An Introduction to Statistics for Canadian Social Scientists

Description

Contents Preface Part I Introduction and Univariate Statistics 1 Why Should I Want to Learn Statistics? Introduction Why Do So Many People Dislike Statistics? When Did People Start to Think Statistically? When Did People Start to Think Statistically? If I Don’t Plan to Use Statistics in My Career, Should I Still Learn about Them? Organization of This Book Conclusion Glossary Terms 2 How Much Math Do I Need to Learn Statistics? BEDMAS and the Order of Operations Fractions and Decimals Exponents Logarithms Data, Variables, and Observations Levels of Measurement When Four Levels of Measurement Become Three . . . or Even Two Conclusion Glossary Practice Questions 3 Univariate Statistics Frequencies Translating Frequencies Rules for Creating Bar Charts Rates and Ratios Percentages and Percentiles Conclusion Glossary Terms Practice Questions 4 Introduction to Probability Introduction Some Necessary Terminology Sample Space Random Variables Trials and Experiments The Law of Large Numbers Types of Probabilities Empirical versus Theoretical Probabilities Discrete Probabilities The Probability of Unrelated Events The Probability of Related Events Mutually Exclusive Probabilities Non–Mutually Exclusive Probabilities Continuous Probabilities Conclusion Glossary Terms Practice Questions 5 The Normal Curve The History of the Normal (Gaussian) Distribution Illustrating the Normal Curve Some Useful Terms for Describing Distributions Conclusion Glossary Terms Practice Questions 6 Measures of Central Tendency and Dispersion Introduction Measures of Central Tendency Mode Median Mean Measures of Variability Range Mean Deviation Variance and the Standard Deviation Conclusion Glossary Terms Practice Questions Note 7 Standard Deviations, Standard Scores, and the Normal Distribution Introduction How Does the Standard Deviation Relate to the Normal Curve? More on the Normal Distribution An Extension of the Standard Deviation: The Standard Score One-Tailed Assessments Probabilities and the Normal Distribution Conclusion Glossary Terms Practice Questions 8 Sampling Introduction Probability Samples Simple Random Sample Systematic Random Sample Stratified/Hierarchical Random Sample Cluster Sample Non-Probability/Non-Random Sampling Strategies Convenience Sample Snowball Sample Quota Sample Sampling Error Tips for Reducing Sampling Error Conclusion Glossary Terms Practice Questions 9 Generalizing from Samples to Populations Introduction The Sample Distribution of Means and the Central Limit Theorem Confidence Intervals The t -Distribution What Is a Degree of Freedom? One-Tailed versus Two-Tailed Estimates The Sample Distribution of Proportions Using Degrees of Freedom and the t-Distribution to Estimate Population Proportions The Binomial Distribution Conclusion Glossary Terms Part II Bivariate Statistics 10 Testing Hypotheses: Comparing Large and Small Samples to a Known Population Introduction What’s a Hypothesis? One-Tailed and Two-Tailed Hypothesis Tests The Return of Gosset: Student’s t-Distribution Hypothesis Testing with One Small Sample and a Population Calculating Confidence Intervals in the One-Sample Case Single Sample Proportions Measuring Association with the Same Group Measured Twice Conclusion Glossary Terms Practice Questions 11 Testing Hypotheses: Comparing Two Samples Introduction The Standard Error of the Difference between Means Comparing Proportions with Two Samples One- and Two-Tailed Tests, Again Conclusion Glossary Terms Practice Questions 12 Bivariate Statistics for Nominal Data Introduction Analysis with Two Nominal Variables The Chi-Square Test of Statistical Significance Measures of Association for Nominal Data Phi Cramer’s V The Proportional Reduction of Error: Lambda Conclusion Glossary Terms Practice Questions 13 Bivariate Statistics for Ordinal Data Introduction Contingency Tables/Cross-Tabulations Kruskal’s Gamma (γ) Somers’ d Kendall’s Tau-b Spearman’s rho What about Statistical Significance? Conclusion: Which One to Use? Glossary Terms Practice Questions 14 Bivariate Statistics for Interval/Ratio Data Introduction Pearson’s r : The