Statistical Analysis Course

Lesson 1 • Introduction to Statistics and Data

Defines statistics, its role in decision-making, and core terminology. Establishes vocabulary used throughout the entire course.

Lesson 2 • Data Visualization Fundamentals

Introduces charts and plots suited to each data type. Effective visualization reveals patterns that summary statistics alone may obscure.

Lesson 3 • Measures of Variability and Spread

Quantifies data dispersion using range, variance, and standard deviation. Variability measures complement central tendency for full data description.

Lesson 4 • Measures of Central Tendency

Covers mean, median, and mode computation and interpretation. Connects each measure to data distribution shape and skewness.

Lesson 1 • Sampling Distributions and the Central Limit Theorem

Derives the sampling distribution of the mean and explains the Central Limit Theorem. This theorem justifies normal-based inference for large samples.

Lesson 2 • Conditional Probability and Independence

Introduces conditional probability and Bayes' theorem for updating beliefs. Independence concepts underpin assumptions in regression and hypothesis testing.

Lesson 3 • Discrete Probability Distributions

Covers binomial, Poisson, and geometric distributions with real-world contexts. Discrete models apply to count data encountered in quality control and surveys.

Lesson 4 • Core Probability Concepts

Defines probability, sample spaces, and events using classical and empirical approaches. Provides the mathematical foundation for all inferential methods ahead.

Lesson 1 • Sample Size Determination

Derives formulas for minimum sample sizes given desired precision and confidence. Proper sizing prevents underpowered studies and unnecessary data collection costs.

Lesson 2 • Point Estimation Principles

Defines estimators and desirable properties such as unbiasedness and efficiency. Understanding estimator quality guides selection of the best summary statistic.

Lesson 3 • Confidence Intervals for Means

Constructs Z-based and t-based intervals for population means. The t-distribution is introduced for small samples with unknown population variance.

Lesson 4 • Confidence Intervals for Proportions

Builds intervals for population proportions using the normal approximation. Proportion intervals are essential for survey analysis and quality audits.

Lesson 1 • Logic and Structure of Hypothesis Tests

Explains null and alternative hypotheses, significance levels, and decision rules. This logical framework applies to every test introduced in subsequent chapters.

Lesson 2 • Tests for Proportions and Variances

Extends hypothesis testing to proportions and variance using Z and chi-square tests. These tests address categorical outcomes and process variability questions.

Lesson 3 • Statistical Power and Effect Size

Defines power as the probability of correctly rejecting a false null hypothesis. Effect size measures practical importance independent of sample size.

Lesson 4 • Multiple Testing and Error Control

Addresses inflated Type I error rates when conducting many simultaneous tests. Correction methods maintain overall error control in complex analyses.

Lesson 1 • Post-Hoc Comparisons

Identifies which group pairs differ after a significant ANOVA result. Controlled post-hoc procedures maintain experiment-wise error rates.

Lesson 2 • One-Way ANOVA

Partitions total variance into between-group and within-group components to test mean equality. ANOVA avoids inflated error rates from multiple pairwise t-tests.

Lesson 3 • Tests for Two Proportions and Variances

Applies Z-tests and F-tests to compare proportions and variances between two groups. F-test results inform variance assumptions in subsequent t-tests.

Lesson 4 • Two-Way ANOVA and Interaction Effects

Analyzes two categorical factors simultaneously and tests for interaction. Interaction effects reveal when one factor's impact depends on another factor's level.

Lesson 1 • Prediction and Extrapolation

Generates point predictions and prediction intervals for new observations. Extrapolation risks are quantified to guide responsible model use.

Lesson 2 • Inference in Simple Regression

Tests hypotheses about regression coefficients and constructs confidence intervals. Inference determines whether the predictor has a statistically significant effect.

Lesson 3 • Simple Linear Regression Model

Derives the least-squares regression line and interprets slope and intercept. The model quantifies how a one-unit predictor change affects the response.

Lesson 4 • Regression Diagnostics

Evaluates model assumptions through residual analysis and influence measures. Violations of assumptions bias estimates and invalidate inference.

Lesson 1 • Multicollinearity Detection and Remedies

Identifies correlated predictors that inflate standard errors and destabilize estimates. Remedies restore reliable coefficient estimation and model interpretability.

Lesson 2 • Variable Selection Methods

Applies forward, backward, and stepwise selection alongside information criteria. Systematic selection balances model fit against parsimony.

Lesson 3 • Regression Assumptions and Remedies

Diagnoses violations of linearity, independence, homoscedasticity, and normality. Transformations and robust methods restore valid inference when assumptions fail.

Lesson 4 • Multiple Regression Fundamentals

Adds multiple predictors to the regression framework and interprets partial slopes. Adjusted R-squared penalizes model complexity to prevent overfitting.

Lesson 1 • Selecting Parametric vs. Nonparametric Tests

Provides a decision framework based on data type, sample size, and assumption checks. Correct test selection ensures valid conclusions across diverse analytical contexts.

Lesson 2 • Nonparametric Correlation and Association

Measures monotonic association using rank-based correlation coefficients. Rank correlations are robust to outliers and non-normal distributions.

Lesson 3 • Nonparametric Tests for Location

Applies rank-based tests as alternatives to t-tests when normality is violated. These tests use ordinal information to compare group medians.

Lesson 4 • Chi-Square Test of Independence

Evaluates association between two categorical variables in a contingency table. Results guide decisions in market research, healthcare, and quality analysis.