Interpreting Results of ANOVA Involving Interaction Terms
Interpretation should always begin with the higher level interaction terms (e.g. three-way interactions before two-interactions, etc.).
Interpretation of the main effects should never be done before interpreting the interaction terms.
The F-test for interaction terms can be significant because of two reasons.
1. True interaction.
2. Differences in magnitude between treatment means.
Differences in magnitude when responses are similar, but the differences between means are great.
An example of this would be yield of a series of varieties having the same relative rank at two locations that differ greatly in yield due to differences in growing conditions (e.g. favorable growing conditions vs. drought conditions).
Examples of Interactions and Differences in Magnitude