Statistics, Updated Edition -- ACCUMULATOR

Dr. Jim McClave is currently President and CEO of Info Tech, Inc., a statistical consulting and software development firm with an international clientele. He is also currently an Adjunct Professor of Statistics at the University of Florida, where he was a full-time member of the faculty for twenty years.  Dr. Terry Sincich obtained his PhD in Statistics from the University of Florida in 1980. He is an Associate Professor in the Information Systems & Decision Sciences Department at the University of South Florida in Tampa. Dr. Sincich is responsible for teaching basic statistics to all undergraduates, as well as advanced statistics to all doctoral candidates, in the College of Business Administration. He has published articles in such journals as the Journal of the American Statistical Association, International Journal of Forecasting, Academy of Management Journal, and Auditing: A Journal of Practice & Theory. Dr. Sincich is a co-author of the texts Statistics, Statistics for Business & Economics, Statistics for Engineering & the Sciences, and A Second Course in Statistics: Regression Analysis.

• 1. Statistics, Data, and Statistical Thinking 1.1 The Science of Statistics1.2 Types of Statistical Applications1.3 Fundamental Elements of Statistics1.4 Types of Data1.5 Collecting Data: Sampling and Related Issues1.6 The Role of Statistics in Critical Thinking and Ethics2. Methods for Describing Sets of Data 2.1 Describing Qualitative Data2.2 Graphical Methods for Describing Quantitative Data2.3 Numerical Measures of Central Tendency2.4 Numerical Measures of Variability2.5 Using the Mean and Standard Deviation to Describe Data2.6 Numerical Measures of Relative Standing2.7 Methods for Detecting Outliers: Box Plots and z-Scores2.8 Graphing Bivariate Relationships (Optional)2.9 Distorting the Truth with Descriptive Statistics3. Probability 3.1 Events, Sample Spaces, and Probability3.2 Unions and Intersections3.3 Complementary Events3.4 The Additive Rule and Mutually Exclusive Events3.5 Conditional Probability3.6 The Multiplicative Rule and Independent Events3.7 Some Additional Counting Rules (Optional)3.8 Bayes's Rule (Optional)4. Discrete Random Variables 4.1 Two Types of Random Variables4.2 Probability Distributions for Discrete Random Variables4.3 Expected Values of Discrete Random Variables4.4 The Binomial Random Variable4.5 The Poisson Random Variable (Optional)4.6 The Hypergeometric Random Variable (Optional)5. Continuous Random Variables 5.1 Continuous Probability Distributions5.2 The Uniform Distribution5.3 The Normal Distribution5.4 Descriptive Methods for Assessing Normality5.5 Approximating a Binomial Distribution with a Normal Distribution (Optional)5.6 The Exponential Distribution (Optional)6. Sampling Distributions 6.1 The Concept of a Sampling Distribution6.2 Properties of Sampling Distributions: Unbiasedness and Minimum Variance6.3 The Sampling Distribution of (x-bar) and the Central Limit Theorem6.4 The Sampling Distribution of the Sample Proportion7. Inferences Based on a Single Sample: Estimation with Confidence Intervals 7.1 Identifying and Estimating the Target Parameter7.2 Confidence Interval for a Population Mean: Normal (z) Statistic7.3 Confidence Interval for a Population Mean: Student's t-Statistic7.4 Large-Sample Confidence Interval for a Population Proportion7.5 Determining the Sample Size7.6 Confidence Interval for a Population Variance (Optional)8. Inferences Based on a Single Sample: Tests of Hypothesis 8.1 The Elements of a Test of Hypothesis8.2 Formulating Hypotheses and Setting Up the Rejection Region8.3 Observed Significance Levels: p-Values8.4 Test of Hypothesis about a Population Mean: Normal (z) Statistic8.5 Test of Hypothesis about a Population Mean: Student's t-Statistic8.6 Large-Sample Test of Hypothesis about a Population Proportion8.7 Calculating Type II Error Probabilities: More about β (Optional)8.8 Test of Hypothesis about a Population Variance (Optional)9. Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses 9.1 Identifying the Target Parameter9.2 Comparing Two Population Means: Independent Sampling9.3 Comparing Two Population Means: Paired Difference Experiments9.4 Comparing Two Population Proportions: Independent Sampling9.5 Determining the Sample Size9.6 Comparing Two Population Variances: Independent Sampling (Optional)10. Analysis of Variance: Comparing More than Two Means 10.1 Elements of a Designed Study10.2 The Completely Randomized Design: Single Factor10.3 Multiple Comparisons of Means10.4 The Randomized Block Design10.5 Factorial Experiments: Two Factors11. Simple Linear Regression 11.1 Probabilistic Models11.2 Fitting the Model: The Least Squares Approach11.3 Model Assumptions11.4 Assessing the Utility of the Model: Making Inferences about the Slope β111.5 The Coefficients of Correlation and Determination11.6 Using the Model for Estimation and Prediction11.7 A Complete Example12. Multiple Regression and Model Building 12.1 Multiple-Regression ModelsPART I: First-Order Models with Quantitative Independent Variables12.2 Estimating and Making Inferences about the β Parameters12.3 Evaluating Overall Model Utility12.4 Using the Model for Estimation and PredictionPART II: Model Building in Multiple Regression12.5 Interaction Models12.6 Quadratic and Other Higher Order Models12.7 Qualitative (Dummy) Variable Models12.8 Models with Both Quantitative and Qualitative Variables (Optional)12.9 Comparing Nested Models (Optional)12.10 Stepwise Regression (Optional)PART III: Multiple Regression Diagnostics12.11 Residual Analysis: Checking the Regression Assumptions12.12 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation13. Categorical Data Analysis 13.1 Categorical Data and the Multinomial Experiment13.2 Testing Categorical Probabilities: One-Way Table13.3 Testing Categorical Probabilities: Two-Way (Contingency) Table13.4 A Word of Caution about Chi-Square Tests14. Nonparametric Statistics (available online) 14.1 Introduction: Distribution-Free Tests14.2 Single-Population Inferences14.3 Comparing Two Populations: Independent Samples14.4 Comparing Two Populations: Paired Difference Experiment14.5 Comparing Three or More Populations: Completely Randomized Design14.6 Comparing Three or More Populations: Randomized Block Design14.7 Rank CorrelationAPPENDICES A. Summation NotationB. TablesC. Calculation Formulas for Analysis of VarianceShort Answers to Selected Odd-Numbered Exercises Index