Correlation Coefficient A Rough Interpretation of r A Visual Representation of r What r Tells Us about Explained Variance A More Precise Interpretation of r The Correlation Matrix Using a t-Test to Assess the Significance of r What to Do When Your Independent and Dependent Variables Are Measured at Different Levels of Measurement Measuring Association between Interval/Ratioand Nominal or Ordinal Variables: Using the Lowest Common Measure of Association Conclusion Glossary Terms Practice Questions 15 One-Way Analysis of Variance Introduction What Is ANOVA? The Sum of Squares: An Easier Way The F-Distribution Is This New? Limitations of ANOVA Conclusion Glossary Terms Practice Questions Part III Multivariate Techniques 16 Regression 1—Modelling Continuous Outcomes Introduction Ordinary Least-Squares Regression: The Idea Onward from Bivariate Correlation: Multivariate Analysis Regression: The Formula Multiple Regression Standardized Partial Slopes (Beta Weights) The Multiple Correlation Coefficient Requirements/Assumptions of Ordinary Least Squares Regression Creating and Working with Dummy Variables Interpreting Dummy Variable Coefficients Inference and Regression Conclusion: A Final Note on OLS Regression Glossary Terms Practice Questions 17 Regression 2—Modelling Discrete/Dichotomous Outcomes with Logistic Regression Introduction Logistic Regression: The Idea Logistic Regression: The Formula Modelling Logistic Regression Interpreting the Coefficients of a Logistic Regression Equation A Note on Estimating Logistic Regression Equations Conclusion Glossary Terms Practice Questions Notes Part IV Advanced Topics 18 Regression Diagnostics Introduction When Ordinary Least Squares Regression Goes Wrong Influential Cases as a Source of Error Heteroscedasticity as a Source of Error Multicollinearity as a Source of Error Conclusion Glossary Terms Practice Questions 19 Strategies for Dealing with Missing Data Introduction What Effect Does Item Non-Response Have on Results? The Four Kinds of Item Non-Response What to Do about Missing Data 1. Do Nothing: List-Wise and Pair-Wise Deletion 2. Do Something: Single Imputation Strategies 3. Do Multiple Things: Multiple Imputation Multiple Imputation: Advantages and Disadvantages over Single Imputation Conclusion Glossary Term Notes Appendices Appendix A: Area under the Normal Curve Appendix B: The Student’s t-Table Appendix C: Chi-Square Appendix D: The F-Distribution Appendix E: Area under the Normal Curve: A Condensed Version Appendix F: Random Numbers between 1 and 1000 Appendix G: Summary of Equations and Symbols Equations Symbols Appendix H: Solution Key Solution Key for Practice Questions Solution Key for Boxes IBM SPSS Lab Manual Contents Preface Lab #1: Introduction to SPSS Lab #2: Identifying Types of Variables: Levels of Measures Lab #3: Univariate Statistics Lab #4: Introduction to Probability Lab #5: The Normal Curve Lab #6: Measures of Central Tendency and Dispersion Lab #7: Standard Deviations, Standard Scores, and the Normal Distribution Lab #8: Sampling Lab #9: Hypothesis Testing: Testing the Significance of the Difference between Two Means Lab #10: Hypothesis Testing: One- and Two-Tailed Tests Lab #11: Bivariate Statistics for Nominal Data Lab #12: Bivariate Statistics for Ordinal Data Lab #13: Bivariate Statistics for Interval/Ratio Data Lab #14: Analysis of Variance Lab #15: OLS Regression: Modelling Continuous Outcomes STATA Lab Manual Contents Preface Lab #1: Introduction to STATA Lab #2: Identifying Types of Variables: Levels of Measurement Lab #3: Univariate Statistics Lab #4: Introduction to Probability Lab #5: The Normal Curve Lab #6: Measures of Central Tendency and Dispersion Lab #7: Standard Deviations, Standard Scores, and the Normal Distribution Lab #8: Sampling Lab #9: Hypothesis Testing: Testing the Significance of the Difference between Two Means Lab #10: Hypothesis Testing: One- and Two-Tailed Tests Lab #11: Bivariate Statistics for Nominal Data Lab #12: Bivariate Statistics for Ordinal Data Lab #13: Bivariate Statistics for Interval/Ratio Data Lab #14: Analysis of Variance Lab #15: OLS Regression: Modelling Continuous Outcomes Glossary References Index