Statistics

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.   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 the 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 Statistics

1.2 Types of Statistical Applications

1.3 Fundamental Elements of Statistics

1.4 Types of Data

1.5 Collecting Data

1.6 The Role of Statistics in Critical Thinking

Statistics in Action: USA Weekend Teen Surveys — Are Boys Really from Mars and Girls from Venus?

Using Technology: Creating and Listing Data in MINITAB

 

2. Methods for Describing Sets of Data

2.1 Describing Qualitative Data

2.2 Graphical Methods for Describing Quantitative Data

2.3 Summation Notation

2.4 Numerical Measures of Central Tendency

2.5 Numerical Measures of Variability

2.6 Interpreting the Standard Deviation

2.7 Numerical Measures of Relative Standing

2.8 Methods for Detecting Outliers (Optional)

2.9 Graphing Bivariate Relationships (Optional)

2.10 Distorting the Truth with Descriptive Techniques

Statistics In Action: The "Eye Cue" Test: Does Experience Improve Performance?

Using Technology: Describing Data in MINITAB

 

3. Probability

3.1 Events, Sample Spaces, and Probability

3.2 Unions and Intersections

3.3 Complementary Events

3.4 The Additive Rule and Mutually Exclusive Events

3.5 Conditional Probability

3.6 The Multiplicative Rule and Independent Events

3.7 Random Sampling

3.8 Some Counting Rules (Optional)

3.9 Bayes’ Rule (Optional)

Statistics In Action: Lotto Buster! — Can You Improve Your Chances of Winning the Lottery?

Using Technology: Generating a Random Sample in MINITAB

 

4. Discrete Random Variables

4.1 Two Types of Random Variables

4.2 Probability Distributions for Discrete Random Variables

4.3 Expected Values of Discrete Random Variables

4.4 The Binomial Random Variable

4.5 The Poisson Random Variable (Optional)

4.6 The Hypergeometric Random Variable (Optional)

Statistics in Action: Probability in a Reverse Cocaine Sting — Was Cocaine Really Sold?

Using Technology: Binomial, Poisson, and Hypergeometric Probabilities in MINITAB

 

5. Continuous Random Variables

5.1 Continuous Probability Distributions

5.2 The Uniform Distribution

5.3 The Normal Distribution

5.4 Descriptive Methods for Assessing Normality

5.5 Approximating a Binomial Distribution with a Normal Distribution (Optional)

5.6 The Exponential Distribution (Optional)

Statistics in Action: Super Weapons Development — Is the Hit Ratio Optimized?

Using Technology: Normal Probability Plots in MINITAB

 

6. Sampling Distributions

6.1 What is a Sampling Distribution?

6.2 Properties of Sampling Distributions: Unbiasedness and Minimum Variance (Optional)

6.3 The Central Limit Theorem

Statistics in Action: The Insomnia Pill — Will It Take Less Time to Fall Asleep?

Using Technology: Simulating a Sampling Distribution in MINITAB

 

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

7.1 Identifying the Target Parameter

7.2 Large-Sample Confidence Interval for a Population Mean

7.3 Small-Sample Confidence Interval for a Population Mean

7.4 Large-Sample Confidence Interval for a Population Proportion

7.5 Determining the Sample Size

Statistics in Action: Speed–Can a High School Football Player Improve His Sprint Time?

Using Technology: Confidence Intervals in MINITAB

 

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

8.1 The Elements of a Test of Hypothesis

8.2 Large-Sample Test of Hypothesis About a Population Mean

8.3 Observed Significance Levels: p-Values

8.4 Small-Sample Test of Hypothesis About a Population Mean

8.5 Large-Sample Test of Hypothesis About a Population Proportion

8.6 Calculating Type II Error Probabilities: More About β (Optional)

8.7 Test of Hypothesis About a Population Variance (Optional)

Statistics in Action: Diary of a Kleenex User — How Many Tissues in a Box?

