From Data to Insights

✍ Scribed by Gianmarco Alberti

• Publisher: Chapman and Hall/CRC
• Year: 2024
• Tongue: English
• Leaves: 170
• Edition: 1
• Category: Library

✦ Synopsis

This book offers a clear and accessible guide to cross-tabulation analysis, transforming a complex subject into an accessible topic. It diverges from traditional statistical texts, adopting a conversational tone that addresses common questions and concerns. The author demystifies intricate concepts, with clear explanations and relatable analogies that make the material approachable for readers with varying levels of mathematical expertise.

Unique in its approach, the book avoids overwhelming readers with complex formulas and instead focuses on the principles underlying cross-tabulation analysis. This method ensures that the content is applicable regardless of specific statistical software used, making it a versatile resource.

Targeted at a diverse audience, the book covers the spectrum from foundational elements to comparatively more advanced topics in cross-tabulation analysis. It includes a comprehensive glossary and an appendix of detailed examples, providing practical insight and aiding understanding of key concepts. This book is an invaluable resource for students, researchers, and educators alike, offering a fresh perspective on cross-tabulation analysis that emphasises clarity and practical application.

Key Features:

• Employs a conversational style, making complex statistical concepts in cross-tabulation analysis accessible and engaging for all readers.
• Combines minimal use of formulas with practical examples, ensuring easy comprehension and application, even for those with minimal mathematical background.
• Features a consistent running example for continuity, complemented by diverse real-world scenarios to solidify understanding of key concepts.
• Independently valuable without reliance on specific statistical software, emphasising fundamental principles for adaptability across various platforms.
• Progressively guides readers from foundational basics to comparatively more advanced methods, supplemented by a comprehensive glossary and detailed appendix for an enriched learning.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Foreword
Preface
Chapter 1 Cross-Tabulations
1.1 Introduction
1.2 Defining the Book’s Boundaries
1.3 How to Use This Book
1.4 The Building Blocks: Understanding Statistical Variables
1.5 Cross-Tab 101: The Basics Unveiled
1.6 Key Takeaways
Chapter 2 Cross-Tab Analysis and Introduction to the Chi-Squared Test
2.1 How to Look at Cross-Tabs
2.1.1 Exploring Relationships
2.1.2 Grasping the Concept of Independence
2.1.3 Wrapping up on Independence
2.2 Assessing Independence: The Chi-Squared Test
2.3 Understanding Statistical Significance
2.3.1 Introduction
2.3.2 The Chi-Squared Test p-Value
2.3.3 Independence and the Variability of the Chi-Squared Statistic
2.3.4 p-Value and the 0.05 Threshold
2.3.5 The Bottom-Up Approach to Significance: Monte Carlo Simulated p-Value
2.3.6 Beyond the Titanic: Conceptualising Statistical Generalisation
2.4 Key Takeaways
Chapter 3 The Chi-Squared Test: Advanced Insights
3.1 The Smoking Gun: Tracking Down Chi-Squared Residuals
3.1.1 Standardised Residuals
3.1.2 Adjusted Standardised Residuals
3.1.3 Wrapping Up on the Standardised Residuals Analysis
3.1.4 From Tiles to Tales: Visualising Residuals with Mosaic Plots
3.2 Statistical Significance and Sample Size: Things to Consider
3.3 Small Numbers, Big Questions
3.3.1 The Chi-Squared Test and Small Expected Frequencies in 2 × 2 Cross-Tabs
3.3.2 The (N − 1)/N Correction
3.3.3 The Fisher’s Test
3.3.4 Locked Margins, Unlocked Secrets: The Fisher’s Test Debate
3.3.5 (N − 1)/N Correction and Fisher’s Test: Things to Consider
3.4 Addressing Small Expected Frequencies in Larger Tables
3.4.1 Introduction
3.4.2 Pooling Levels
3.4.3 (N − 1)/N Correction and Fisher’s Test for Larger Cross-Tabs
3.4.4 Permutation and Monte Carlo Methods
3.5 Choices in Chi-Squared Testings with Small Expected Frequencies
3.6 Key Takeaways
Chapter 4 Strength in Numbers: Measuring Dependence
4.1 Chi-Square-Based Measures of Association
4.1.1 Contingency Coefficient
4.1.2 Phi Coefficient
4.1.3 Limitations of Phi: Phi Corrected
4.1.4 Cramér’s V Coefficient
4.1.5 Limitations of Cramér’s V
4.1.6 From Numbers to Meaningful Magnitudes: Interpreting Association Measures
4.1.7 Reflections on the Chi-Square-Based Measures of Association
4.2 Measures of Association Not Based on the Chi-Squared
4.2.1 Goodman–Kruskal’s Lambda
4.2.2 Odds Ratio
4.2.3 Rescaling the Odds ratio: Yule’s Q
4.2.4 Nuances and Limitations of Yule’s Q
4.2.5 Odds Ratios in Cross-Tabs with Two Rows and at Least Three Columns
4.2.6 Odds Ratios in Cross-Tabs of Any Size
4.3 Key Takeaways
Chapter 5 The Third Dimension: Adding Depth to Your Analysis
5.1 Stratified 2 × 2 Cross-Tabs
5.1.1 Introduction
5.1.2 Partial and Marginal Tables
5.1.3 Expect the Unexpected: The Simpson’s Paradox
5.1.4 Peeling the Strata: Variable Associations through Layers
5.1.5 Conditional Independence and Homogeneous Association
5.2 Delving Deeper: Analytical Tests and Evaluations
5.2.1 Conditional Independence and the Cochran–Mantel–Haenszel’s Test
5.2.2 Homogeneous Association and the Breslow–Day’s Test
5.2.3 The Mantel–Haenszel Estimate of a Common Odds Ratio
5.2.4 Beyond the Common Odds Ratio: The Cramér's V Alternative
5.2.5 Variability in Association Across Layers: Heterogeneity and the Ratio of Conditional Ratios
5.2.6 Fishing in Multiple Ponds: Correcting the Significance Threshold
5.2.7 Putting It All Together
5.3 Key Takeaways
Chapter 6 The Grand Finale: A Complete Cross-Tab Analysis
6.1 Another Step-by-Step Example
6.1.1 Religiosity and Abortion Opinion
6.1.2 Religiosity and Abortion Opinion Controlling for Gender
6.2 Being More Formal: From Sport Shoes to Tie
6.2.1 Reporting Cross-Tab Analysis Results
6.2.2 Report of Religiosity and Abortion Opinion
6.2.3 Report of Religiosity and Abortion Opinion Controlling for Gender
6.3 Key Takeaways
Chapter 7 Your Next Steps in Cross-Tab Mastery
7.1 Expanding Horizon: The World beyond 2 × 2 Tables
7.2 When Things Get Complex: Advanced Analytical Techniques
7.2.1 Unveiling Intricacies with Log-Linear Modelling
7.2.2 Visualising Associations with Correspondence Analysis
7.2.3 Employing Logistic Regression for Predictive Analysis
7.3 Concluding Thoughts on Advanced Analytical Techniques
7.4 The Explorer’s Toolkit: Recommended Readings and Resources
7.4.1 Introduction
7.4.2 Essential Readings for Chapter 1
7.4.3 Essential Readings for Chapter 2
7.4.4 Essential Readings for Chapter 3
7.4.5 Essential Readings for Chapter 4
7.4.6 Essential Readings for Chapters 5 and 6
7.4.7 Essential Readings for Chapter 7
7.5 Parting Thoughts on Cross-Tab Analysis
Appendix: Worked Examples of Odds and Odds Ratios
Glossary of Terms
Index