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Table of Contents o Chapter 1 ? A Gentle Introduction o Don?t Panic! o How Much Math Do I Need to Do Statistics? o The General Purpose of Statistics: Understanding the World o Another Purpose of Statistics: Making an Argument or a Decision o What Is a Statistician? * One Role: The Curious Detective * Another Role: The Honest Attorney * A Final Role: A Good Storyteller o Liberal and Conservative Statisticians o Descriptive and Inferential Statistics o Experiments Are Designed to Test Theories and Hypotheses o Oddball Theories o Bad Science and Myths o Eight Essential Questions of Any Survey or Study * Who was surveyed or studied? * Why did the people participate in the study? * Was there a control group and did the control group receive a placebo? * How many people participated in the study? * How were the questions worded to the participants in the study? * Was causation assumed from a correlational study? * Who paid for the study? * Was the study published in a peer-reviewed journal? o On Making Samples Representative of the Population o Experimental Design and Statistical Analysis as Controls o The Language of Statistics o On Conducting Scientific Experiments o The Dependent Variable and Measurement o Operational Definitions o Measurement Error o Measurement Scales: The Difference Between Continuous and Discrete Variables o Types of Measurement Scales o Rounding Numbers and Rounding Error o Statistical Symbols o History Trivia ? Achenwall to Nightingale o Key Terms, Symbols, and Definitions o Chapter 1 Practice Problems o Chapter 1 Test Questions o Chapter 2 ? Descriptive Statistics: Understanding Distributions of Numbers o Chapter 2 Goals * Learn the purposes of graphs and tables * Learn how a good graph stopped a cholera epidemic * Learn how bad graphs and tables contributed to the Space Shuttle Challenger explosion * Learn how to make graphs and tables * Understand how to avoid chart junk * Learn how to make a frequency distribution * Understand the essential characteristics of frequency distributions o The Purpose of Graphs and Tables: Making Arguments and Decisions o How a Good Graph Stopped a Cholera Epidemic o How Bad Graphs and Tables Contributed to the Space Shuttle Challenger Explosion o How a Poor PowerPoint Presentation Contributed to the Space Shuttle Columbia Disaster o A Summary of the Purpose of Graphs and Tables * Document the sources of statistical data and its characteristics * Make appropriate comparisons * Demonstrate the mechanisms of cause and effect and express the mechanisms quantitatively * Recognize the inherent multivariate nature of analytic problems * Inspect and evaluate alternative hypotheses o Graphical Cautions o Frequency Distributions o Shapes of Frequency Distributions o Grouping Data into Intervals o Advice on Grouping Data into Intervals * Choose interval widths that reduce your data to five to ten intervals * Choose the size of your interval widths based on understandable units, for example, multiples of five or ten * Make sure that your chosen intervals do not overlap o The Cumulative Frequency Distribution o Cumulative Percentages, Percentiles, and Quartiles o Stem-and-Leaf Plot o Non-Normal Frequency Distributions o On the Importance of the Shapes of Distributions o Additional Thoughts About Good Graphs Versus Bad Graphs * Low Density Graphs * Chart Junk * Changing Scales Mid-Stream (or Mid-Axis) * Labeling the Graph Badly * The Multicolored Graph * PowerPoint Graphs and Presentations o History Trivia ? De Moivre to Tukey o Key Terms and Definitions o Chapter 2 Practice Problems o Chapter 2 Test Questions o Chapter 3 ? Statistical Parameters o Measures of Central Tendency * The Mean * The Median * The Mode o Choosing Between Measures of Central Tendency o Klinkers and Outliers o Uncertain or Equivocal Results o Measures of Variation * The Range * The Standard Deviation o Correcting for Bias in the Sample Standard Deviation o How the Square Root of x2 is Almost Equivalent to Taking the Absolute Value of x o The Computational Formula for Standard Deviation o The Variance