Detailed Topics
Statistics for Undergraduate Studies
Uni e-Prep Course by NTU Available in SF@NS
Ch 1 Describing Data with Graphs
1.1 Variables and Data
1.2 Types of Variables
1.3 Graphs for Categorical Data 11 Exercises
1.4 Graphs for Quantitative Data
Pie Charts and Bar Charts
Line Charts
Dotplots
Stem and Leaf Plots
Interpreting Graphs with a Critical Eye
1.5 Relative Frequency Histograms
Ch 2 Describing Data with Numerical Measures
2.1 Describing a Set of Data with Numerical Measures
2.2 Measures of Center
2.3 Measures of Variability
2.4 On the Practical Significance of the Standard Deviation
2.5 A Check on the Calculation of s
2.6 Measures of Relative Standing
2.7 The Five-Number Summary and the Box Plot
Ch 3 Describing Bivariate Data
3.1 Bivariate Data
3.2 Graphs for Categorical Variables
3.3 Scatterplots for Two Quantitative Variables
3.4 Numerical Measures for Quantitative Bivariate Data
Ch 4 Probability and Probability Distributions
4.1 The Role of Probability in Statistics
4.2 Events and the Sample Space
4.3 Calculating Probabilities Using Simple Events
4.4 Useful Counting Rules (Optional)
4.5 Event Relations and Probability Rules
Calculating Probabilities for Unions and Complements
4.6 Independence, Conditional Probability, and the Multiplication Rule
4.7 Bayes’ Rule (Optional)
4.8 Discrete Random Variables and Their Probability Distributions
Random Variables
Probability Distributions
The Mean and Standard Deviation for a Discrete Random Variable
Ch 5 Several Useful Discrete Distributions
5.1 Introduction
5.2 The Binomial Probability Distribution
5.3 The Poisson Probability Distribution
5.4 The Hypergeometric Probability Distribution
Ch 6 The Normal Probability Distribution
6.1 Probability Distributions for Continuous Random Variables
6.2 The Normal Probability Distribution
6.3 Tabulated Areas of the Normal Probability Distribution
The Standard Normal Random Variable
Calculating Probabilities for a General Normal Random Variable
6.4 The Normal Approximation to the Binomial Probability Distribution (Optional)
Ch 7 Sampling Distributions
7.1 Introduction
7.2 Sampling Plans and Experimental Designs
7.3 Statistics and Sampling Distributions
7.4 The Central Limit Theorem
7.5 The Sampling Distribution of the Sample Mean Standard Error
7.6 The Sampling Distribution of the Sample Proportion
7.7 A Sampling Application: Statistical Process Control (Optional)
A Control Chart for the Process Mean: The x Chart
A Control Chart for the Proportion Defective: The p Chart
Ch 8 Large-Sample Estimation
8.1 Where We’ve
8.2 Where We’re Going—Statistical Inference
8.3 Types of Estimators
8.4 Point Estimation
8.5 Interval Estimation
Constructing a Confidence Interval
Large-Sample Confidence Interval for a Population Mean mu
Interpreting the Confidence Interval
Large-Sample Confidence Interval for a Population Proportion p
8.6 Estimating the Difference between Two Population Means
8.7 Estimating the Difference between Two Binomial Proportions
8.8 One-Sided Confidence Bounds
8.9 Choosing the Sample Size
Ch 9 Large-Sample Tests of Hypotheses
9.1 Testing Hypotheses about Population Parameters
9.2 A Statistical Test of Hypothesis
9.3 A Large-Sample Test about a Population Mean
The Essentials of the Test
Calculating the p-Value 332 Two Types of Errors
The Power of a Statistical Test
9.4 A Large-Sample Test of Hypothesis for the Difference between Two Population Means
Hypothesis Testing and Confidence Intervals
9.5 A Large-Sample Test of Hypothesis for a Binomial Proportion
Statistical Significance and Practical Importance
9.6 A Large-Sample Test of Hypothesis for the Difference between Two Binomial Proportions
9.7 Some Comments on Testing Hypotheses
