Statistics

Preface Acknowledgments About the Author Chapter 1: A Gentle Introduction How Much Math Do I Need to Do Statistics? The General Purpose of Statistics: Understanding the World What Is a Statistician? Liberal and Conservative Statisticians Descriptive and Inferential Statistics Experiments Are Designed to Test Theories and Hypotheses Oddball Theories Bad Science and Myths Eight Essential Questions of Any Survey or Study On Making Samples Representative of the Population Experimental Design and Statistical Analysis as Controls The Language of Statistics On Conducting Scientific Experiments The Dependent Variable and Measurement Operational Definitions Measurement Error Measurement Scales: The Difference Between Continuous and Discrete Variables Types of Measurement Scales Rounding Numbers and Rounding Error Statistical Symbols Summary History Trivia: Achenwall to Nightingale Key Terms Chapter 1 Practice Problems Chapter 1 Test Yourself Questions SPSS Lesson 1 Chapter 2: Descriptive Statistics: Understanding Distributions of Numbers The Purpose of Graphs and Tables: Making Arguments and Decisions A Summary of the Purpose of Graphs and Tables Graphical Cautions Frequency Distributions Shapes of Frequency Distributions Grouping Data Into Intervals Advice on Grouping Data Into Intervals The Cumulative Frequency Distribution Cumulative Percentages, Percentiles, and Quartiles Stem-and-Leaf Plot Non-normal Frequency Distributions On the Importance of the Shapes of Distributions Additional Thoughts About Good Graphs Versus Bad Graphs History Trivia: De Moivre to Tukey Key Terms Chapter 2 Practice Problems Chapter 2 Test Yourself Questions SPSS Lesson 2 Chapter 3: Statistical Parameters: Measures of Central Tendency and Variation Measures of Central Tendency Choosing Among Measures of Central Tendency Klinkers and Outliers Uncertain or Equivocal Results Measures of Variation Correcting for Bias in the Sample Standard Deviation How the Square Root of x2 Is Almost Equivalent to Taking the Absolute Value of x The Computational Formula for Standard Deviation The Variance The Sampling Distribution of Means, the Central Limit Theorem, and the Standard Error of the Mean The Use of the Standard Deviation for Prediction Practical Uses of the Empirical Rule: As a Definition of an Outlier Practical Uses of the Empirical Rule: Prediction and IQ Tests Some Further Comments History Trivia: Fisher to Eels Key Terms Chapter 3 Practice Problems Chapter 3 Test Yourself Questions SPSS Lesson 3 Chapter 4: Standard Scores, the z Distribution, and Hypothesis Testing Standard Scores The Classic Standard Score: The z Score and the z Distribution Calculating z Scores More Practice on Converting Raw Data Into z Scores Converting z Scores to Other Types of Standard Scores The z Distribution Interpreting Negative z Scores Testing the Predictions of the Empirical Rule With the z Distribution Why Is the z Distribution So Important? How We Use the z Distribution to Test Experimental Hypotheses More Practice With the z Distribution and T Scores Summarizing Scores Through Percentiles History Trivia: Karl Pearson to Egon Pearson Key Terms Chapter 4 Practice Problems Chapter 4 Test Yourself Questions SPSS Lesson 4 Chapter 5: Inferential Statistics: The Controlled Experiment, Hypothesis Testing, and the z Distribution Hypothesis Testing in the Controlled Experiment Hypothesis Testing: The Big Decision How the Big Decision Is Made: Back to the z Distribution The Parameter of Major Interest in Hypothesis Testing: The Mean Nondirectional and Directional Alternative Hypotheses A Debate: Retain the Null Hypothesis or Fail to Reject the Null Hypothesis The Null Hypothesis as a Nonconservative Beginning The Four Possible Outcomes in Hypothesis Testing Significance Levels Significant and Nonsignificant Findings Trends, and Does God Really Love the .05 Level of Significance