1 Definitions

• Key Concepts
• Levels of Measurement
• Measures of Central Tendency
• Measures of Dispersion
• Shapes of Distributions
• Univariate Statistics

2 Probability

• Axioms
• Probability Rules
  • Marginal Rule Explanation
  • Bayes’ Rule Explanation
  • Examples

3 Expectations

• Mean
• Variance
• Standard Deviation
• Covariance
• Correlation
• Autocorrelation
• Expectation Rules
  • Exercises
• Summary

4 Probability Distributions

• Random Variables
  • Discrete Random Variables
  • Continuous Random Variables
• Permutations and Combinations
  • Permutations
  • Combinations
• The Hypergeometric Distribution
  • Mean and Variance
• The Binomial Distribution
  • Bernoulli Trial
  • Binomial Distribution
  • Mean and Variance
  • Shape
  • Examples
• The Poisson Distribution
  • Properties
  • Example
  • Approximating the Binomial Distribution
• Normal Distributions
  • Properties
  • Applications
  • Rules
  • Examples
  • Approximating the Binomial Distribution
• Exponential Distributions
  • Properties
  • Examples
• Gamma Distributions
  • Properties
  • Example
• Chi-Square Distributions
  • Properties

5 Sampling

• Estimation
• Sample Statistics
• Sample Distributions
  • Central Limit Theorem
  • Why Does Sample Mean Variance V(X̄) Have Denominator n?
  • Why Does Sample Variance S² Have n - 1 in the Denominator?
  • Shape of X̄
• The T Distribution
• Confidence Intervals

6 One Sample Hypothesis Testing

• Concepts
• The Testing
• Test Statistics
  • Z Test Statistic
  • T Test Statistic
  • Hypothesis Testing Using Confidence Intervals
  • Pearson Chi-square Test Statistic
  • Fisher’s Exact Test
• Examples
  • Example 1 (One-Sided Z-Statistic with One Sample)
  • Example 2 (Two-Sided Z-Statistic with One Sample)
  • Example 3 (Z-Statistic with Multiple Samples)
  • Example 4 (T-Statistic)
  • Example 5 (Chi-square-Statistic for Goodness-of-Fit Test)
  • Example 6 (Chi-square-Statistic for Test of Independence)
  • Example 7 (Chi-square-Statistic for Test of Homogeneity
  • Example 8 (Fisher’s Exact Test)

7 Two Samples Hypothesis Testing

• Case 1: Variances Are Known
  • Example
• Case 2: Variances Are Unknown But Equal
  • Example
• Case 3: Variances Are Unknown and Unequal
  • Example
• Case 4: Matched Pairs with Unknown Variances
  • Example
• Case 5: Difference Between Two Proportions
  • Example

8 Analysis of Variance (ANOVA)

• One-Way Analysis of Variance
  • Simple One-Factor Model
  • The Test
  • Example
  • Post Hoc Tests
• Two-Way Analysis of Variance
  • Two-Treatments Model
  • Tests of Interest
  • Example

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Credits

• ChatGPT
• Sociology Graduate Statistics | University of Notre Dame
• STAT 414 Introduction to Probability Theory | Penn State
• STAT 504 Analysis of Discrete Data | Penn State
• H. Pishro-Nik, “Introduction to probability, statistics, and random processes”, available at https://www.probabilitycourse.com, Kappa Research LLC, 2014.
• EconMacro