Applied Statistics Learning Roadmap

Phase 1: Foundations (Weeks 1-8)

1.1 Statistical Fundamentals

• Descriptive statistics (mean, median, variance, skewness, kurtosis)
• Probability distributions (normal, binomial, Poisson, exponential)
• Sampling methods and sampling distributions
• Central Limit Theorem and law of large numbers
• Estimation theory (point estimates, properties of estimators)

1.2 Inferential Statistics Basics

• Hypothesis testing framework (null/alternative hypotheses, p-values, Type I/II errors)
• Confidence intervals and interval estimation
• Statistical power and sample size determination
• One-sample and two-sample tests (t-tests, z-tests)
• Non-parametric tests (Mann-Whitney, Wilcoxon, Kruskal-Wallis)

1.3 Data Fundamentals

• Data types and measurement scales (nominal, ordinal, interval, ratio)
• Data quality, cleaning, and preprocessing
• Missing data mechanisms and imputation basics
• Exploratory data analysis (EDA) techniques
• Data visualization principles and tools

1.4 Practical Computing Skills

• Excel for basic analysis and visualization
• Introduction to R or Python for statistics
• Data import, manipulation, and basic visualization
• Reproducible research practices

Phase 2: Core Statistical Methods (Weeks 9-20)

2.1 Regression Analysis

• Simple linear regression (estimation, interpretation, diagnostics)
• Multiple linear regression (model building, variable selection)
• Assumptions and residual diagnostics
• Transformations and non-linear relationships
• Model comparison and selection criteria (AIC, BIC, R²)
• Regularized regression (Ridge, Lasso, Elastic Net)

2.2 Analysis of Variance (ANOVA)

• One-way ANOVA and F-tests
• Two-way and multi-way ANOVA
• Post-hoc comparisons and pairwise tests
• Contrasts and orthogonal contrasts
• Assumptions: normality, homogeneity of variance
• Fixed and random effects models

2.3 Categorical Data Analysis

• Chi-square tests for independence and goodness-of-fit
• Fisher's exact test
• Contingency tables and association measures
• Logistic regression (binary and multinomial)
• Log-linear models
• Odds ratios and relative risk

2.4 Experimental Design

• Completely randomized designs
• Blocked designs and matched pairs
• Factorial designs and interactions
• Randomization and control groups
• Confounding, bias, and validity threats
• Power analysis for design planning

Phase 3: Advanced Statistical Methods (Weeks 21-32)

3.1 Generalized Linear Models (GLMs)

• GLM framework and link functions
• Logistic regression (practical applications)
• Poisson regression (count data)
• Negative binomial regression
• Overdispersion and quasi-likelihood
• Model diagnostics and residual analysis

3.2 Mixed Effects Models

• Hierarchical data structures
• Random intercepts and random slopes
• Variance components and intra-class correlation
• Maximum likelihood and restricted ML estimation
• Model interpretation and prediction
• Random effects vs. fixed effects

3.3 Time Series Analysis

• Trend, seasonality, and decomposition
• Autocorrelation and partial autocorrelation
• ARIMA models and Box-Jenkins methodology
• SARIMA and seasonal methods
• Exponential smoothing
• Forecasting and forecast evaluation metrics

3.4 Survival Analysis

• Censoring and survival data structures
• Kaplan-Meier survival curves
• Log-rank test
• Cox proportional hazards regression
• Cumulative incidence and competing risks
• Model diagnostics and validation

3.5 Multivariate Analysis

• Principal Component Analysis (PCA)
• Factor analysis and latent variable models
• Cluster analysis (hierarchical, k-means, density-based)
• Discriminant analysis
• Canonical correlation analysis
• Dimension reduction techniques

Phase 4: Specialized Applications (Weeks 33-40)

4.1 Survey Sampling & Design

• Sampling designs (simple random, stratified, cluster)
• Weighting, finite population correction
• Survey estimation and variance estimation
• Complex survey analysis

4.2 Bayesian Methods in Practice

• Prior elicitation and selection
• Bayesian estimation and credible intervals
• Bayesian hypothesis testing and model comparison
• Practical Bayesian inference for common problems

4.3 Causal Inference Essentials

• Observational studies and potential outcomes framework
• Propensity score methods
• Difference-in-differences designs
• Regression discontinuity designs
• Sensitivity analysis

4.4 Quality Control & Process Improvement

• Control charts (Shewhart, EWMA, CUSUM)
• Process capability indices
• Design of Experiments (DOE) for optimization
• Six Sigma methodology
• Acceptance sampling

4.5 Machine Learning & Prediction

• Cross-validation and model evaluation
• Classification methods (KNN, decision trees, SVM)
• Ensemble methods (random forests, boosting, bagging)
• Regularization and overfitting
• Feature selection and engineering