Week 15/Module 14 - ANOVA

This page introduces ANOVA as a method for comparing means across three or more groups simultaneously, explaining why it is preferable to running multiple t-tests, and serves as a conceptual starting point for learners before they engage with the mechanics of the technique.

This page details the key assumptions that must be met before applying ANOVA—such as normality, homogeneity of variance, and independence—and helps learners and instructors verify that data are appropriate for the analysis before proceeding.

This page explains the logic behind the F-statistic, showing how ANOVA partitions total variability into between-group and within-group components and uses their ratio to determine whether observed mean differences exceed chance, giving learners the conceptual foundation for interpreting ANOVA results.

This page covers the one-way ANOVA procedure—involving a single independent variable—walking learners through the hypotheses, sum-of-squares calculations, ANOVA table construction, and decision rules for testing whether group means differ significantly.

This page extends ANOVA to designs with two or more independent variables (two-way ANOVA), explaining main effects and interaction effects so learners can analyze situations where multiple factors simultaneously influence an outcome.

This page covers post-hoc tests (e.g., Tukey, Bonferroni) used after a significant omnibus F-test to identify which specific group pairs differ, guiding learners and instructors on how to fully interpret and report ANOVA results.

A conceptual reading that introduces Analysis of Variance as a method for testing whether three or more group means differ, explaining how between-group variability is compared to within-group variability and summarized in the F-statistic, which learners use as the entry point to the module.

A reading covering the three core conditions for valid one-way ANOVA — within-group normality, equal population variances (homoscedasticity), and independence of observations — that learners use to check whether the F-test is appropriate for their data and what to do when assumptions fail.

An explanatory page on the logic behind the F-statistic, showing why running repeated pairwise t-tests inflates the Type I error rate and how the ratio of between-group to within-group mean squares provides a single omnibus test instead.

A reading on the one-way ANOVA procedure for comparing means across levels of a single factor, walking learners through the sums-of-squares partition, the ANOVA table, and the hypothesis test using engineering examples such as suppliers, curing temperatures, and machine settings.

A reading extending ANOVA to experiments that vary two or more factors at once, introducing two-way ANOVA, main effects, and interaction effects so learners can analyze designs like catalyst type crossed with reaction temperature.

A reading on what to do after a significant F-test, covering post-hoc pairwise comparison procedures that control the family-wise error rate and guidance on interpreting and reporting which specific group means differ.

A consolidated, single-page compilation of all the module's readings on ANOVA — from the introduction and assumptions through the F-statistic, one-way and multi-factor designs, and post-hoc testing — useful for review, printing, or offline study of the complete Week 15 material.

A comprehensive reading covering ANOVA concepts including its definition, assumptions, F-statistic derivation, and one-way ANOVA procedures, which learners study as the primary text reference for the module.

A landing page that consolidates all module 14 instructional resources — including a PowerPoint, a recorded lecture, and a Google Colab notebook — giving learners a single access point for ANOVA materials.