Full Description
Intermediate Social Statistics expertly guides students through a broad range of statistical methods, starting with an overview of fundamental concepts such as basic descriptive statistics and inferential statistics, before moving on to more advanced techniques, including two- and three-way crosstabulations, multiple regression and logistic regression, path analysis, and more. Taking a conceptual approach, the text emphasizes teaching students why we use particular statistics, what statistics can tell us, how statistics could mislead us, and what to do to prevent being misled or misleading others. This approach allows students to learn not only how to apply statistical techniques but also, importantly, the rationale behind the various methods and formulas they'll use in social statistics.
Offering a rich variety of illustrative examples and graphics, helpful review exercises, and easy-to-follow instruction, Intermediate Social Statistics helps students master concepts and sharpen their practical skills, allowing them to navigate the world of statistics with confidence.
Contents
Key Formulae ; Brief Contents ; Detailed Contents ; Preface ; Acknowledgements ; PART I: DESCRIPTIVE STATISTICS FOR ONE VARIABLE ; 1. Levels of Measurement ; Learning Objectives ; The Stevens' Classification ; - Nominal Measures ; - Ordinal Measures ; - Interval Measures ; - Ratio Measures ; - Dichotomies ; - Treating Ordinal Variables as Interval ; Two Related Classifications ; Graphing ; Summary ; Review Questions on Levels of Measurement ; Notes ; 2. Measures of Central Tendency ; Learning Objectives ; Definitions and Notation ; Links to Levels of Measurement ; Potentially Unstable Results ; - Instability of the Mode ; - Instability of the Median ; - Instability of the Mean ; Measures of Central Tendency as Averages ; Relations Among the Mode, Median, and Mean ; Summary ; Review Questions on Central Tendency ; Notes ; 3. Measures of Dispersion ; Learning Objectives ; Measures for Nominal Variables ; - The Index of Diversity ; - The Index of Qualitative Variation ; - An Information Theoretic (Entropy) Measure of Dispersion ; Quantile-Based Measures of Dispersion ; - An Alternative - The MAD ; The Standard Deviation ; - Calculating a Standard Deviation ; - Instability of the Standard Deviation ; - The Standard Deviation with Ordinal Data ; - Standardizing Variables ; - The Standard Deviation and the Tails of a Distribution ; - The Special Case of the Dichotomy ; Summary ; Review Questions on Measures of Dispersion ; Notes ; 4. Describing the Shape of a Distribution ; Learning Objectives ; Modes ; Skewness and Kurtosis ; Formulae for Skewness and Kurtosis ; Summary ; Review Questions on Shapes of Distributions ; Note ; 5. Summarizing a Distribution ; Learning Objectives ; The Five-Number Summary ; Graphing a Distribution ; - Boxplots ; - Pie Charts, Bar Charts, and Histograms ; - The Dot Chart ; - Smoothed Histograms ; - Back-to-Back Histograms ; - The Population Pyramid ; - Cumulative Distributions ; Creating a Mean and Standard Deviation Table ; Summary ; Review Questions on Summarizing a Distribution ; PART II: STATISTICAL INFERENCE ; 6. Sampling Distributions ; The Normal Distribution ; - The Normal Distribution ; The t Distribution ; - The Sampling Distribution for the Mean When t Applies ; The Chi-Square Distribution ; Relations among the Normal, t, and Chi-Square Distributions ; The Effect of Sample Size ; Summary ; Review Questions on Sampling Distributions ; Notes ; 7. The Standard Model of Statistical Inference ; Learning Objectives ; Central Ideas ; - Tests with Chi-Square ; - Statistical Power ; - Confidence Intervals ; Summary ; Review Questions on the Standard Model of Statistical Inference ; Note ; 8. The Bayesian