o The Sampling Distribution of Means, the Central Limit Theorem, and the Standard Error of the Mean o The Use of the Standard Deviation for Prediction o Practical Uses of the Empirical Rule: As a Definition of an Outlier o Practical Uses of the Empirical Rule: Prediction and IQ Tests o Some Further Comments o History Trivia ? Fisher to Eels o Key Terms, Symbols and Definitions o Chapter 3 Practice Problems o Chapter 3 Test Questions o Chapter 4 ? Standard Scores, the Z Distribution, and Hypothesis Testing o Standard Scores o The Classic Standard Score: The Z Score and the Z Distribution o Calculating Z Scores o More Practice on Converting Raw Data into Z Scores o Converting from Z Scores to Other Types of Standard Scores o The Z Distribution o Interpreting Negative Z Scores o Testing the Predictions of the Empirical Rule with the Z Distribution o Why is the Z Distribution So Important? o How We Use the Z Distribution to Test Experimental Hypotheses o More Practice with the Z Distribution and T Scores o Summarizing Scores Through Percentiles o History Trivia ? Karl Pearson to Egon Pearson o Key Terms, Symbols, and Definitions o Chapter 4 Practice Problems o Chapter 4 Test Questions o Chapter 5 ? Inferential Statistics: The Controlled Experiment, Hypothesis Testing, and the Z Distribution o Hypothesis Testing in the Controlled Experiment o Hypothesis Testing: The Big Decision o How the Big Decision Is Made: Back to the Z Distribution o The Parameter of Major Interest in Hypothesis Testing: The Mean o Non-Directional and Directional Alternative Hypotheses o A Debate: Retain the Null Hypothesis or Fail to Reject the Null Hypothesis o The Null Hypothesis as a Non-Conservative Beginning o The Four Possible Outcomes in Hypothesis Testing * Correct Decision: Retain H0, When H0 is Actually True * Type I Error: Reject H0, When H0 is Actually True * Correct Decision: Reject H0, When H0 is Actually False * Type II Error: Retain H0, When H0 is Actually False o Significance Levels o Significant and Non-Significant Findings o Trends and Does God Really Love the .05 Level of Significance More Than the .06 Level? o Directional or Non-Directional Alternative Hypotheses: Advantages and Disadvantages o Did Nuclear Fusion Occur? o Baloney Detection * How reliable is the source of the claim? * Does this source often make similar claims? * Have the claims been verified by another source? * How does the claim fit with known natural scientific laws? * Can the claim be disproven or has only supportive evidence been sought? * Do the claimant?s personal beliefs and biases drive their conclusions or vice versa? o Conclusions about Science and Pseudoscience o The Most Critical Elements in the Detection of Baloney in Suspicious Studies and Fraudulent Claims o Can Statistics Solve Every Problem? o Probability * The Lady Tasting Tea * The Definition of the Probability of an Event * The Multiplication Theorem of Probability * Combinations Theorem of Probability * Permutations Theorem of Probability * Gambler?s Fallacy * Coda o History Trivia ? Egon Pearson to Karl Pearson o Key Terms, Symbols, and Definitions o Chapter 5 Practice Problems o Chapter 5 Test Questions o Chapter 6 ? An Introduction to Correlation o Correlation: Use and Abuse o A Warning: Correlation Does Not Imply Causation * Marijuana use and heroin use are positively correlated * Milk use is positively correlated to cancer rates * Weekly church attendance is negatively correlated with drug abuse * Lead levels are positively correlated to antisocial behavior * The risk of getting Alzheimer?s Dementia is negatively correlated with smoking cigarettes * Sexual activity is negatively correlated with increases in education * An active sex life is positively correlated with longevity * Coffee drinking is negatively correlated with suicidal risk o Another Warning: Chance Is Lumpy o Correlation and Prediction o The Four Common Types of Correlation * Pearson?s r * Spearman?s r * Point-Biserial r * Phi (í) Correlation o The Pearson Product-Moment Correlation Coefficient o Testing for the Significance of a Correlation Coefficient o Obtaining the