1. Foundations of Inferential Statistics

  • Definition and Purpose
  • Difference Between Descriptive and Inferential Statistics
  • Populations vs. Samples
  • Sampling Error and Sampling Distribution
  • Law of Large Numbers and Central Limit Theorem

2. Estimation

  • Point Estimation
    • Sample Mean, Proportion, Variance
    • Properties of Estimators: Unbiasedness, Consistency, Efficiency
  • Interval Estimation (Confidence Intervals)
    • Confidence Intervals for Means (σ known and σ unknown)
    • Confidence Intervals for Proportions
    • Confidence Intervals for Variance
    • Margin of Error
    • Interpretation of Confidence Levels

3. Hypothesis Testing

  • Steps in Hypothesis Testing
    • Null and Alternative Hypotheses
    • Test Statistic and Sampling Distribution
    • p-value and Significance Level (α)
    • Type I and Type II Errors
    • Power of a Test
  • One-tailed vs. Two-tailed Tests
  • Parametric Tests
    • Z-test (mean, proportion)
    • t-test (one-sample, independent, paired)
    • F-test (variance ratio test)
    • ANOVA (one-way, two-way)
  • Non-Parametric Tests
    • Chi-square test (goodness-of-fit, independence)
    • Mann–Whitney U test
    • Wilcoxon signed-rank test
    • Kruskal–Wallis test

4. Regression and Correlation

  • Simple Linear Regression

    Least Squares Estimation
    • Interpretation of Coefficients
    • Coefficient of Determination (R²)
    • Standard Error of Estimat
  • Multiple Linear Regression
  • Multicollinearity, Heteroskedasticity, Autocorrelation
  • Model Diagnostics and Validation
  • Correlation Analysis
    • Pearson’s r
    • Spearman’s ρ
    • Partial and Multiple Correlation

5. Analysis of Variance (ANOVA)

  • One-Way ANOVA
  • Two-Way ANOVA (With and Without Interaction)
  • Post-Hoc Tests (Tukey, Bonferroni, Scheffé)
  • Assumptions and Diagnostics

6. Categorical Data Analysis

  • Chi-Square Tests (Independence, Homogeneity, Goodness of Fit)
  • Fisher’s Exact Test
  • Logistic Regression
  • Odds Ratio and Relative Risk

7. Advanced Inferential Techniques

  • Multivariate Analysis (MANOVA)
  • Factor Analysis
  • Discriminant Analysis
  • Canonical Correlation
  • Cluster Analysis
  • Principal Component Analysis (PCA) (borderline inferential/descriptive)

8. Resampling and Simulation Methods

  • Bootstrapping
  • Jackknife Method
  • Monte Carlo Simulation
  • Permutation Tests

9. Bayesian Inference

  • Prior, Likelihood, Posterior
  • Bayesian Updating
  • Credible Intervals vs. Confidence Intervals
  • Bayesian Hypothesis Testing

10. Model Selection and Evaluation

  • Akaike Information Criterion (AIC)
  • Bayesian Information Criterion (BIC)
  • Cross-Validation
  • Adjusted R²
  • Likelihood Ratio Tests