Statistics

1. Introduction. 1.1 Why Study Statistics? 1.2 What Is Statistics? 1.3 More About Inferential Statistics. 1.4 Three Types of Data. 1.5 Levels of Measurement. 1.6 Types of Variables. 1.7 How to Use This Book. Summary. Important Terms. Review Questions. Part I: Descriptive Statistics. 2. Describing Data with Tables and Graphs. Tables (Frequency Distributions). 2.1 Frequency Distributions for Quantitative Data. 2.2 Guidelines. 2.3 Outliers. 2.4 Relative Frequency Distributions. 2.5 Cumulative Frequency Distributions. 2.6 Frequency Distributions for Qualitative (Nominal) Data. 2.7 Interpreting Distributions Constructed by Others. Graphs. 2.8 Graphs for Quantitative Data. 2.9 Typical Shapes. 2.10 A Graph for Qualitative (Nominal) Data. 2.11 Misleading Graphs. 2.12 Doing It Yourself. Summary. Important Terms. Review Questions. 3. Describing Data with Averages. 3.1 Mode. 3.2 Median. 3.3 Mean. 3.4 Which Average? 3.5 Averages for Qualitative and Ranked Data. Summary. Important Terms. Key Equation. Review Questions. 4. Describing Variability. 4.1 Intuitive Approach. 4.2 Range. 4.3 Variance. 4.4 Standard Deviation. 4.5 DETAILS: Standard Deviation. 4.6 Degrees of Freedom (df). 4.7 Interquartile Range (IQR). 4.8 Measures of Variability for Qualitative and Ranked Data. Summary. Important Terms. Key Equations. Review Questions. 5. Normal Distributions and Standard Scores ( z ). 5.1 The Normal Curve. 5.2 z Scores. 5.3 Standard Normal Curve. 5.4 Solving Normal Curve Problems. 5.5 Finding Proportions. 5.6 Finding Scores. 5.7 More about z Scores. Summary. Important Terms. Key Equations. Review Questions. 6. Describing Relationships: Correlation. 6.1 An Intuitive Approach. 6.2 Scatterplots. 6.3 A Correlation Coefficient for Quantitative Data: r. 6.4 DETAILS: z Score Formula for r. 6.5 DETAILS: Computation Formula for r. 6.6 Outliers Again. 6.7 Other Types of Correlation Coefficients. 6.8 Computer Output. Summary. Important Terms. Key Equations. Review Questions. 7. Regression. 7.1 Two Rough Predictions. 7.2 A Regression Line. 7.3 Least Squares Regression Line. 7.4 Standard Error of Estimate, S y x . 7.5 Assumptions. 7.6 Multiple Regression Equations. 7.7 Regression Toward The Mean. Summary. Important Terms. Key Equations. Review Questions. Part II: Inferential Statistics. 8. Populations, Samples, and Probability. Populations and Samples. 8.1 Populations. 8.2 Samples. 8.3 Random Sampling. 8.4 Tables of Random Numbers. 8.5 Random Assignment of Subjects. Surveys or Experiments? Probability. 8.7 Definition. 8.8 Addition Rule. 8.9 Multiplication Rule. 8.10 Probability and Statistics. Summary. Important Terms. Key Equations. Review Questions. 9. Sampling Distribution of the Mean. 9.1 What is a Sampling Distribution? 9.2 Creating a Sampling Distribution from Scratch. 9.3 Some Important Symbols. 9.4 Mean of All Sample Means 9.5 Standard Error of the Means 9.6 Shape of the Sampling Distribution. 9.7 Other Sampling Distributions. Summary. Important Terms. Key Equations. Review Questions. 10. Introduction to Hypothesis Testing: the z Test. 10.1 Testing a Hypothesis about SAT Scores. 10.2 z Test for a Population Mean. 10.3 Step-by-Step Procedure. 10.4 Statement of the Research Problem. 10.5 Null Hypothesis ( H 0 ). 10.6 Alternative Hypothesis ( H 1 ). 10.7 Decision Rule. 10.8 Calculations. 10.9 Decision. 10.10 Interpretation. Summary. Important Terms. Key Equations. Review Questions. 11. More about Hypothesis Testing. 11.1 Why Hypothesis Tests? 11.2 Strong or Weak Decisions. 11.3 One-Tailed and Two-Tailed Tests. 11.4 Choosing a Level of Significance ( a ). 11.5 Testing a Hypothesis about Vitamin C. 11.6 Four Possible Outcomes. 11.7 If H 0 Really Is True. 11.8 If H 0 Really Is False Because of a Large Effect. 11.9 If H 0 Really Is False Because of a Small Effect. 11.10 Influence of Sample Size. 11.11 Power and Sample Size. Summary. Important Terms. Review Questions. 12. Estimation (Confidence Intervals). 12.1 Point Estimate for m . 12.2 Confidence Interval (CI) for m. 12.3 Interpretation of a Confidence Interval. 12.4 Level of Confidence. 12.5 Effect of Sample Size. 12.6 Hypothesis Tests or Confidence Intervals? 