Statistical inference & hypothesis testing

2024-07-25

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Lecture 2 Outline

  • Purpose and foundations of inferential statistics
    • Probability and random variables
    • Meaningful probability distributions
    • Sampling distributions and Central Limit Theorem
  • Getting to know the “language” of hypothesis testing
    • The null and alternative hypothesis
    • The probability of error? (α or “significance level”)
    • The p-value probability and tests interpretation
    • Confidence Intervals
    • Types of errors (Type 1 and Type 2)
    • Effective vs statistical significance
  • Hypothesis tests examples
    • Comparing sample mean to a hypothesized population mean (Z test & t test)
    • Comparing two independent sample means (t test)
    • Comparing sample means from 3 or more groups (ANOVA)
  • A closer look at testing assumptions (with examples)
    • Testing two groups that are not independent
    • Testing if the data are not normally distributed: non-parametric tests
    • Testing samples without homogeneous variance of observations