Elementary Statistics

Part One. Descriptive Statistics



1. Introduction to Statistics

1.1. An Overview of Statistics

1.2. Data Classification

1.3. Data Collection and Experimental Design



2. Descriptive Statistics

2.1. Frequency Distributions and Their Graphs

2.2. More Graphs and Displays

2.3. Measures of Central Tendency

2.4. Measures of Variation

2.5. Measures of Position



Part Two. Probability & Probability Distributions



3. Probability

3.1. Basic Concepts of Probability and Counting

3.2. Conditional Probability and the Multiplication Rule

3.3. The Addition Rule

3.4. Additional Topics in Probability and Counting



4. Discrete Probability Distributions

4.1. Probability Distributions

4.2. Binomial Distributions

4.3. More Discrete Probability Distributions



5. Normal Probability Distributions

5.1. Introduction to Normal Distributions and the Standard Normal Distribution

5.2. Normal Distributions: Finding Probabilities

5.3. Normal Distributions: Finding Values

5.4. Sampling Distributions and the Central Limit Theorem

5.5. Normal Approximations to Binomial Distributions



Part Three. Statistical Inference



6. Confidence Intervals

6.1. Confidence Intervals for the Mean (Large Samples)

6.2. Confidence Intervals for the Mean (Small Samples)

6.3. Confidence Intervals for Population Proportions

6.4. Confidence Intervals for Variance and Standard Deviation



7. Hypothesis Testing with One Sample

7.1. Introduction to Hypothesis Testing

7.2. Hypothesis Testing for the Mean (Large Samples)

7.3. Hypothesis Testing for the Mean (Small Samples)

7.4. Hypothesis Testing for Proportions

7.5. Hypothesis Testing for Variance and Standard Deviation



8. Hypothesis Testing with Two Samples

8.1. Testing the Difference Between Means (Large Independent Samples)

8.2. Testing the Difference Between Means (Small Independent Samples)

8.3. Testing the Difference Between Means (Dependent Samples)

8.4. Testing the Difference Between Proportions



Part Four. More Statistical Inference



9. Correlation and Regression

9.1 Correlation

9.2. Linear Regression

9.3. Measures of Regression and Prediction Intervals

9.4. Multiple Regression



10. Chi-Square Tests and the F-Distribution

10.1. Goodness-of-Fit Test

10.2. Independence

10.3. Comparing Two Variances

10.4. Analysis of Variance



11. Nonparametric Tests

11.1. The Sign Test

11.2. The Wilcoxon Tests

11.3. The Kruskal-Wallis Test

11.4. Rank Correlation

11.5. The Runs Test



Appendix A. Alternative Presentation of the Standard Normal Distribution

Standard Normal Distribution Table (0-to-z)

Alternative Presentation of the Standard Normal Distribution

Appendix B. Tables

Table 1 Random Numbers

Table 2 Binomial Distribution

Table 3 Poisson Distribution

Table 4 Standard Normal Distribution

Table 5 t-Distribution

Table 6 Chi-Square Distribution

Table 7 F-Distribution

Table 8 Critical Values for the Sign Test

Table 9 Critical Values for the Wilcoxon Signed-Rank Test

Table 10 Critical Values for the Spearman Rank Correlation

Table 11 Critical Values for the Pearson Correlation Coefficient

Table 12 Critical Values for the Number of Runs

Appendix C. Normal Probability Plots and Their Graphs



Answers to the Try It Yourself Exercises

Odd Answers

Index

Photo Credits