From Data to Insights A Beginner's Guide to Cross-Tabulation Analysis

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