Modern Elementary Statistics

Preface

Chapter 1: Introduction

1.1              The Growth of Modern Statistics

1.2              Sources of Statistical Data

1.3              The Nature of Statistical Data

 

Chapter 2: Summarizing Data: Listing and Grouping

2.1              Listing Numerical Data

2.2              Stem-and-Leaf Displays

2.3              Frequency Distribution

2.4              Graphical Presentations

2.5              Summarizing Two-Variable Data

 

Chapter 3: Summarizing Data: Measures of Location

3.1              Population and Samples

3.2              The Mean

3.3              The Weighted Mean

3.4              The Median

3.5              Other Fractiles

3.6              The Mode

3.7              The Description of Grouped Data

3.8              Technical Note (Summations)

 

Chapter 4: Summarizing Data: Measures of Variation

4.1              The Range

4.2              The Standard Deviation and the Variance

4.3              Applications of the Standard Deviation

4.4              The Description of Grouped Data

4.5              Some Further Descriptions

 

Chapter 5: Possibilities and Probabilities

5.1              Counting

5.2              Permutations

5.3              Combinations

5.4              Probability

 

Chapter 6: Some Rules of Probability

6.1              Samples Spaces and Events

6.2              The Postulates of Probability

6.3              Probabilities and Odds

6.4              Addition Rules

6.5              Conditional Probability

6.6              Multiplication Rules

6.7              Bayes’ Theorem

 

Chapter 7: Expectations and Decisions

7.1              Mathematical Expectation

7.2              Decision Making

7.3              Statistical Decision Problems

 

Chapter 8: Probability Distributions

8.1              Random Variables

8.2              Probability Distributions

8.3              The Binomial Distribution

8.4              The Hypergeometric Distribution

8.5              The Poisson Distribution

8.6              The Multinomial Distribution

8.7              The Mean of a Probability Distribution

8.8              The Standard Deviation of a Probability Distribution

 

Chapter 9: The Normal Distribution

9.1              Continuous Distributions

9.2              The Normal Distribution

9.3              A Check for Normality

9.4              Applications of the Normal Distribution

9.5              The Normal Approximation to the Binomial

 

Chapter 10: Sampling and Sampling Distributions

10.1          Random Sampling

10.2          Sample Designs

10.3          Systematic Sampling

10.4          Stratified Sampling

10.5          Cluster Sampling

10.6          Sampling Distributions

10.7          The Standard Error of the Mean

10.8          The Central Limit Theorem

10.9          Some Further Considerations

10.10      Technical Note (Simulation)

 

Chapter 11: Problems of Estimation

11.1          The Estimation of Means

11.2          The Estimation of Means

11.3          The Estimation of Standard Deviations

11.4          The Estimation of Proportions

 

Chapter 12: Tests of Hypotheses: Means

12.1          Tests of Hypotheses

12.2          Significance Tests

12.3          Tests Concerning Means

12.4          Tests Concerning Means ( unknown)

12.5          Differences Between Means

12.6          Differences Between Means ( unknown)

12.7          Difference Between Means (Paired data)

 

Chapter 13: Tests of Hypotheses: Standard Deviations

13.1          Tests Concerning Standard Deviations

13.2          Tests Concerning Two Standard Deviations

 

Chapter 14: Tests of Hypotheses Based on Count Data

14.1          Tests Concerning Proportions

14.2          Tests Concerning Proportions (Large Samples)

14.3          Differences Between Proportions

14.4          The Analysis of r x c Table

14.5          Goodness of Fit

 

Chapter 15: Analysis of Variance

15.1          Difference among k Means: An Example

15.2          The Design of Experiments: Randomization

15.3          One-Way Analysis of Variance

15.4          Multiple Comparisons

15.5          The Design of Experiments: Blocking

15.6          Two-Way Analysis of Variance

15.7          Two-Way Analysis of Variance Without Interaction

15.8          The Design of Experiments: Replication

15.9          Two-Way Analysis of Variance with Interaction

15.10      The Design of Experiments: Further Considerations

 

Chapter 16: Regression

16.1          Curve Fitting

16.2          The Method of Least Squares

16.3          Regression Analysis

16.4          Multiple Regression

16.5          Nonlinear Regression

 

Chapter 17: Correlation

17.1          The Coefficient of Correlation

17.2          The Interpretation of r

17.3          Correlation Analysis

17.4          Multiple and Partial Correlation

 

Chapter 18: Nonparametric Tests

18.1          The Sign Test

18.2          The Sign Test (Large Samples)

18.3          The Signed-Rank Test

18.4          The Signed-Rank Test (Large Samples)

18.5          The U Test

18.6          The U Test (Large Samples)

18.7          The H Test

18.8          Tests of Randomness: Runs

18.9          Tests of Randomness: Runs (Large Samples)

18.10      Tests of Randomness: Runs Above and Below the Median

18.11      Rank Correlation

18.12      Some Further Considerations