Data Science Statistics Course

Lesson 1 • Descriptive Statistics Essentials

Summarise datasets using measures of centre, spread, and shape. These summaries form the baseline for all inferential and predictive work in later chapters.

Lesson 2 • Visualising Distributions

Translate raw data into histograms, box plots, and density curves to reveal shape and outliers. Visualisation skills anchor every exploratory analysis in the course.

Lesson 3 • Types and Structures of Data

Distinguish nominal, ordinal, interval, and ratio scales and their analytical implications. Correct data classification prevents misapplied statistical methods downstream.

Lesson 1 • Conditional Probability and Independence

Compute conditional probabilities and test statistical independence between events. Independence assumptions drive many model choices in regression and classification.

Lesson 2 • Random Variables and Expectation

Formalise random variables, compute expectations, and derive variance algebraically. Mastery here enables rigorous treatment of estimators in the next chapter.

Lesson 3 • Discrete Probability Distributions

Model count-based outcomes using binomial, Poisson, and geometric distributions. Recognising the correct discrete model prevents systematic prediction errors.

Lesson 4 • Core Rules of Probability

Define sample spaces, events, and the axioms governing probability assignments. These rules are the logical foundation for all distributional models covered next.

Lesson 1 • Confidence Intervals for Means

Construct Z-based and t-based confidence intervals for population means. Correct interval interpretation prevents the common misconception of probability statements about fixed parameters.

Lesson 2 • Bootstrap and Resampling Methods

Generate empirical sampling distributions via bootstrap resampling without distributional assumptions. Bootstrap methods extend interval estimation to complex statistics lacking closed-form solutions.

Lesson 3 • The Central Limit Theorem in Practice

Demonstrate how sample means converge to normality regardless of population shape. This theorem justifies the normal-based inference methods used throughout the course.

Lesson 4 • Point Estimation Methods

Derive estimators using method of moments and maximum likelihood estimation. Understanding estimator derivation prepares learners to evaluate data model parameter outputs.

Lesson 1 • Logic of Hypothesis Testing

Define null and alternative hypotheses, significance levels, and the decision framework. This logic governs every formal test introduced in this and subsequent chapters.

Lesson 2 • Tests for Proportions and Variances

Conduct z-tests for proportions and chi-square and F-tests for variance comparisons. These tests extend hypothesis testing to categorical outcomes and variance equality checks.

Lesson 3 • Multiple Testing and Corrections

Control family-wise error rate and false discovery rate when conducting many simultaneous tests. Multiple testing corrections are mandatory in genomics, A/B testing, and feature selection.

Lesson 4 • Errors, Power, and Sample Size

Quantify Type I error, Type II error, and statistical power to design adequately powered studies. Power analysis determines sample size requirements before data collection.

Lesson 1 • Regression Diagnostics and Assumptions

Verify linearity, homoscedasticity, normality of residuals, and independence through diagnostic plots. Undetected violations invalidate inference and degrade prediction accuracy.

Lesson 2 • Simple Linear Regression

Estimate slope and intercept via ordinary least squares and interpret coefficients. Simple regression establishes the geometric and algebraic framework extended to multiple predictors.

Lesson 3 • Measuring Association Between Variables

Compute Pearson and Spearman correlations and test their significance. Correlation analysis motivates regression modeling and reveals multicollinearity risks.

Lesson 4 • Regularisation and Variable Selection

Apply Ridge, Lasso, and stepwise selection to manage overfitting and choose predictors. Regularisation bridges classical regression and machine learning model building.

Lesson 1 • Contingency Tables and Chi-Square Tests

Construct two-way tables and test independence using chi-square statistics. Contingency analysis is foundational for survey data, A/B tests, and feature association screening.

Lesson 2 • Multinomial and Ordinal Regression

Extend logistic regression to outcomes with more than two unordered or ordered categories. These models handle survey ratings, product tiers, and multi-class classification tasks.

Lesson 3 • Model Evaluation for Classification

Assess logistic regression performance using confusion matrices, ROC curves, and AUC. Proper evaluation metrics prevent misleading accuracy claims on imbalanced datasets.

Lesson 4 • Binary Logistic Regression

Model binary outcomes using the logit link, maximum likelihood, and log-odds interpretation. Logistic regression is the primary classification baseline in data science workflows.

Lesson 1 • Post-Hoc Multiple Comparisons

Identify which group pairs differ after a significant ANOVA using controlled comparison procedures. Post-hoc tests prevent inflated error rates from unplanned pairwise comparisons.

Lesson 2 • Principles of Experimental Design

Apply randomisation, replication, and blocking to eliminate confounding and maximise precision. Sound design is more powerful than any post-hoc statistical adjustment.

Lesson 3 • Repeated Measures and Mixed Designs

Account for within-subject correlation in longitudinal and crossover experiments. Repeated measures designs increase power by removing individual difference variance.

Lesson 4 • Two-Way and Factorial ANOVA

Analyse main effects and interactions between two or more categorical factors simultaneously. Factorial designs reveal synergistic effects invisible to one-factor-at-a-time experiments.

Lesson 1 • Markov Chain Monte Carlo Methods

Sample from intractable posteriors using Metropolis-Hastings and Gibbs sampling algorithms. MCMC enables Bayesian inference for complex hierarchical and nonconjugate models.

Lesson 2 • Bayesian Model Comparison

Compare models using Bayes factors, WAIC, and leave-one-out cross-validation. Bayesian model selection penalises complexity without requiring a fixed significance threshold.

Lesson 3 • Bayesian Inference Framework

Formalise prior, likelihood, and posterior and contrast Bayesian with frequentist logic. This framework enables probabilistic statements about parameters rather than about data.

Lesson 4 • Bayesian Estimation and Credible Intervals

Summarise posteriors using MAP estimates, posterior means, and credible intervals. Credible intervals have the direct probability interpretation that confidence intervals lack.