Critical Values of the t Distribution * Choose a one-tailed or two-tailed test of significance * Choose the level of significance * Determine the degrees of freedom (df) * Determine whether the t from the formula (called the derived t) exceeds the tabled critical values from the t distribution o If the Null Hypothesis is Rejected o Representing the Pearson Correlation Graphically: The Scatterplot o Fitting the Points with a Straight Line: The Assumption of a Linear Relationship o Interpretation of the Slope of the Best-Fitting Line o The Assumption of Homoscedasticity o The Coefficient of Determination: How Much One Variable Accounts for Variation in Another Variable: The Interpretation of r2 o Quirks in the Interpretation of Significant and Nonsignificant Correlation Coefficients o Linear Regression o Reading the Regression Line * R * R Square * Adjusted R Square o Final Thoughts About Regression Analysis o Spearman?s Correlation o Significance Test for Spearman?s r o Ties in Ranks o Point-Biserial Correlation o Testing for the Significance of the Point-Biserial Correlation Coefficient o Phi í Correlation o Testing for the Significance of Phi o History Trivia ? Galton to Fisher o Key Terms, Symbols, and Definitions o Chapter 6 Practice Problems o Chapter 6 Test Questions o Chapter 7 ?The t Test for Independent Groups o The Statistical Analysis of the Controlled Experiment o One t Test But Two Designs o Assumptions of the Independent t Test * Independent Groups * Normality of the Dependent Variable * Homogeneity of Variance o The Formula for the Independent t Test o You Must Remember This! An Overview of Hypothesis Testing with the t Test o What Does the t Test Do?: Components of the t Test Formula o What if the Two Variances Are Radically Different from One Another? o A Computational Example o Steps in the t Test Formula o Testing the Null Hypothesis o Steps in Determining Significance o The Power of a Statistical Test o Effect Size o The Correlation Coefficient of Effect Size o Confidence Intervals o Estimating the Standard Error o History Trivia ? Gosset and Guinness Brewery o Key Terms and Definitions o Chapter 7 Practice Problems o Chapter 7 Test Questions o Chapter 8 ?The t Test for Dependent Groups o Variations on the Controlled Experiment: o Design 1 o Design 2 o Design 3 o Assumptions of the Dependent t Test o Why the Dependent t Test May Be More Powerful than the Independent t Test o How to Increase the Power of a t Test o Drawbacks of the Dependent t Test Designs o One-Tailed or Two-Tailed Tests of Significance o Hypothesis Testing and the Dependent t Test: Design 1 o Design 1: Same Participants or Repeated Measures: A Computational Example o Determination of Effect Size o Design 2: Matched Pairs: A Computational Example o Determination of Effect Size o Design 3: Same Participants and Balanced Presentation: A Computational Example o Determination of Effect Size o History Trivia ? Fisher to Pearson o Key Terms and Definitions o Chapter 8 Practice Problems o Chapter 8 Test Questions o Chapter 9 ? Analysis of Variance: One Factor Completely Randomized Design o A Limitation of Multiple t Tests and a Solution o The Equally Unacceptable Bonferroni Solution o The Acceptable Solution: An Analysis of Variance o The Null and Alternative Hypotheses in Analysis of Variance o The Beauty and Elegance of the F Test Statistic o The F Ratio o How Can There Be Two Different Estimates of Within-Groups Variance? o ANOVA Designs o ANOVA Assumptions o Pragmatic Overview o What a Significant ANOVA Indicates o A Computational Example o Determining Effect Size in ANOVA o History Trivia ? Gosset to Fisher o Key Terms and Definitions o Chapter 9 Practice Problems o Chapter 9 Test Questions o Chapter 10 ? After a Significant Analysis of Variance: Multiple Comparison Tests o Multiple Comparison Tests o Conceptual Overview of Tukey?s Test o Computation of Tukey?s HSD Test o What to Do if the Error Degrees of Freedom Are Not Listed in the Table of Tukey?s q Values o Determining What It All Means o On the Importance of Nonsignificant Mean Differences o Final Results of ANOVA o Tukey?s