12.7 Confidence Interval for Population Percent. Summary. Important Terms. Key Equation. Review Questions. 13. t Test for One Sample. 13.1 Gas Mileage Investigation. 13.2 Sampling Distribution of t. 13.3 t Test. 13.4 Common Theme of Hypothesis Tests. 13.5 Reminder about Degrees of Freedom. 13.6 DETAILS: Estimating the Standard Error. 13.7 DETAILS: Calculations for t Test. 13.8 Confidence Intervals for m Based on t. 13.9 Assumptions. Summary. Important Terms. Key Equations. Review Questions. 14. t Test for Two Independent Samples. 14.1 EPO Experiment. 14.2 Statistical Hypotheses. 14.3 Sampling Distribution 14.4 t Test. 14.5 DETAILS: Calculations for t Test. 14.6 p-Values. 14.7 Statistically Significant Results. 14.8 Estimating Effect Size: Point Estimates and Confidence Intervals. 14.9 Estimating Effect Size: Cohen's d. 14.10 Reports in the Literature. 14.11 Assumptions. 14.12 Computer Output. Summary. Important Terms. Key Equations. Review Questions. 15. t Test for Two Related Samples (Repeated Measures). 15.1 EPO Experiment with Repeated Measures. 15.2 Statistical Hypotheses. 15.3 Sampling Distribution. 15.4 t Test. 15.5 DETAILS: Calculations for t Test. 15.6 Estimating Effect Size. 15.7 Assumptions. 15.8 Overview: Three t Tests for Population Means. 15.9 t Test for the Population Correlation Coefficient, Summary. Important Terms. Key Equations. Review Questions. 16. Analysis of Variance (One Factor). 16.1 Testing a Hypothesis about Aggression and Sleep Deprivation. 16.2 Two Sources of Variability. 16.3 F Test. 16.4 DETAILS: Variance Estimates. 16.5 DETAILS: Mean Squares ( MS ) and the F Ratio. 16.6 Table for F Distribution. 16.7 ANOVA Summary Tables. 16.8 F Test Is Nondirectional. 16.9 Estimating Effect Size. 16.10 Multiple Comparisons. 16.11 Overview: Flow Chart for ANOVA. 16.12 Reports in the Literature. 16.13 Assumptions. 16.14 Computer Output. Summary. Important Terms. Key Equations. Review Questions. 17. Analysis of Variance (Repeated Measures). 17.1 Sleep Deprivation Experiment with Repeated Measures. 17. 2 F Test. 17.3 Two Complications. 17.4 DETAILS: Variance Estimates. 17.5 DETAILS: Mean Square ( MS ) and the F Ratio. 17.6 Table for F Distribution. 17.7 ANOVA Summary Tables. 17.8 Estimating Effect Size. 17.9 Multiple Comparisons. 17.10 Reports in the Literature. 17.11 Assumptions. Summary. Important Terms. Key Equations. Review Questions. 18. Analysis of Variance (Two Factors). 18.1 A Two-Factor Experiment: Responsibility in Crowds. 18.2 Three F Tests. 18.3 Interaction. 18.4 DETAILS: Variance Estimates. 18.5 DETAILS: Mean Squares ( MS ) and F Ratios. 18.6 Table for F Distribution. 18.7 Estimating Effect Size. 18.8 Multiple Comparisons. 18.9 Simple Effects. 18.10 OVERVIEW: Flow Chart for Two-Factor ANOVA. 18.11 Reports in the Literature. 18.12 Assumptions. 18.13 Other Types of ANOVA. Summary. Important Terms. Key Equations. Review Questions. 19. Chi-Square ( c ^2) Test for Qualitative (Nominal) Data. One-variable c ^2 Test. 19.1 Survey of Blood Types. 19.2 Statistical Hypotheses. 19.3 DETAILS: Calculation of c ^2. 19.4 Table for c ^2 Distribution. 19.5 c ^2 Test. Two-variable c ^2 Test. 19.6 Lost Letter Study. 9.7 Statistical Hypotheses. 9.8 DETAILS: Calculation of c ^2. 19.9 Table for c ^2 Distribution. 19.10 c ^2 Test. 19.11 Estimating Effect Size. 19.12 Odds Ratios. 19.13 Reports in the Literature. 19.14 Some Precautions. 19.15 Computer Output. Summary. Important Terms. Key Equations. Review Questions. 20. Tests for Ranked (Ordinal) Data. 20.1 Use Only When Appropriate. 20.2 A Note on Terminology. 20.3 Mann-Whitney U Test (Two Independent Samples). 20.4 Wilcoxon T Test (Two Related Samples). 20.5 Kruskal-Wallis H Test (Three or More Independent Samples). 20.6 General Comment: Ties. Summary. Important Terms. Review Questions. 21. Postscript: Which Test? 21.1 Descriptive or Inferential Statistics? 21.2 Hypothesis Tests or Confidence Intervals? 21.3 Quantitative or Qualitative Data? 21.4 Distinguishing between the Two Types of Data. 21.5 One, Two, or More Groups?21.6 Concluding Comments. Review Questions . Appendices. A. Math Review. B. Answers to Selected Questions. C. Tables. D. Glossary. Index.