ANOVA and Experimental Design Course

Lesson 1 • Variables and Measurement Scales

Defines independent, dependent, and covariate variables across four measurement scales. Correct variable classification determines which ANOVA model applies.

Lesson 2 • Hypothesis Testing Fundamentals

Introduces null and alternative hypotheses, p-values, and Type I/II errors. Provides the inferential logic underlying every ANOVA test.

Lesson 3 • Core Statistical Concepts Review

Covers populations, samples, distributions, and descriptive statistics. Establishes the quantitative vocabulary needed for all subsequent ANOVA work.

Lesson 4 • Experimental vs. Observational Designs

Contrasts randomized experiments with quasi-experiments and observational studies. Students learn when causal inference is and is not warranted.

Lesson 1 • The F-Ratio and Its Distribution

Derives the F-ratio from mean squares and links it to the F-distribution. Students learn to locate critical values and compute exact p-values.

Lesson 2 • Why ANOVA Instead of Multiple t-Tests

Explains familywise error rate inflation when running repeated t-tests. Motivates ANOVA as the correct tool for comparing three or more group means simultaneously.

Lesson 3 • ANOVA Assumptions and Diagnostics

Covers normality, homogeneity of variance, and independence assumptions. Diagnostic checks prevent invalid conclusions from assumption violations.

Lesson 4 • Partitioning Total Variance

Decomposes total sum of squares into between-group and within-group components. This partition is the computational heart of every ANOVA model.

Lesson 1 • False Discovery Rate Methods

Introduces Benjamini-Hochberg FDR control as an alternative to familywise methods. FDR procedures offer greater power in large-scale comparison settings.

Lesson 2 • The Multiple Comparisons Problem

Quantifies how familywise error accumulates across pairwise tests. Establishes the need for error-rate control before introducing correction methods.

Lesson 3 • Pairwise Post-Hoc Procedures

Covers Tukey HSD, Bonferroni, and Scheffé methods with their assumptions. Students match each procedure to the appropriate research context.

Lesson 1 • Unbalanced Designs and Type III SS

Addresses unequal cell sizes and the choice among Type I, II, and III sums of squares. Type III SS is standard for unbalanced factorial designs in most fields.

Lesson 2 • Higher-Order Factorial Extensions

Extends two-way logic to three-way and higher designs with three-way interactions. Students learn to manage complexity and interpret higher-order interaction tables.

Lesson 3 • Main Effects in Two-Way ANOVA

Computes and interprets the main effect of each factor independently. Main effects describe average factor influence collapsed across levels of the other factor.

Lesson 4 • Two-Factor Design Structure

Defines crossed factorial designs and cell structure for two factors. Understanding cell means and marginal means is prerequisite to interaction interpretation.

Lesson 1 • One-Way Repeated Measures Computation

Partitions variance into subjects, conditions, and residual components. Students build the ANOVA table and compute the F-ratio for within-subjects effects.

Lesson 2 • Mixed Designs: Between and Within Factors

Combines one between-subjects factor with one within-subjects factor in a single model. Mixed designs require separate error terms for each type of effect.

Lesson 3 • Within-Subjects Design Logic

Explains how repeated measurement removes between-subject variance from error. This efficiency gain is the primary advantage of within-subjects designs.

Lesson 4 • Sphericity Assumption and Tests

Defines sphericity as equal variance of difference scores across condition pairs. Mauchly's test detects violations that inflate Type I error in repeated measures ANOVA.

Lesson 1 • ANCOVA Assumptions and Diagnostics

Covers linearity, homogeneity of regression slopes, and covariate independence from treatment. Violations of these assumptions invalidate adjusted mean comparisons.

Lesson 2 • Computing Adjusted Means

Derives least-squares adjusted means by removing covariate influence from group means. Adjusted means represent group performance at the covariate's grand mean.

Lesson 3 • Multiple Covariates and Model Building

Extends ANCOVA to multiple covariates and evaluates incremental variance explained. Students balance model complexity against degrees of freedom loss.

Lesson 4 • Rationale and Goals of ANCOVA

Explains how covariates reduce error variance and adjust group means for pre-existing differences. ANCOVA bridges regression and ANOVA into a unified linear model.

Lesson 1 • Randomized Complete Block Designs

Groups experimental units into homogeneous blocks to remove nuisance variation. Blocking is the most widely used strategy for increasing ANOVA precision.

Lesson 2 • Incomplete Block Designs

Covers balanced incomplete block (BIB) designs when full blocks are infeasible. Students compute adjusted treatment means and assess design efficiency.

Lesson 3 • Split-Plot and Split-Split-Plot Designs

Assigns hard-to-change factors to whole plots and easy-to-change factors to subplots. Split-plot designs require distinct error terms for each stratum.

Lesson 4 • Latin Square and Graeco-Latin Designs

Controls two nuisance factors simultaneously using Latin square row-column structure. Students construct valid squares and analyze the resulting ANOVA model.

Lesson 1 • Effect Size Estimation for Planning

Guides estimation of expected effect sizes from prior literature, pilot data, or theory. Accurate effect size input is the most critical step in power analysis.

Lesson 2 • Sample Size for One-Way and Factorial ANOVA

Computes required N for one-way, two-way, and higher factorial designs. Students account for the number of cells, alpha level, and desired power level.

Lesson 3 • Power for Repeated Measures Designs

Adjusts power calculations for within-subjects correlation and sphericity corrections. Repeated measures designs typically require fewer participants than between-subjects designs.

Lesson 4 • Power Analysis Fundamentals

Defines statistical power as the probability of correctly rejecting a false null hypothesis. The four-parameter relationship links alpha, power, effect size, and sample size.