Using Technology: Tests of Hypothesis in MINITAB

 

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

9.1 Identifying the Target Parameter

9.2 Comparing Two Population Means: Independent Sampling

9.3 Comparing Two Population Means: Paired Difference Experiments

9.4 Comparing Two Population Proportions: Independent Sampling

9.5 Determining the Sample Size

9.6 Comparing Two Population Variances: Independent Sampling (Optional)

Statistics in Action: Do Homework Assignments Designed to Involve Family Members Really Work?

Using Technology: Two-Sample Inferences in MINITAB

 

10. Analysis of Variance: Comparing More Than Two Means

10.1 Elements of a Designed Experiment

10.2 The Completely Randomized Design

10.3 Multiple Comparisons of Means

10.4 The Randomized Block Design

10.5 Factorial Experiments

Statistics in Action: On the Trail of the Cockroach: Do Roaches Travel at Random?

Using Technology: Analysis of Variance in MINITAB

 

11. Simple Linear Regression

11.1 Probabilistic Models

11.2 Fitting the Model: The Least Squares Approach

11.3 Model Assumptions

11.4 Assessing the Utility of the Model: Making Inferences About the Slope β1

11.5 The Coefficients of Correlation and Determination

11.6 Using the Model for Estimation and Prediction

11.7 A Complete Example

Statistics in Action: Can "Dowsers" Really Detect Water?

Using Technology: Simple Linear Regression in MINITAB

 

12. Multiple Regression and Model Building

12.1 Multiple Regression Models

12.2 The First-Order Model: Inferences About the Individual β-Parameters

12.3 Evaluating the Overall Utility of a Model

12.4 Using the Model for Estimation and Prediction

12.5 Model Building: Interaction Models

12.6 Model Building: Quadratic and other Higher-Order Models

12.7 Model Building: Qualitative (Dummy) Variable Models

12.8 Model Building: Models with both Quantitative and Qualitative Variables

12.9 Model Building: Comparing Nested Models (Optional)

12.10 Model Building: Stepwise Regression (Optional)

12.11 Residual Analysis: Checking the Regression Assumptions

12.12 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

Statistics in Action: Modeling Condo Sales: Are There Differences in Auction Prices?

Using Technology: Multiple Regression in MINITAB

 

13. Categorical Data Analysis

13.1 Categorical Data and the Multinomial Distribution

13.2 Testing Categorical Probabilities: One-Way Table

13.3 Testing Categorical Probabilities: Two-Way (Contingency) Table

13.4 A Word of Caution About Chi-Square Tests

Statistics in Action: College Students and Alcohol — Is Drinking Frequency Related to Amount?

Using Technology: Chi-Square Analyses in MINITAB

 

14. Nonparametric Statistics

14.1 Introduction: Distribution-Free Tests

14.2 Single Population Inferences

14.3 Comparing Two Populations: Independent Samples

14.4 Comparing Two Populations: Paired Difference Experiment

14.5 Comparing Three or More Populations: Completely Randomized Design

14.6 Comparing Three or More Populations: Randomized Block Design

14.7 Rank Correlation

Statistics in Action: How Vulnerable are Wells to Groundwater Contamination?  

Using Technology: Nonparametric Analyses in MINITAB

 

Appendix A: Tables

Table I   Random Numbers

Table II Binomial Probabilities

Table III Poisson Probabilities

Table IV Normal Curve Areas

Table V Exponentials

Table VI Critical Values of t

Table VII Critical Values of χ2

Table VIII Percentage Points of the F Distribution, α=.10

Table IX Percentage Points of the F Distribution, α=.05

Table X Percentage Points of the F Distribution, α=.025

Table XI Percentage Points of the F Distribution, α=.01

Table XII Critical Values of TL and TU for the Wilcoxon Rank Sum Test

Table XIII Critical Values of T0 in the Wilcoxon Signed Rank Test

Table XIV Critical Values of Spearman's Rank Correlation Coefficient

 

Appendix B: Calculation Formulas for Analysis of Variance

 

Short Answers to Selected Odd-Numbered Exercises