So far in this module, ANOVA has been used to compare means across the levels of a single factor. Many engineering experiments, however, vary two or more factors at once — for example, testing how both catalyst type and reaction temperature affect yield, or how both material and coating thickness affect fatigue life. Multi-factor ANOVA (most commonly the two-way ANOVA) lets you test all of these influences in one analysis instead of running separate one-way ANOVAs for each factor.
Two new ideas drive this topic. A main effect is the influence of one factor on the response, averaged across the levels of the other factor. An interaction effect occurs when the effect of one factor depends on the level of the other — for instance, when a higher temperature helps one catalyst but hurts another. Because interactions change how main effects should be described, you always check the interaction term first. The two-way ANOVA table reflects this structure: total variation is partitioned into a row-factor component, a column-factor component, an interaction component, and error, with an F-statistic and p-value for each.
As you watch, pay attention to three things: how the sums of squares and degrees of freedom are split among the factors, the interaction, and error; how each F-ratio is formed and tested; and how interaction plots (parallel versus non-parallel lines) are read. Also notice the practical question of when a multi-factor design is worth using — replication, balanced designs, and the efficiency of studying several factors in a single experiment.
A worked engineering-oriented treatment of the two-way ANOVA from LearnChemE, produced by chemical engineering faculty at the University of Colorado Boulder. In roughly fifteen minutes it should walk through the structure of a two-factor analysis — setting up the data layout, partitioning the sums of squares across the two factors, the interaction, and error, and building the resulting ANOVA table with F-statistics and p-values. Expect the calculations to be tied to a concrete example rather than presented abstractly.
LearnChemE is a well-established engineering education channel, so the notation and example context match this course better than generic statistics tutorials, and the length allows full coverage of the two-way ANOVA structure and result interpretation.
Part 1 of a short lecture series introducing the background and logic of two-way (factorial) ANOVA. It is positioned as the conceptual setup: why researchers move from one factor to two, how factorial designs are organized into cells by crossing factor levels, and what main effects and interaction effects mean before any computation begins.
At under eight minutes, it gives a clean conceptual bridge from one-way to multi-factor ANOVA and defines main versus interaction effects — exactly the framing subtopics of this page — before you take on the arithmetic.
Part 3 of the same lecture series, focused on carrying out and reading the two-way ANOVA analysis. It should cover the output side: the separate F-tests for each factor and for the interaction, the associated p-values, and how those results are translated into statements about the data.
It targets the interpretation subtopic directly, showing how to read multiple F-statistics from one table — the skill most students find hardest when moving beyond one-way ANOVA.
These videos focus on the multi-factor portion of the module. The LearnChemE lecture reinforces the variance-partitioning logic from MO3 by extending it to two factors plus an interaction term, showing how each F-ratio is built from its own mean square over the error mean square. The two short PSYC 300 lectures support MO4 most directly: Part 1 defines main effects and interaction effects and explains when a factorial design is appropriate, while Part 3 demonstrates reading the F-statistics and p-values for each variance component and deciding what the pattern of significance means. Together they prepare you to recognize when an interaction makes a main effect misleading, which is also the situation in which follow-up comparisons from MO5 must be interpreted with care.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.