Statistics

1. Statistics, Data, and Statistical Thinking.


The Science of Statistics. Types of Statistical Applications. Fundamental Elements of Statistics. Types of Data. Collecting Data. The Role of Statistics in Critical Thinking.



2. Methods for Describing Sets of Data.


Describing Qualitative Data. Graphical Methods for Describing Quantitative Data. Summation Notation. Numerical Measures of Central Tendency. Numerical Measures of Variability. Interpreting the Standard Deviation. Numerical Measures of Relative Standing. Methods for Detecting Outliers (Optional). Graphing Bivariate Relationships (Optional). Distorting the Truth with Descriptive Techniques.



3. Probability.


Events, Sample Spaces, and Probability. Unions and Intersections. Complementary Events. The Additive Rule and Mutually Exclusive Events. Conditional Probability. The Multiplicative Rule and Independent Events. Random Sampling. Some Counting Rules (Optional).



4. Discrete Random Variables.


Two Types of Random Variables. Probability Distributions for Discrete Random Variables. Expected Values of Discrete Random Variables. The Binomial Random Variable. The Poisson Random Variable (Optional). The Hypergeometric Random Variable (Optional).



5. Continuous Random Variables.


Continuous Probability Distributions. The Uniform Distribution. The Normal Distribution. Descriptive Methods for Assessing Normality. Approximating a Binomial Distribution with a Normal Distribution (Optional). The Exponential Distribution (Optional).



6. Sampling Distributions.


What Is a Sampling Distribution? Properties of Sampling Distributions: Unbiasedness and Minimum Variance (Optional). The Central Limit Theorem.



7. Inferences Based on a Single Sample: Estimation with Confidence Intervals.


Large-Sample Confidence Interval for a Population Mean. Small-Sample Confidence Interval for a Population Mean. Large-Sample Confidence Interval for a Population Proportion. Determining the Sample Size.



8. Inferences Based on a Single Sample: Tests of Hypotheses.


The Elements of a Test of Hypothesis. Large-Sample Test of Hypothesis about a Population Mean. Observed Significance Levels: p-Values. Small-Sample Test of Hypothesis about a Population Mean. Large-Sample Test of Hypothesis about a Population Proportion. Calculating Type II Error Probabilities: More about ...b (Optional). Test of Hypothesis about a Population Proportion.



9. Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses.


Comparing Two Population Means: Independent Sampling. Comparing Two Population Means: Paired Difference Experiments. Comparing Two Population Proportions: Independent Sampling. Determining the Sample Size. Comparing Two Population Variances: Independent Sampling (Optional).



10. Analysis of Variance: Comparing More Than Two Means.


Elements of a Designed Experiment. The Completely Randomized Design. Multiple Comparisons of Means. The Randomized Block Design. Factorial Experiments.



11. Simple Linear Regression.


Probabalistic Models. Fitting the Model: The Least Squares Approach. Model Assumptions. An Estimator of ...s2. Assessing the Utility of the Model: Making Inferences about the Slope ...b1. The Coefficient of Correlation. The Coefficient of Determination. Using the Model for Estimation and Prediction. A Complete Example.



12. Multiple Regression and Model Building.


Multiple Regression Models. The First-Order Model: Estimating and Interpreting the ...b Parameters. Model Assumptions. Inferences About the Individual ...b Parameters. Checking the Overall Utility of a Model. Using the Model for Estimation and Prediction. Model Building: Interaction Models. Model Building: Quadratic and Other Higher-Order Models. Model Building: Qualitative (Dummy) Variable Models. Model Building: Models with Both Quantitative and Qualitative Variables. Model Building: Comparing Nested Models. Model Building: Stepwise Regression. Residual Analysis: Checking the Regression Assumptions. Some Pitfalls: Estimability, Multicollinearity, and Extrapolation.



13. Categorical Data Analysis.


Categorical Data and the Multinomial Distribution. Testing Categorical Probabilities: One-Way Table. Testing Categorical Probabilities: Two-Way (Contingency) Table. A Word of Caution about Chi-Square Tests.



14. Nonparametric Statistics.


Introduction: Distribution-Free Tests. Single Population Inferences: The Sign Test. Comparing Two Populations: The Wilcoxon Rank Sum Test for Independent Samples. Comparing Two Populations: The Wilcoxon Signed Rank Test for the Paired Difference Experiment. The Kruskal-Wallis H-Test for a Completely Randomized Design. The Friedman F r-Test for a Randomized Block Design. Spearman's Rank Correlation Coefficient.



Appendix A. Tables.


Random Numbers. Binomial Probabilities. Poisson Probabilities. Normal Curve Areas. Exponentials. Critical Values of t. Critical Values of ...c2. Percentage Points of the F Distribution, ...a= .10. Percentage Points of the F Distribution, ...a=.05. Percentage Points of the F Distribution, ...a=.025. Percentage Points of the F Distribution, ...a=.01. Critical Values of TL and TU for the Wilcoxon Rank Sum Test: Independent Samples. Critical Values of TO in the Wilcoxon Paired Difference Signed Rank Test. Critical Values of Spearman's Rank Correlation Coefficient.



Appendix B. Data Sets.


Coronary Artery Patients' Blood Loss Data. Car & Driver Data. Starting Salaries of USF Graduates. Sealed Milk Bids Data. Federal Trade Commission Rankings of Domestic Cigarette Brands.



Appendix C. Calculation Formulas for Analysis of Variance.


Short Answers to Selected Odd-Numbered Exercises.


Index.