Introduction to Statistics
Welcome to Statistics!
For the Student
R Programming
For the Instructor
Course Learning Outcomes
1
Introduction to Data
1.1
Chapter Overview
1.2
Statistics Terminology
R: Entering Data
Section Exercises
1.3
Sampling and Design
1.3.1
Statistical Sampling
1.3.2
Experimental Design
R: Random Number Generation
Section Exercises
1.4
Frequency Distributions
1.4.1
Qualitative Variables
1.4.2
Quantitative Variables
R: Histograms
2
Descriptive Measures
2.1
Chapter Overview
2.2
Measures of Central Tendency
R: Finding Measures of Center
2.3
Measures of Variability
R: Finding Measures of Variability
2.4
Measures of Position
2.4.1
Box Plots
R: Measures of Position
R: Box Plots
2.5
Descriptive Measures for Populations
3
Regression and Correlation
3.1
Chapter Overview
3.2
Linear Equations
Scatterplots in R
3.3
Correlation
Correlation in R
3.4
Finding a Regression Line
3.4.1
The Coefficient of Determination
Finding a Regression Line in R
3.5
Prediction: A Cautionary Tale
4
Probability Concepts
4.1
Chapter Overview
4.2
Experiments, Sample Spaces, and Events
4.3
Probability Distributions
4.3.1
Venn Diagrams
4.3.2
Probability Axioms
Exercises
4.4
Rules of Probability
4.4.1
Addition Rules
4.4.2
Complements
4.5
Conditional Probability
4.5.1
Multiplication Rules
5
Random Variables
5.1
Chapter Overview
5.2
Discrete Random Variables
5.2.1
The Mean and Standard Deviation
5.3
The Binomial Distribution
5.3.1
Mean and Variance
Binomial Probabilities in R
5.4
The Normal Distribution
5.4.1
Z-Scores
5.4.2
Empirical Rule for Variables
5.5
Area Under the Standard Normal Curve
R: Normal Distribution Probabilities
5.6
Working with Normally Distributed Variables
5.6.1
Normal Distribution Probabilities
5.6.2
Percentiles
6
Introduction to Confidence Intervals
6.1
Chapter Overview
6.2
Sampling Distributions
6.2.1
Sampling Error
6.2.2
The Central Limit Theorem
6.3
Developing Confidence Intervals
6.3.1
Interpreting a Confidence Interval
6.3.2
Exercises
6.4
Other Levels of Confidence
R: Finding Critical Values
6.4.1
Breaking Down a Confidence Interval
6.4.2
Confidence Level, Precision, and Sample Size
6.4.3
Exercises
6.5
Confidence Intervals for a Mean
6.5.1
The T-Distribution
R: T Critical Values
R: Confidence Intevals for a Mean
7
Introduction to Hypothesis Testing
7.1
Chapter Overview
7.2
Logic of Hypothesis Testing
7.2.1
Decision Errors
7.3
Confidence Interval Approach to Hypothesis Testing
7.4
Critical Value Approach to Hypothesis Testing
7.4.1
Test statistics
7.5
P-Value Approach to Hypothesis Testing
7.5.1
P-Values
R: Hypothesis Tests for a Mean
8
Inference for a Proportion
8.1
Chapter Overview
8.2
Confidence Intervals for a Proportion
8.3
Hypothesis Tests for a Proportion
8.3.1
Confidence Interval Approach
8.3.2
Critical Value Approach
8.3.3
P-Value Approach
R: Hypothesis Tests for a Proportion
9
Inference: Comparing Parameters
9.1
Chapter Overview
9.2
Hypothesis Tests for Two Proportions
9.2.1
Confidence Intervals for Two Proportions
9.2.2
Critical Values, Test Statistics, and P-Values
R: Hypothesis Tests for Two Proportions
9.3
Hypothesis Tests for Two Means
9.3.1
Paired Samples
9.3.2
Independent Samples
R: Hypothesis Tests for Two Means
10
Chi-Square Tests
10.1
Chapter Overview
10.2
Inference for a Population Variance
10.2.1
The Chi-Square Distribution
10.3
The Ratio of Two Variances
10.4
Goodness of Fit
10.5
Contingency Tables
11
ANOVA
11.1
Chapter Overview
11.2
What is the Analysis of Variance (ANOVA)
11.3
The F-Distribution
11.4
Multiple Comparisons and Type I Error Rate
Appendices
Appendix A: Important Links and Additional Resources
Applets
Run R Online
Appendix B: Average Deviance
Appendix C: Deriving a Confidence Interval
References
Published with bookdown
Introduction to Statistics
References