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OpenStax: Introduction to Statistics with R

This repository will detail R code solutions for the 2017 edition of OpenStax's Introduction to Statistics. Huge thanks to the authors, and to Rick Baraniuk for having the vision to place open-source, remixable textbooks online.

Table of Contents

  1. Sampling and Data
  • Definitions of Statistics, Probability, and Key Terms
  • Data, Sampling, and Variation in Data and Sampling
  • Frequency, Frequency Tables, and Levels of Measurement
  • Experimental Design and Ethics
  • Data Collection Experiment
  • Sampling Experiment

  1. Descriptive Statistics

  1. Probability Topics
  • Terminology
  • Independent and Mutually Exclusive Events
  • Two Basic Rules of Probability
  • Contingency Tables
  • Tree and Venn Diagrams
  • Probability Topics

  1. Discrete Random Variables
  • Probability Distribution Function (PDF) for a Discrete Random Variable
  • Mean or Expected Value and Standard Deviation
  • Binomial Distribution
  • Geometric Distribution
  • Hypergeometric Distribution
  • Poisson Distribution
  • Discrete Distribution (Playing Card Experiment)
  • Discrete Distribution (Lucky Dice Experiment)

  1. Continuous Random Variables
  • Continuous Probability Functions
  • The Uniform Distribution
  • The Exponential Distribution
  • Continuous Distribution

  1. The Normal Distribution
  • The Standard Normal Distribution
  • Using the Normal Distribution
  • Normal Distribution (Lap Times)
  • Normal Distribution (Pinkie Length)

  1. The Central Limit Theorem
  • The Central Limit Theorem for Sample Means (Averages)
  • The Central Limit Theorem for Sums
  • Using the Central Limit Theorem
  • Central Limit Theorem (Pocket Change)
  • Central Limit Theorem (Cookie Recipes)

  1. Confidence Intervals
  • A Single Population Mean using the Normal Distribution
  • A Single Population Mean using the Student t Distribution
  • A Population Proportion
  • Confidence Interval (Home Costs)
  • Confidence Interval (Place of Birth)
  • Confidence Interval (Women's Heights)

  1. Hypothesis Testing with One Sample
  • Null and Alternative Hypotheses
  • Outcomes and the Type I and Type II Errors
  • Distribution Needed for Hypothesis Testing
  • Rare Events, the Sample, Decision and Conclusion
  • Additional Information and Full Hypothesis Test Examples
  • Hypothesis Testing of a Single Mean and Single Proportion

  1. Hypothesis Testing with Two Samples
  • Two Population Means with Unknown Standard Deviations
  • Two Population Means with Known Standard Deviations
  • Comparing Two Independent Population Proportions
  • Matched or Paired Samples
  • Hypothesis Testing for Two Means and Two Proportions

  1. The Chi-Square Distribution
  • Facts About the Chi-Square Distribution
  • Goodness-of-Fit Test
  • Test of Independence
  • Test for Homogeneity
  • Comparison of the Chi-Square Tests
  • Test of a Single Variance
  • Lab 1: Chi-Square Goodness-of-Fit
  • Lab 2: Chi-Square Test of Indepence

  1. Linear Regression and Correlation
  • Linear Equations
  • Scatter Plots
  • The Regression Equation
  • Testing the Significance of the Correlation Coefficient
  • Prediction
  • Outliers
  • Regression (Distance from School)
  • Regression (Textbook Cost)
  • Regression (Fuel Efficiency)

  1. F Distribution and One-Way ANOVA
  • One-Way ANOVA
  • The F Distribution and the F-Ratio
  • Facts About the F Distribution
  • Test of Two Variances
  • Lab: One-Way ANOVA

  1. Review Exercises
  2. Practice Tests (1-4) and Final Exams