Statistics Alive! 3/e

Wendy J. Steinberg entered academia midcareer, having spent the first part of her career in high-stakes test development. She holds a PhD in educational psychology with dual concentrations, one in measurement and the other in development and cognition. Teaching is her passion. She views education as a sacred task that teachers and students alike should treat with reverence. She wants this textbook in the hands of every statistics student so that tears will be banished forever from the classroom. A portion of the sale of each textbook goes to charity Matthew Price holds a PhD in clinical psychology and has spent his career pursuing two goals. The first is helping victims of trauma and the second is teaching statistics. From his time in undergraduate statistics, he saw the challenge that this topic posed to many talented students. He has since spent many late nights making heads or tails out of how to teach the probability of heads and tails in an approachable and enjoyable manner. He is honored to assist in writing this textbook to continue to help all of those students who have yet to discover the awesomeness of stats.

List of Figures List of Tables Preface Supplemental Material for Use With Statistics Alive! Acknowledgments About the Authors PART I. PRELIMINARY INFORMATION: "FIRST THINGS FIRST" Module 1. Math Review, Vocabulary, and Symbols Getting Started Common Terms and Symbols in Statistics Fundamental Rules and Procedures for Statistics More Rules and Procedures Module 2. Measurement Scales What Is Measurement? Scales of Measurement Continuous Versus Discrete Variables Real Limits PART II. TABLES AND GRAPHS: "ON DISPLAY" Module 3. Frequency and Percentile Tables Why Use Tables? Frequency Tables Relative Frequency or Percentage Tables Grouped Frequency Tables Percentile and Percentile Rank Tables SPSS Connection Module 4. Graphs and Plots Why Use Graphs? Graphing Continuous Data Symmetry, Skew, and Kurtosis Graphing Discrete Data SPSS Connection PART III. CENTRAL TENDENCY: "BULL'S-EYE" Module 5. Mode, Median, and Mean What Is Central Tendency? Mode Median Mean Skew and Central Tendency SPSS Connection PART IV. DISPERSION: "FROM HERE TO ETERNITY" Module 6. Range, Variance, and Standard Deviation What Is Dispersion? Range Variance Standard Deviation Mean Absolute Deviation Controversy: N Versus n - 1 SPSS Connection PART V. THE NORMAL CURVE AND STANDARD SCORES: "WHAT'S THE SCORE?" Module 7. Percent Area and the Normal Curve What Is a Normal Curve? History of the Normal Curve Uses of the Normal Curve Looking Ahead Module 8. z Scores What Is a Standard Score? Benefits of Standard Scores Calculating z Scores Comparing Scores Across Different Tests SPSS Connection Module 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" Module 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 Module 11. The Binomial Distribution What Are Dichotomous Events? Finding Probabilities by Listing and Counting Finding Probabilities 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" Module 12. Sampling, Variables, and Hypotheses From Description to Inference Sampling Variables Hypotheses Module 13. Errors and Significance Random Sampling Revisited Sampling Error Significant Difference The Decision Table Type I Error Type II Error Module 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?" Module 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 Module 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 Module 17. One-Sample t Test Z Test Versus t Test Comparison of Z-Test and 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 SPSS Connection Module 18. Interpreting and Reporting One-Sample t: Error, Confidence, and Parameter Estimates What It Means to Reject the Null Refining Error Decision Making With a One-Sample t Test Dichotomous Decisions Versus Reports of Actual p Parameter Estimation: Point and Interval SPSS Connection PART IX. THE TWO-SAMPLE TEST: "OURS IS BETTER THAN YOURS" Module 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 Module 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 SPSS Connection Module 21. t Test With Unequal Sample Sizes What Makes Sample Sizes Unequal? Comparison of Special-Case and Generalized Formulas Calculating a t Test With Unequal Sample Sizes Interpreting a t Test With Unequal Sample Sizes SPSS Connection Module 22. t Test With Related Samples What Makes Samples Related? Comparison of Special-Case and Related-Samples Formulas Advantage and Disadvantage of Related Samples Direct-Difference Formula Calculating a t Test With Related Samples Interpreting a t Test With Related Samples SPSS Connection Module 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 SPSS Connection PART X. THE MULTISAMPLE TEST: "OURS IS BETTER THAN YOURS OR THEIRS" Module 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 Module 25. One-Way ANOVA: Independent Samples and Equal Sample Sizes What Is a One-Way ANOVA? Inferential Logic and ANOVA Deviation Score Method Raw Score Method Remaining Steps for Both Methods: Mean Squares and F Interpreting a One-Way ANOVA The ANOVA Summary Table SPSS Connection PART XI. POST HOC TESTS: "SO WHO'S RESPONSIBLE?" Module 26. Tukey HSD Test Why Do We Need a Post Hoc Test? Calculating the Tukey HSD Interpreting the Tukey HSD SPSS Connection Module 27. Scheffe Test Why Do We Need a Post Hoc Test? Calculating the Scheffe Interpreting the Scheffe SPSS Connection PART XII. MORE THAN ONE INDEPENDENT VARIABLE: "DOUBLE DUTCH JUMP ROPE" Module 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 Module 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 SPSS Connection PART XIII. NONPARAMETRIC STATISTICS: "WITHOUT FORM OR VOID" Module 30. One-Variable Chi-Square: Goodness of Fit What Is a Nonparametric Test? Chi-Square as a Goodness-of-Fit Test Formula for Chi-Square Inferential Logic and Chi-Square Calculating a Chi-Square Goodness of Fit Interpreting a Chi-Square Goodness of Fit Looking Ahead SPSS Connection Module 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 SPSS Connection PART XIV. EFFECT SIZE AND POWER: "HOW MUCH IS ENOUGH?" Module 32. Measures of Effect Size What Is Effect Size? For Two-Sample t Tests For ANOVA F Tests For Chi-Square Tests Module 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" Module 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 SPSS Connection Module 35. Pearson r What Is a Correlation Coefficient? Calculation of a Pearson r Formulas for Pearson r z-Score Scatterplots and r Calculating Pearson r: Deviation Score Method Interpreting a Pearson r Coefficient Looking Ahead SPSS Connection Module 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 Causation PART XVI. LINEAR PREDICTION: "YOU'RE SO PREDICTABLE" Module 37. Linear Prediction Correlation Permits Prediction Logic of a Prediction Line Equation for the Best-Fitting Line Using a Prediction Equation to Predict Scores on Y Another Calculation Example SPSS Connection Module 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 Another Calculation Example Module 39. Introduction to Multiple Regression What Is Regression? Prediction Error, Revisited Why Multiple Regression? The Multiple Regression Equation Multiple Regression and Predicted Variance Hypothesis Testing in Multiple Regression An Example The General Linear Model SPSS Connection PART XVII. REVIEW: "SAY IT AGAIN, SAM" Module 40. 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 Appendix H: Odd Solutions to Textbook Exercises References Index