Statistics Alive!

List of Figures List of Tables Preface Supplemental Material for Use With Statistics Alive! Acknowledgments Part I. Preliminary Information: "First Things First" 1. Math Review, Vocabulary, and Symbols Getting Started Vocabulary and Symbols Some Rules and Procedures More Rules and Procedures 2. Measurement Scales What Is Measurement? Scales of Measurement Continuous Versus Discrete Variables Real Limits Part II. Tables and Graphs: "On Display" 3. Frequency and Percentile Tables Why Use Tables? Frequency Tables Relative Frequency Tables Grouped Frequency Tables Percentile and Percentile Rank Tables 4. Graphs and Plots Why Use Graphs? Graphing Continuous Data Symmetry, Skew, and Kurtosis Graphing Discrete Data Part III. Central Tendency: "Bull's-Eye" 5. Mode, Median, and Mean What Is Central Tendency? Mode Median Mean Skew and Central Tendency Part IV. Dispersion: "From Here to Eternity" 6. Range, Variance, and Standard Deviation What Is Dispersion? Range Variance Standard Deviation Average Absolute Deviation Controversy: N Versus n - 1 Part V. The Normal Curve and Standard Scores: "What's the Score?" 7. Percent Area and the Normal Curve What Is a Normal Curve? History of the Normal Curve Uses of the Normal Curve Looking Ahead 8. z Scores What Is a Standard Score? Benefits of Standard Scores Calculating z Scores Comparing Scores Across Different Tests 9. Score Transformations and Their Effects Why Transform Scores? Effects on Central Tendency Effects on Dispersion A Graphic Look at Transformations Summary of Transformation Effects Some Common Transformed Scores Looking Ahead Part VI. Probability: "Odds Are" 10. Probability Definitions and Theorems Why Study Probability? Probability as a Proportion Equally Likely Model Mutually Exclusive Outcomes Addition Theorem Independent Outcomes Multiplication Theorem A Brief Review Probability and Inference 11. The Binomial Distribution What Are Dichotomous Events? Finding Probabilities by Listing and Counting Finding Probabilites by the Binomial Formula Finding Probabilities by the Binomial Table Probability and Experimentation Looking Ahead Nonnormal Data Part VII. Inferential Theory: "Of Truth and Relativity" 12. Sampling, Variables, and Hypotheses From Description to Inference Sampling Variables Hypotheses 13. Errors and Significance Random Sampling Revisited Sampling Error Significant Difference The Decision Table Type 1 Error Type 2 Error 14. The z Score as a Hypothesis Test Inferential Logic and the z Score Constructing a Hypothesis Test for a z Score Looking Ahead Part VIII. The One-Sample Test: "Are They From Our Part of Town?" 15. Standard Error of the Mean Central Limit Theorem Sampling Distribution of the Mean Calculating the Standard Error of the Mean Sample Size and the Standard Error of the Mean Looking Ahead 16. Normal Deviate Z Test Prototype Logic and the Z Test Calculating a Normal Deviate Z Test Examples of Normal Deviate Z Tests Decision Making With a Normal Deviate Z Test Looking Ahead 17. One-Sample t-Test Z Test Versus t Test Comparison of Z-Test Versus t-Test Formulas Degrees of Freedom Biased and Unbiased Estimates When Do We Reject the Null Hypothesis? One-Tailed Versus Two-Tailed Tests The t Distribution Versus the Normal Distribution The t Table Versus the Normal Curve Table Calculating a One-Sample t Test Interpreting a One-Sample t Test Looking Ahead 18. Interpreting and Reporting One-Sample t: Error, Confidence, and Parameter Estimates What Is Confidence? Refining Error and Confidence Decision Making With a One-Sample t Test Dichotomous Decisions Versus Reports of Actual p Parameter Estimation: Point and Interval Part IX. The Two-Sample Test: "Ours Is Better Than Yours" 19. Standard Error of the Difference Between the Means One-Sample Versus Two-Sample Studies Sampling Distribution of the Difference Between the Means Calculating the Standard Error of the Difference Between the Means Importance of the Size of the Standard Error of the Difference Between the Means Looking Ahead 20. t Test With Independent Samples and Equal Sample Sizes A Two-Sample Study Inferential Logic and the Two-Sample t Test Calculating a Two-Sample t Test Interpreting a Two-Sample t Test Looking Ahead 21. t Test With Unequal Sample Sizes What Makes Sample Sizes Unequal? Comparison of Special-Case and Generalized Formulas More Clarification of the Underlying Logic Calculating a t Test With Unequal Sample Sizes Interpreting a t Test With Unequal Sample Sizes 22. t Test With Related Samples What Makes Samples Related? Comparison of