with Unequal Ns o History Trivia o Key Terms, Symbols and Definitions o Chapter 10 Practice Problems o Chapter 10 Test Questions o Chapter 11 ? Analysis of Variance: One Factor Repeated Measures Design o The Repeated Measures ANOVA o Assumptions of the One Factor Repeated Measures ANOVA o Computational Example o Determining Effect Size in ANOVA o Key Terms and Definitions o Chapter 11 Practice Problems o Chapter 11 Test Questions o Chapter 12 ? Analysis of Variance: Two Factor Completely Randomized Design o Factorial Designs o The Most Important Feature of a Factorial Design: The Interaction o Fixed and Random Effects and In Situ Designs o The Null Hypothesis in a Two Factor ANOVA o Assumptions and Unequal Numbers of Participants o Computational Example * Computation of the First Main Effect * Computation of the Second Main Effect * Computation of the Interaction Between the Two Main Effects o Interpretation of the Results o Key Terms and Definitions o Chapter 12 Practice Problems o Chapter 12 Test Questions o Chapter 13 ? Post Hoc Analysis of Factorial ANOVA o Main Effect Interpretation: Gender o Why a Multiple Comparison Test is Unnecessary for a Two-Level Main Effect, and When is a Multiple Comparison Test Necessary o Main Effect: Age Levels o Multiple Comparison Test for the Main Effect for Age o When Is a Multiple Comparison Test Necessary for a Significant Main Effect? o Warning: Limit Your Main Effect Conclusions when the Interaction is Significant o Multiple Comparison Tests o Interpretation of Interaction Effect o Final Summary o Writing Up the Results Journal Style o Language to Avoid o Exploring the Possible Outcomes in a Two Factor ANOVA o Determining Effect Size in a Two Factor ANOVA o History Trivia ? Fisher and Smoking o Key Terms, Symbols, and Definitions o Chapter 13 Practice Problems o Chapter 13 Test Questions o Chapter 14 ? Factorial Analysis of Variance: Additional Designs o The Split-Plot Design o Overview of the Split-Plot ANOVA o Computational Example * Main Effect: Social Facilitation * Main Effect: Trials * Interaction Effect: Social Facilitation x Trials o Two Factor ANOVA: Repeated Measures on Both Factors Design o Overview of the Repeated Measures ANOVA o Computational Example o History Trivia o Key Terms and Definitions o Chapter 14 Practice Problems o Chapter 14 Test Questions o Chapter 15 ? Nonparametric Statistics ? The Chi Square Test o Overview of the Purpose of Chi Square o Overview of Chi Square Designs o Chi Square Designs o Chi Square Test: Two-Cell Design (Equal Probabilities Type) * Computation of the Two-Cell Design o The Chi Square Distribution o Assumptions of the Chi Square Test o Chi Square Test: Two-Cell Design (Different Probabilities Type) * Computation of the Two-Cell Design o Interpreting a Significant Chi Square Test for a Newspaper o Chi Square Test: Three-Cell Experiment (Equal Probabilities Type)) * Computation of the Three Cell Design o Chi Square Test: Two by Two Design * Computation of the Chi Square Test: Two by Two Design o What to Do After a Chi Square Test Is Significant o When Cell Frequencies Are Less Than Five Revisited o History Trivia ? Pearson and Biometrika o Key Terms, Symbols, and Definitions o Chapter 15 Practice Problems o Chapter 15 Test Questions o Chapter 16 ? Other Statistical Parameters and Tests o Health Science Statistics o Test Characteristics o Risk Assessment o Parameters of Mortality and Morbidity o Multivariate Statistics o Analysis of Covariance o Multivariate Analysis of Variance o Multivariate Analysis of Covariance o Factor Analysis o Multiple Regression o Canonical Correlation o Linear Discriminant Function Analysis o Cluster Analysis o A Summary of Multivariate Statistics o Coda o Key Terms and Definitions o Chapter 16 Practice Problems o Chapter 16 Test Questions o Appendix A: Z Distribution o Appendix B: The t Distribution o Appendix C: Spearman?s Correlation o Appendix D: The Chi Square Distribution o Appendix E: The F Distribution o Appendix F: Tukey?s Table o References o Index

Library of Congress Subject Headings for this publication:

Mathematical statistics -- Textbooks.