More Than the .06 Level? Directional or Nondirectional Alternative Hypotheses: Advantages and Disadvantages Did Nuclear Fusion Occur? Baloney Detection Conclusions About Science and Pseudoscience The Most Critical Elements in the Detection of Baloney in Suspicious Studies and Fraudulent Claims Can Statistics Solve Every Problem? Probability History Trivia: Egon Pearson to Karl Pearson Key Terms Chapter 5 Practice Problems Chapter 5 Test Yourself Questions SPSS Lesson 5 Chapter 6: An Introduction to Correlation and Regression Correlation: Use and Abuse A Warning: Correlation Does Not Imply Causation Another Warning: Chance Is Lumpy Correlation and Prediction The Four Common Types of Correlation The Pearson Product-Moment Correlation Coefficient Testing for the Significance of a Correlation Coefficient Obtaining the Critical Values of the t Distribution If the Null Hypothesis Is Rejected Representing the Pearson Correlation Graphically: The Scatterplot Fitting the Points With a Straight Line: The Assumption of a Linear Relationship Interpretation of the Slope of the Best-Fitting Line The Assumption of Homoscedasticity The Coefficient of Determination: How Much One Variable Accounts for Variation in Another Variable-The Interpretation of r2 Quirks in the Interpretation of Significant and Nonsignificant Correlation Coefficients Linear Regression Reading the Regression Line Final Thoughts About Multiple Regression Analyses: A Warning About the Interpretation of the Significant Beta Coefficients Spearman's Correlation Significance Test for Spearman's r Ties in Ranks Point-Biserial Correlation Testing for the Significance of the Point-Biserial Correlation Coefficient Phi (F) Correlation Testing for the Significance of Phi History Trivia: Galton to Fisher Key Terms Chapter 6 Practice Problems Chapter 6 Test Yourself Questions SPSS Lesson 6 Chapter 7: The t Test for Independent Groups The Statistical Analysis of the Controlled Experiment One t Test but Two Designs Assumptions of the Independent t Test The Formula for the Independent t Test You Must Remember This! An Overview of Hypothesis Testing With the t Test What Does the t Test Do? Components of the t Test Formula What If the Two Variances Are Radically Different From One Another? A Computational Example Marginal Significance The Power of a Statistical Test Effect Size The Correlation Coefficient of Effect Size Another Measure of Effect Size: Cohen's d Confidence Intervals Estimating the Standard Error History Trivia: Gosset and Guinness Brewery Key Terms Chapter 7 Practice Problems Chapter 7 Test Yourself Questions SPSS Lesson 7 Chapter 8: The t Test for Dependent Groups Variations on the Controlled Experiment Assumptions of the Dependent t Test Why the Dependent t Test May Be More Powerful Than the Independent t Test How to Increase the Power of a t Test Drawbacks of the Dependent t Test Designs One-Tailed or Two-Tailed Tests of Significance Hypothesis Testing and the Dependent t Test: Design 1 Design 1 (Same Participants or Repeated Measures): A Computational Example Design 2 (Matched Pairs): A Computational Example Design 3 (Same Participants and Balanced Presentation): A Computational Example History Trivia: Fisher to Pearson Key Terms Chapter 8 Practice Problems Chapter 8 Test Yourself Questions SPSS Lesson 8 Chapter 9: Analysis of Variance (ANOVA): One-Factor Completely Randomized Design A Limitation of Multiple t Tests and a Solution The Equally Unacceptable Bonferroni Solution The Acceptable Solution: An Analysis of Variance The Null and Alternative Hypotheses in ANOVA The Beauty and Elegance of the F Test Statistic The F Ratio How Can There Be Two Different Estimates of Within-Groups Variance? ANOVA Designs ANOVA Assumptions Pragmatic Overview What a Significant ANOVA Indicates A Computational Example Degrees of Freedom for the Numerator Degrees of Freedom for the