10 How to Choose the Appropriate Statistical Test
  4. 5. Effect Size and Power
    Sections
    1. 5.1 Relative Treatment Magnitude
    2. 5.2 Standardized Effect Size
    3. 5.3 Controlling Type I and Type II Errors
    4. 5.4 Controlling Power Through Sample Size
    5. 5.5 Practical Advice on Sample Size
  5. 6. Sample Size
    Sections
    1. 6.1 Factors Affecting the Size of the Sample
    2. 6.2 Methods of Determining the Sample Size

Describing and Preparing Data

  1. 7. Describing Data
    Sections
    1. 7.1 The Study
    2. 7.2 Frequencies
    3. 7.3 Central Tendency
    4. 7.4 Variability
    5. 7.5 Visualizing Data
    6. 7.6 Describing Groups
    7. 7.7 Reporting the Results
    8. 7.8 Summary
  2. 8. Assumptions and Outliers
    Sections
    1. 8.1 Normality
    2. 8.2 Tests of Normality
    3. 8.3 Homogeneity of Variances or Homoscedasticity
    4. 8.4 Outliers
  3. 9. Normalization, Standardization, and Data Transformation
    Sections
    1. 9.1 Scaling/Rescaling
    2. 9.2 Distribution Normalization
    3. 9.3 Summary

Comparing Groups

  1. 10. t-Tests and Their Rank-Based Alternatives
    Sections
    1. 10.1 The One-Sample z Test
    2. 10.2 One-Sample t-Test
    3. 10.3 The One-Sample Wilcoxon Signed-Rank Test
    4. 10.4 Independent Samples t-Test
    5. 10.5 The Mann-Whitney U Test
    6. 10.6 Mood’s Median Test
    7. 10.7 Paired Samples t-Test
    8. 10.8 The Wilcoxon Signed-Rank Test
    9. 10.9 The Sign Test
  2. 11. Equivalence Testing
    Sections
    1. 11.1 The Theory
    2. 11.2 Assumptions
    3. 11.3 The Study
    4. 11.4 The Whole Clip
    5. 11.5 Second by Second
    6. 11.6 Summary
  3. 12. ANOVA: Analysis of Variance
    Sections
    1. 12.1 Why Not Several t-Tests?
    2. 12.2 The Theory
    3. 12.3 Assumptions
    4. 12.4 The Study
    5. 12.5 Following Up a Significant F
    6. 12.6 When the Variances Are Not Equal: Welch’s ANOVA
    7. 12.7 The Kruskal-Wallis Test
    8. 12.8 Reporting the Results
    9. 12.9 Summary
  4. 13. Factorial ANOVA and Interactions
    Sections
    1. 13.1 Main Effects and Interactions
    2. 13.2 The Theory
    3. 13.3 Assumptions
    4. 13.4 The Study
    5. 13.5 Interactions in Regression
    6. 13.6 Summary
  5. 14. ANCOVA: Analysis of Covariance
    Sections
    1. 14.1 The Theory
    2. 14.2 Assumptions
    3. 14.3 The Study
    4. 14.4 Summary
  6. 15. MANOVA: Multiple Analysis of Variance
    Sections
    1. 15.1 Outliers
    2. 15.2 Assumptions
    3. 15.3 The MANOVA Test

Repeated Measures

  1. 16. Repeated-Measures ANOVA
    Sections
    1. 16.1 The Theory
    2. 16.2 Assumptions
    3. 16.3 The Study
    4. 16.4 The Friedman Test
    5. 16.5 Cochran’s Q Test
    6. 16.6 The Multilevel Approach
    7. 16.7 Summary
  2. 17. Mixed Designs
    Sections
    1. 17.1 The Theory
    2. 17.2 Assumptions
    3. 17.3 The Study
    4. 17.4 The Multilevel Approach
    5. 17.5 Summary

Relationships Between Variables

  1. 18. Correlations
    Sections
    1. 18.1 From Covariance to Correlation
    2. 18.2 Pearson Correlations Test
    3. 18.3 Spearman Correlations Test
    4. 18.4 Kendall Correlations Test
    5. 18.5 Partial and Semi-Partial Correlations
    6. 18.6 Point-Biserial and Biserial Correlations
    7. 18.7 Bootstrapped Confidence Intervals
    8. 18.8 Reporting Correlations
    9. 18.9 Summary
  2. 19. Chi-Square Test
    Sections
    1. 19.1 Goodness-of-Fit Test
    2. 19.2 The Binomial Test
    3. 19.3 Test of Independence
    4. 19.4 When the Expected Counts Are Too Small
    5. 19.5 Fisher’s Exact Test
    6. 19.6 Simulated p-Values and Combining Categories
    7. 19.7 McNemar’s Test
    8. 19.8 Summary
  3. 20. Simple Linear Regression
    Sections
    1. 20.1 The Theory
    2. 20.2 Assumptions
    3. 20.3 The Study
    4. 20.4 Summary
  4. 21. Multiple Linear Regression Analysis
    Sections
    1. 21.1 Assumptions
    2. 21.2 The Study
    3. 21.3 Preliminary Steps
    4. 21.4 Summary Statistics
    5. 21.5 Unusual Cases: Discrepancy, Leverage, and Influence
    6. 21.6 Residuals Analysis
    7. 21.7 Linearity
    8. 21.8 Enter or Full Model
    9. 21.9 Hierarchical Regression
    10. 21.10 Backward Model
    11. 21.11 Summary
  5. 22. Categorical Predictors
    Sections
    1. 22.1 Coding Schemes
    2. 22.2 The Study
    3. 22.3 A Predictor With Two Categories
    4. 22.4 A Predictor With Three Categories
    5. 22.5 Categorical and Continuous Predictors Together
    6. 22.6 Summary
  6. 23. Multiple Logistic Regression
    Sections
    1. 23.1 The Study
    2. 23.2 Assumptions
    3. 23.3 Analysis
    4. 23.4 Model Fit and Model Comparison
    5. 23.5 Additional Analysis - TL/DR
  7. 24. Mediation Analysis
    Sections
    1. 24.1 The Theory
    2. 24.2 Assumptions
    3. 24.3 The Study
    4. 24.4 Summary
  8. 25. Path Analysis
    Sections
    1. 25.1 The Theory
    2. 25.2 Assumptions
    3. 25.3 The Study
    4. 25.4 Summary
  1. References