ANOVA Course

Lesson 1 • Hypothesis Testing Logic

Explains null and alternative hypotheses, decision rules, and p-values. Provides the inferential framework that ANOVA extends.

Lesson 2 • Probability and Sampling Distributions

Introduces probability rules and key sampling distributions. Links sample statistics to population parameters via the central limit theorem.

Lesson 3 • Effect Size and Statistical Power

Defines effect size and power as complements to p-values. Prepares learners to design studies with adequate sensitivity before running ANOVA.

Lesson 4 • Descriptive Statistics Essentials

Covers central tendency, variability, and data shape. Establishes the numerical language used throughout all ANOVA analyses.

Lesson 1 • Computing the ANOVA Summary Table

Walks through hand calculation of SS, MS, and F. Builds intuition for how each component reflects data variability.

Lesson 2 • The ANOVA Model and Notation

Formalises the linear model underlying one-way ANOVA. Learners translate research questions into model equations and identify each term.

Lesson 3 • Conceptual Basis of ANOVA

Explains why ANOVA controls familywise error better than multiple t-tests. Motivates the variance-partitioning approach central to all ANOVA designs.

Lesson 4 • Interpreting and Reporting Results

Translates F-ratio and p-value into substantive conclusions. Covers APA-style reporting standards for one-way ANOVA outputs.

Lesson 1 • Reporting Comparisons and Contrasts

Standardises how to present post-hoc and contrast results in tables and text. Emphasises effect sizes and confidence intervals alongside p-values.

Lesson 2 • The Multiple Comparisons Problem

Revisits familywise error in the context of pairwise testing. Establishes why correction procedures are mandatory after a significant F-test.

Lesson 3 • Pairwise Post-Hoc Procedures

Compares Tukey HSD, Bonferroni, and Scheffé methods. Learners match each procedure to study conditions based on power and control trade-offs.

Lesson 4 • Trend Analysis

Applies polynomial contrasts to detect linear, quadratic, and higher-order trends across ordered groups. Connects trend analysis to dose-response research questions.

Lesson 1 • Simple Effects Analysis

Decomposes a significant interaction by examining one factor at each level of the other. Provides the follow-up strategy when interactions are present.

Lesson 2 • Reporting Factorial ANOVA Results

Structures complete reporting of main effects, interactions, and follow-up tests. Learners produce publication-ready tables and interaction plots.

Lesson 3 • Computing Two-Way ANOVA

Extends sum-of-squares partitioning to include the interaction term. Learners build the two-way ANOVA summary table from raw data.

Lesson 4 • Factorial Design Logic

Introduces crossed factors, cells, and the efficiency advantage of factorial designs. Learners map research questions onto two-way layouts.

Lesson 5 • Main Effects and Interactions

Defines main effects and the interaction effect conceptually and mathematically. Learners distinguish additive from non-additive models using cell mean patterns.

Lesson 1 • Mixed Designs: Between and Within Factors

Combines one between-subjects factor with one within-subjects factor in a single model. Learners interpret the mixed interaction and identify correct error terms.

Lesson 2 • Partitioning Variance in Repeated Measures

Extends SS partitioning to isolate subject variance from error. Learners see how removing individual differences reduces error and increases power.

Lesson 3 • Sphericity Assumption

Defines sphericity as equal variances of difference scores across condition pairs. Learners test and correct for sphericity violations using established adjustments.

Lesson 4 • Within-Subjects Design Rationale

Contrasts within-subjects and between-subjects designs on power and efficiency. Motivates repeated measures ANOVA for longitudinal and crossover studies.

Lesson 1 • Testing Homogeneity of Regression Slopes

Demonstrates the interaction test used to verify the parallel slopes assumption. Learners interpret the treatment-by-covariate interaction as an assumption check.

Lesson 2 • Reporting ANCOVA Results

Structures results to include covariate statistics, adjusted means, and effect sizes. Learners produce complete ANCOVA tables and narrative summaries.

Lesson 3 • Computing and Interpreting ANCOVA

Walks through adjusted SS computation and adjusted mean estimation. Learners compare unadjusted and adjusted group means to quantify covariate impact.

Lesson 4 • Purpose and Logic of ANCOVA

Explains how covariates statistically equate groups and reduce residual variance. Distinguishes ANCOVA from blocking and from regression-based adjustment.

Lesson 1 • Kruskal-Wallis Test

Presents the rank-based analog to one-way ANOVA for independent groups. Learners compute the H statistic and interpret results relative to chi-square critical values.

Lesson 2 • Choosing Between Parametric and Nonparametric

Synthesises decision criteria for selecting ANOVA versus rank-based alternatives. Learners apply a structured decision framework to realistic data scenarios.

Lesson 3 • When Parametric Assumptions Fail

Identifies conditions under which ANOVA results are unreliable. Guides the decision to switch to nonparametric methods based on data characteristics.

Lesson 4 • Effect Size for Nonparametric Tests

Calculates epsilon-squared and Kendall's W as effect size measures for rank-based tests. Connects nonparametric effect sizes to their parametric counterparts.

Lesson 1 • Random and Mixed Effects Models

Distinguishes fixed from random factors and their implications for inference and generalisability. Learners compute expected mean squares to identify correct F-ratio denominators.

Lesson 2 • ANOVA as the General Linear Model

Unifies ANOVA, regression, and ANCOVA under the general linear model framework. Learners recode group membership as dummy variables and reproduce ANOVA results via regression.

Lesson 3 • Nested Designs

Introduces hierarchical structures where levels of one factor are unique to levels of another. Learners identify nesting, specify correct error terms, and interpret nested effects.

Lesson 4 • MANOVA: Multivariate Extension

Extends ANOVA to multiple dependent variables analysed simultaneously. Learners interpret Wilks' lambda and follow up significant MANOVA with univariate tests.