Applied statistics course

Lesson 1 • Populations, Samples, and Parameters

Defines population parameters versus sample statistics and explains why sampling is necessary. Connects directly to inference concepts introduced in later chapters.

Lesson 2 • Random Variables and Distributions

Explains discrete and continuous random variables and their probability distributions. Prepares students for working with named distributions in subsequent chapters.

Lesson 3 • Data Types and Measurement Scales

Covers nominal, ordinal, interval, and ratio scales and their implications for analysis. Establishes the vocabulary needed throughout the entire course.

Lesson 4 • Statistical Thinking in Practice

Frames statistical reasoning as a decision-making tool in professional contexts. Reinforces chapter concepts by applying them to realistic problem scenarios.

Lesson 1 • Measures of Spread and Shape

Teaches variance, standard deviation, range, IQR, skewness, and kurtosis. Complements central tendency measures to give a complete distributional picture.

Lesson 2 • Exploratory Data Analysis Workflow

Presents a systematic EDA process for uncovering patterns, anomalies, and relationships. Integrates all descriptive tools into a repeatable professional workflow.

Lesson 3 • Data Visualization Fundamentals

Introduces histograms, box plots, bar charts, and scatter plots for exploratory analysis. Visualization skills developed here support every subsequent analytical chapter.

Lesson 1 • Poisson and Geometric Distributions

Covers count-based and waiting-time discrete distributions with real-world applications. Extends discrete distribution toolkit beyond the binomial.

Lesson 2 • Central Limit Theorem

Proves and demonstrates the CLT through simulation and mathematical argument. Justifies the use of normal-based inference for large samples regardless of population shape.

Lesson 3 • Other Key Continuous Distributions

Introduces t, chi-square, F, and exponential distributions and their roles in inference. Prepares students for the specific tests covered in the next two chapters.

Lesson 4 • Binomial and Bernoulli Distributions

Derives the binomial distribution from Bernoulli trials and computes probabilities and moments. Establishes discrete distribution reasoning used in hypothesis testing later.

Lesson 1 • Sample Size Determination

Teaches how to calculate required sample sizes for desired precision and power. Bridges estimation and hypothesis testing by introducing the power concept early.

Lesson 2 • Confidence Intervals for Proportions

Derives CIs for population proportions using normal approximation and exact methods. Extends interval estimation to binary outcome data common in surveys.

Lesson 3 • Confidence Intervals for Means

Constructs z-based and t-based confidence intervals for population means. Directly applies CLT and t-distribution knowledge from the previous chapter.

Lesson 4 • Bootstrap and Resampling Methods

Introduces the bootstrap as a distribution-free approach to constructing CIs. Expands estimation capability beyond parametric assumptions.

Lesson 1 • Tests for Proportions and Variances

Extends hypothesis testing to proportions and variance comparisons using chi-square and F-tests. Broadens the testing toolkit beyond mean-based comparisons.

Lesson 2 • Logic and Structure of Hypothesis Tests

Establishes null and alternative hypotheses, test statistics, and decision rules. Provides the conceptual scaffold for every specific test covered in this chapter.

Lesson 3 • Statistical Power and Error Control

Quantifies power, explains its determinants, and demonstrates power analysis for test design. Connects sample size planning from Chapter 4 to hypothesis testing decisions.

Lesson 4 • P-Values and Statistical Significance

Defines the p-value precisely and explains its correct interpretation and common misuses. Addresses the ongoing debate around significance thresholds in applied research.

Lesson 1 • Simple Linear Regression Model

Derives the ordinary least squares estimators for slope and intercept. Introduces the regression equation as a tool for prediction and explanation.

Lesson 2 • Inference in Simple Regression

Applies hypothesis testing and confidence intervals to regression coefficients. Connects Chapter 5 inference methods directly to the regression context.

Lesson 3 • Measuring Linear Association

Covers Pearson and Spearman correlation coefficients and their assumptions. Establishes the relationship-quantification foundation for regression modeling.

Lesson 4 • Regression Diagnostics and Assumptions

Teaches residual analysis and formal tests for linearity, homoscedasticity, and normality. Ensures students can validate model assumptions before drawing conclusions.

Lesson 1 • Multicollinearity and Variance Inflation

Diagnoses multicollinearity using VIF and condition indices and applies remedies. Addresses a critical threat to coefficient interpretability in multiple regression.

Lesson 2 • Variable Selection Strategies

Compares stepwise, best-subset, and information-criterion-based selection methods. Teaches principled model parsimony without overfitting.

Lesson 3 • Multiple Linear Regression Fundamentals

Generalizes OLS to multiple predictors and interprets partial regression coefficients. Builds directly on simple regression skills from Chapter 6.

Lesson 4 • Categorical Predictors and Interactions

Encodes categorical variables as dummy variables and models interaction effects. Expands the regression framework to handle mixed predictor types.

Lesson 1 • Two-Way ANOVA and Factorial Designs

Extends ANOVA to two factors and their interaction, enabling efficient multi-factor experiments. Connects to interaction modeling introduced in Chapter 7.

Lesson 2 • Post-Hoc Multiple Comparisons

Applies Tukey, Bonferroni, and Scheffé procedures to identify which group means differ. Controls family-wise error rate after a significant ANOVA result.

Lesson 3 • Randomized Block and Repeated Measures

Introduces blocking to control nuisance variation and repeated measures for within-subject designs. Improves experimental precision and handles correlated observations.

Lesson 4 • One-Way ANOVA

Partitions total variance into between-group and within-group components to test mean equality. Generalizes the two-sample t-test to three or more groups.