Special-Case and Related-Samples Formulas Advantage and Disadvantage of Related Samples Computational Formula Calculating a t Test With Related Samples Interpreting a t Test With Related Samples 23. Interpreting and Reporting Two-Sample t: Error, Confidence, and Parameter Estimates What Is Confidence? Refining Error and Confidence Decision Making With a Two-Sample t Test Dichotomous Decisions Versus Reports of Actual p Parameter Estimation: Point and Interval Part X. The Multisample Test: "Ours Is Better Than Yours or Theirs" 24. ANOVA Logic: Sums of Squares, Partitioning, and Mean Squares When Do We Use ANOVA? ANOVA Assumptions Partitioning of Deviation Scores From Deviation Scores to Variances From Variances to Mean Squares From Mean Squares to F Looking Ahead 25. One-Way ANOVA: Independent Samples and Equal Sample Sizes What Is a One-Way ANOVA? Inferential Logic and ANOVA Sums of Squares Formulas: Deviation Score Method Calculating Sums of Squares: Deviation Score Method Sums of Squares Formulas: Raw Score Method Calculating Sums of Squares: Raw Score Method Remaining Steps Interpreting a One-Way ANOVA The ANOVA Summary Table Part XI. Post Hoc Tests: "So Who's Responsible?" 26. Tukey HSD Test Why Do We Need a Post Hoc Test? Calculating the Tukey HSD Interpreting the Tukey HSD 27. Scheffe Test Why Do We Need a Post Hoc Test? Calculating the Scheffe Interpreting the Scheffe Part XII. More Than One Independent Variable: "Double Dutch Jump Rope" 28. Main Effects and Interaction Effects What Is a Factorial ANOVA? Factorial ANOVA Designs Number and Type of Hypotheses Main Effects Interaction Effects Looking Ahead 29. Factorial ANOVA Review of Factorial ANOVA Designs Data Setup and Preliminary Expectations Sums of Squares Formulas Calculating Factorial ANOVA Sums of Squares: Raw Score Method Factorial Mean Squares and Fs Interpreting a Factorial F Test The Factorial ANOVA Summary Table Part XIII. Nonparametric Statistics: "Without Form or Void" 30. One-Variable Chi-Square: Goodness of Fit What Is a Nonparametric Test? Chi-Square as a Goodness-of-Fit Test Formula for a Chi-Square Inferential Logic and Chi-Square Calculating a Chi-Square Goodness of Fit Interpreting a Chi-Square Goodness of Fit Looking Ahead 31. Two-Variable Chi-Square: Test of Independence Chi-Square as a Test of Independence Prerequisites for a Chi-Square Test of Independence Formula for a Chi-Square Finding Expected Frequencies Calculating a Chi-Square Test of Independence Interpreting a Chi-Square Test of Independence Part XIV. Effect Size and Power: "How Much Is Enough?" 32. Measures of Effect Size What Is Effect Size? For Two-Sample t Tests For ANOVA F Tests For Chi-Square Tests 33. Power and the Factors Affecting It What Is Power? Factors Affecting Power Putting It Together: Alpha, Power, Effect Size, and Sample Size Looking Ahead Part XV. Correlation: "Whither Thou Goest, I Will Go" 34. Relationship Strength and Direction Experimental Versus Correlational Studies Plotting Correlation Data Relationship Strength Relationship Direction Linear and Nonlinear Relationships Outliers and Their Effects Looking Ahead 35. Pearson r What Is a Correlation Coefficient? Formulas for Pearson r z-Score Scatterplots and r Calculating Pearson r: Raw Score Method Interpreting a Pearson r Coefficient Looking Ahead 36. Correlation Pitfalls Effect of Sample Size on Statistical Significance Statistical Significance Versus Practical Importance Effect of Restriction in Range Effect of Sample Heterogeneity or Homogeneity Effect of Unreliability in the Measurement Instrument Correlation Versus Common Variance Correlation Versus Causation Part XVI. Linear Prediction: "You're So Predictable" 37. Linear Prediction Correlation Permits Prediction Logic of a Prediction Line Concept of Best-Fitting Line Equation for Best-Fitting Line Using a Prediction Equation to Predict Scores on Y 38. Standard Error of Prediction What Is a Confidence Interval? Correlation and Prediction Error Distribution of Prediction Error Calculating the Standard Error of Prediction Using the Standard Error of Prediction to Calculate Confidence Intervals Factors Influencing the Standard Error of Prediction Part XVII. Review: "Say It Again, Sam" 39. Selecting the Appropriate Analysis Review of Descriptive Methods Review of Inferential Methods Appendix A: Normal Curve Table Appendix B: Binomial Table Appendix C: t Table Appendix D: F Table (ANOVA) Appendix E: Studentized Range Statistic (for Tukey HSD) Appendix F: Chi-Square Table Appendix G: Correlation Table References Index About the Author