Introduction to Statistics
Welcome to Statistics!
For the Student
R Programming
For the Instructor
Course Learning Outcomes
1
Introduction to Data
1.1
Statistics Terminology
Section Exercises
1.2
Sampling and Design
1.2.1
Statistical Sampling
1.2.2
Experimental Design
Section Exercises
1.3
Frequency Distributions
1.3.1
Qualitative Variables
1.3.2
Quantitative Variables
Section Exercises
R Lab: Data Basics and Graphs
1.3.3
R as a Calculator
Random Number Generation
Entering Data
Histograms
2
Descriptive Measures
2.1
Measures of Central Tendency
Section Exercises
2.2
Measures of Variability
Section Exercises
2.3
Measures of Position
2.3.1
Box Plots
Section Exercises
2.4
Descriptive Measures for Populations
R Lab: Descriptive Statistics and Boxplots
Finding Measures of Center
Finding Measures of Variability
Measures of Position
Box Plots
3
Regression and Correlation
3.1
Linear Equations
3.2
Correlation
Section Exercises
3.3
Finding a Regression Line
3.3.1
The Coefficient of Determination
3.3.2
Prediction: A Cautionary Tale
Section Exercises
R Lab: Scatterplots and Regression
Scatterplots
Correlation
Finding a Regression Line
4
Probability Concepts
4.1
Experiments, Sample Spaces, and Events
Section Exercises
4.2
Probability Distributions
4.2.1
Venn Diagrams
4.2.2
Probability Axioms
Section Exercises
4.3
Rules of Probability
4.3.1
Addition Rules
4.3.2
Complements
Section Exercises
4.4
Conditional Probability
4.4.1
Multiplication Rules
Section Exercises
5
Random Variables
5.1
Discrete Random Variables
5.1.1
The Mean and Standard Deviation
Section Exercises
5.2
The Binomial Distribution
5.2.1
Mean and Variance
Section Exercises
5.3
The Normal Distribution
5.3.1
Z-Scores
5.3.2
Empirical Rule for Variables
Section Exercises
5.4
Area Under the Standard Normal Curve
Section Exercises
5.5
Working with Normally Distributed Variables
5.5.1
Normal Distribution Probabilities
5.5.2
Percentiles
Section Exercises
R Lab: Probabilities and Percentiles
Binomial Probabilities
Normal Distribution Probabilities
Normal Distribution Percentiles
6
Introduction to Confidence Intervals
6.1
Sampling Distributions
6.1.1
Sampling Error
6.1.2
The Central Limit Theorem
Section Exercises
6.2
Developing Confidence Intervals
6.2.1
Interpreting a Confidence Interval
Section Exercises
6.3
Other Levels of Confidence
6.3.1
Breaking Down a Confidence Interval
Section Exercises
6.4
Confidence Level, Precision, and Sample Size
Section Exercises
6.5
Confidence Intervals for a Mean
6.5.1
The T-Distribution
Section Exercises
R Lab: Confidence Intervals
Finding Z Critical Values
Finding T Critical Values
Confidence Intevals for a Mean
7
Introduction to Hypothesis Testing
7.1
Logic of Hypothesis Testing
7.1.1
Decision Errors
7.2
Confidence Interval Approach to Hypothesis Testing
7.3
Critical Value Approach to Hypothesis Testing
7.3.1
Test statistics
7.4
P-Value Approach to Hypothesis Testing
7.4.1
P-Values
R Lab: Hypothesis Tests for a Mean
8
Inference for a Proportion
8.1
Confidence Intervals for a Proportion
8.2
Hypothesis Tests for a Proportion
8.2.1
Confidence Interval Approach
8.2.2
Critical Value Approach
8.2.3
P-Value Approach
R: Hypothesis Tests for a Proportion
9
Inference: Comparing Parameters
9.1
Hypothesis Tests for Two Proportions
9.1.1
Confidence Intervals for Two Proportions
9.1.2
Critical Values, Test Statistics, and P-Values
9.2
Hypothesis Tests for Two Means
9.2.1
Paired Samples
9.2.2
Independent Samples
R Lab: Comparing Parameters
Hypothesis Tests for Two Proportions
Hypothesis Tests for Two Means
10
Chi-Square Tests
10.1
Inference for a Population Variance
10.1.1
The Chi-Square Distribution
10.2
The Ratio of Two Variances
10.3
Goodness of Fit
10.4
Contingency Tables
11
ANOVA
11.1
What is the Analysis of Variance (ANOVA)
11.2
The F-Distribution
11.3
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