Detailed Topics

Statistics for Undergraduate Studies

University e-Preparation Course

by NTU 

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

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