Alternative ; Learning Objectives ; Frequentist and Personal Probabilities ; Bayes' Theorem ; Estimating a Proportion ; - Effects of Priors and Sample Data ; Credible Intervals ; Numerical Equivalence to Standard Results ; Summary ; Review Questions on the Bayesian Alternative ; Note ; PART III: MEASURES OF ASSOCIATION ; ASSOCIATION AND INDEPENDENCE ; 9. Measures for Nominal and Ordinal Variables ; Learning Objectives ; PRE Measures ; - Lambda ; - Gamma ; - Somers' d ; - Calculating Gamma and d for Tables Larger than 2 x 2 ; - Yule's Q as a Special Case of Gamma ; The Odds Ratio ; - Q as a Function of the Odds Ratio ; - The Usefulness of Q with Changing Marginals ; Summary ; Review Questions on Measures for Nominal and Ordinal Variables ; Notes ; 10. Pearson's r ; Learning Objectives ; Explaining the Formula ; - Calculation ; - Interpretations of r ; - The Sampling Distribution of r ; - Spearman's Rho ; - Phi ; Correlation Matrices ; Graphic Displays for Interval or Ratio Data ; Summary ; Review Questions on Pearson's r ; Note ; PART IV: EXAMINING CROSSTABULATIONS ; 11. Two-Way Tables ; Learning Objectives ; Reading a Crosstabulation ; Heavy and Light Cells ; - Standardized Residuals ; Setting Up Crosstabulations for a Presentation ; Further Graphic Methods of Clarifying a Crosstabulation ; Summary ; Review Questions on Heavy and Light Cells and Graphic Methods ; Notes ; 12. Conditional Tables ; Learning Objectives ; The Columbia Approach ; Specification ; Causal Chains ; Spurious Association ; Distortion ; Conditional Probabilities ; An Illustration with Polytomies ; Summary ; Review Questions on Conditional Tables ; Note ; PART V: REGRESSION ; 13. Bivariate Regression ; Learning Outcomes ; Origins ; The Principle of Least Squares ; - The Logic of the SEE ; - The Logic of r2 ; - Relative Usefulness of the SEE and r2 ; The Form of the Equation ; Interpreting b ; Graphic Display for Bivariate Regression ; Non-linear Trends ; - Truncation ; - Exponential Curves ; - More Than One Slope ; - Handling Nominal Polytomies ; - Quadratic Trends ; Summary ; Review Questions on Bivariate Regression ; Notes ; 14. Multiple Regression ; Learning Objectives ; Why Multiple Regression (MR)? ; Obtaining b's in Multiple Regression ; - Using Least Squares in Bivariate and Multiple Regression ; Interpreting b's in Multiple Regression ; Getting the Right Variables into the Equation ; Interpreting a Table of Regression Results ; Interaction Terms ; - An Example with Two Dichotomies ; Setting Up a Regression Table ; - Creating an Equation ; Graphs Presenting Regression Results ; The Special Case of Analysis of Variance (ANOVA) ; - One-way ANOVA ; - Two-way ANOVA ; - Interactions ; - Analysis of Covariance ; - The F Distribution in Regression and ANOVA ; Summary ; Review Questions on Multiple Regression and ANOVA ; Note ; 15. Path Analysis ; Learning Objectives ; A Famous Path Model ; Setting Up Path Diagrams ; Equations ; Decomposing a Correlation ; Steps in Decomposing a Correlation ; A Further Example ; Summary ; Review Questions on Path Analysis ; Note ; 16. Logistic Regression ; Learning Objectives ; Why Logistic Regression? ; Logits ; Interpreting the b's ; - Converting Odds to Probabilities ; A Sample Logistic Regression Table ; An Extension of the Logistic Model: Multinomial Regression ; Summary ; Review Questions on Logistic Regression ; Note ; Appendix A: Going a Step Further ; A1: Minimizing the Sum of Squared Deviations ; A2: The Mean and Standard Deviation of Z-Scores ; A3: The Standard Deviation of a Proportion ; Appendix B: Some Additional Explanations ; B1: Basic Notes on Logarithms ; B2: Obtaining Expected Values for Chi-Square ; B3: Another Form of Bayesian Hypothesis Testing ; Glossary of Statistical Terms ; Credits ; References ; Index