Denominator Determining Effect Size in ANOVA: Omega Squared (w2) Another Measure of Effect Size: Eta (h) History Trivia: Gosset to Fisher Key Terms Chapter 9 Practice Problems Chapter 9 Test Questions Chapter 9 Test Yourself Questions SPSS Lesson 9 Chapter 10: After a Significant ANOVA: Multiple Comparison Tests Conceptual Overview of Tukey's Test Computation of Tukey's HSD Test What to Do If the Number of Error Degrees of Freedom Is Not Listed in the Table of Tukey's q Values Determining What It All Means Warning! On the Importance of Nonsignificant Mean Differences Final Results of ANOVA Quirks in Interpretation Tukey's With Unequal Ns Key Terms Chapter 10 Practice Problems Chapter 10 Test Yourself Questions SPSS Lesson 10 Chapter 11: Analysis of Variance (ANOVA): One-Factor Repeated-Measures Design The Repeated-Measures ANOVA Assumptions of the One-Factor Repeated-Measures ANOVA Computational Example Determining Effect Size in ANOVA Key Terms Chapter 11 Practice Problems Chapter 11 Test Yourself Questions SPSS Lesson 11 Chapter 12: Factorial ANOVA: Two-Factor Completely Randomized Design Factorial Designs The Most Important Feature of a Factorial Design: The Interaction Fixed and Random Effects and In Situ Designs The Null Hypotheses in a Two-Factor ANOVA Assumptions and Unequal Numbers of Participants Computational Example Key Terms Chapter 12 Practice Problems Chapter 12 Test Yourself Problems SPSS Lesson 12 Chapter 13: Post Hoc Analysis of Factorial ANOVA Main Effect Interpretation: Gender Why a Multiple Comparison Test Is Unnecessary for a Two-Level Main Effect, and When Is a Multiple Comparison Test Necessary? Main Effect: Age Levels Multiple Comparison Test for the Main Effect for Age Warning: Limit Your Main Effect Conclusions When the Interaction Is Significant Multiple Comparison Tests Interpretation of the Interaction Effect Final Summary Writing Up the Results Journal Style Language to Avoid Exploring the Possible Outcomes in a Two-Factor ANOVA Determining Effect Size in a Two-Factor ANOVA History Trivia: Fisher and Smoking Key Terms Chapter 13 Practice Problems Chapter 13 Test Yourself Questions SPSS Lesson 13 Chapter 14: Factorial ANOVA: Additional Designs The Split-Plot Design Overview of the Split-Plot ANOVA Computational Example Two-Factor ANOVA: Repeated Measures on Both Factors Design Overview of the Repeated-Measures ANOVA Computational Example Key Terms and Definitions Chapter 14 Practice Problems Chapter 14 Test Yourself Questions SPSS Lesson 14 Chapter 15: Nonparametric Statistics: The Chi-Square Test and Other Nonparametric Tests Overview of the Purpose of Chi-Square Overview of Chi-Square Designs Chi-Square Test: Two-Cell Design (Equal Probabilities Type) The Chi-Square Distribution Assumptions of the Chi-Square Test Chi-Square Test: Two-Cell Design (Different Probabilities Type) Interpreting a Significant Chi-Square Test for a Newspaper Chi-Square Test: Three-Cell Experiment (Equal Probabilities Type) Chi-Square Test: Two-by-Two Design What to Do After a Chi-Square Test Is Significant When Cell Frequencies Are Less Than 5 Revisited Other Nonparametric Tests History Trivia: Pearson and Biometrika Key Terms Chapter 15 Practice Problems Chapter 15 Test Yourself Questions SPSS Lesson 15 Chapter 16: Other Statistical Topics, Parameters, and Tests Big Data Health Science Statistics Additional Statistical Analyses and Multivariate Statistics A Summary of Multivariate Statistics Coda Key Terms Chapter 16 Practice Problems Chapter 16 Test Yourself Questions Appendix A: z Distribution Appendix B: t Distribution Appendix C: Spearman's Correlation Appendix D: Chi-Square ?2 Distribution Appendix E: F Distribution Appendix F: Tukey's Table Appendix G: Mann-Whitney U Critical Values Appendix H: Wilcoxon Signed-Rank Test Critical Values Appendix I: Answers to Odd-Numbered Test Yourself Questions Glossary References Index