Ch 10 Inference from Small Samples
10.1 Introduction
10.2 Student’s t Distribution
Assumptions behind Student’s t Distribution
10.3 Small-Sample Inferences Concerning a Population Mean
10.4 Small-Sample Inferences for the Difference between Two Population Means: Independent Random Samples
Ch 11 The Analysis of Variance
11.1 The Design of an Experiment
11.2 What Is an Analysis of Variance?
11.3 The Assumptions for an Analysis of Variance
11.4 The Completely Randomized Design: A One-Way Classification
11.5 The Analysis of Variance for a Completely Randomized Design
Partitioning the Total Variation in an Experiment
Testing the Equality of the Treatment Means
Estimating Differences in the Treatment Means
11.6 Ranking Population Means
11.7 The Randomized Block Design: A Two-Way Classification
11.8 The Analysis of Variance for a Randomized Block Design
Partitioning the Total Variation in the Experiment
Testing the Equality of the Treatment and Block Means
Identifying Differences in the Treatment and Block Means
Some Cautionary Comments on Blocking
11.9 The a b Factorial Experiment: A Two-Way Classification
Factorial Experiment
11.10 The Analysis of Variance for an a
11.11 Revisiting the Analysis of Variance Assumptions
Residual Plots
11.12 A Brief Summary
Ch 12 Linear Regression and Correlation
12.1 Introduction
12.2 A Simple Linear Probabilistic Model
12.3 The Method of Least Squares
12.4 An Analysis of Variance for Linear Regression
12.5 Testing the Usefulness of the Linear Regression Model
Inferences Concerning b, the Slope of the Line of Means
The Analysis of Variance F-Test
Measuring the Strength of the Relationship: The Coefficient of Determination
Interpreting the Results of a Significant Regression
12.6 Diagnostic Tools for Checking the Regression Assumptions
Dependent Error Terms
Residual Plots
12.7 Estimation and Prediction Using the Fitted Line
12.8 Correlation Analysis
Ch 13 Multiple Regression Analysis
13.1 Introduction
13.2 The Multiple Regression Model
13.3 A Multiple Regression Analysis
The Method of Least Squares
The Analysis of Variance for Multiple Regression
Testing the Usefulness of the Regression Model
Interpreting the Results of a Significant Regression
Checking the Regression Assumptions
Using the Regression Model for Estimation and Prediction
13.4 A Polynomial Regression Model
13.5 Using Quantitative and Qualitative Predictor Variables in a Regression Model
13.6 Testing Sets of Regression Coefficients
13.7 Interpreting Residual Plots
13.8 Stepwise Regression Analysis
13.9 Misinterpreting a Regression Analysis
Causality
Multicollinearity
13.10 Steps to Follow When Building a Multiple Regression Model
Ch 14 Analysis of Categorical Data
14.1 A Description of the Experiment
14.2 Pearson’s Chi-Square Statistic
14.3 Testing Specified Cell Probabilities: The Goodness-of-Fit Test
14.4 Contingency Tables: A Two-Way Classification
The Chi-Square Test of Independence
14.5 Comparing Several Multinomial Populations: A Two-Way Classification with Fixed Row or Column Totals
14.6 The Equivalence of Statistical Tests
14.7 Other Applications of the Chi-Square Test
Ch 15 Non-Parametric Statistics
15.1 Introduction
15.2 The Wilcoxon Rank Sum Test: Independent Random Samples
Normal Approximation for the Wilcoxon Rank Sum Test
15.3 The Sign Test for a Paired Experiment
Normal Approximation for the Sign Test
15.4 A Comparison of Statistical Tests
15.5 The Wilcoxon Signed-Rank Test for a Paired Experiment
Normal Approximation for the Wilcoxon Signed-Rank Test
15.6 The Kruskal–Wallis H-Test for Completely Randomized Designs
15.7 The Friedman F r -Test for Randomized Block Designs
15.8 Rank Correlation Coefficient