Track 10 · Comparing Groups and Categorical Data · Lesson 6 of 11
Two-way ANOVA foundations
Separate the main effects of two factors from their interaction in a balanced two-way ANOVA, read an interaction plot, and know when main effects stop being meaningful.
An agronomist tests three fertilizer treatments under two irrigation methods. She needs to know not only whether fertilizer matters and whether drip irrigation matters, but whether drip irrigation pays off more when fertilizer is applied — because that changes what she would recommend to farmers who cannot afford both.
In a factorial design every level of factor A is combined with every level of factor B; each combination is a cell. The crop_trial dataset has 3 fertilizer treatments × 2 irrigation methods = 6 cells, with 6 field plots randomly assigned to each — a balanced design (equal in every cell).
Three questions can be asked of such data:
- Main effect of A: do the fertilizer means differ, averaging over irrigation?
- Main effect of B: do the irrigation means differ, averaging over fertilizer?
- Interaction A × B: does the effect of one factor depend on the level of the other?
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Distinguish main effects from an interaction using cell and marginal means
- Read interaction plots: parallel lines versus crossing or fanning lines
- Fit and read a balanced two-way ANOVA table with its degrees of freedom
- Report simple effects instead of main effects when the interaction is strong