Adventages of factorial arrangement
1. provides estimates of interactions.
2. possible increase in precision due to so-called "hidden replication."
3. experimental rates can be applied over a wider range of conditions.
disadvantages of factorial arrangements
1. some treatment combinations may be of little interest.
2. experimental error may become large with a large number of treatments.
3. interpretation may be difficult(especially for 3-way or more interactions).
randomizing factorial arrangements
1. assign numbers to treatment combinations.
2. randomize treatments according to design.
example-RCBD with a 2x4 factorial arrangement
interpreting results of ANOVA involving interaction terms
* interpretation should always begin with the higher level interaction terms(e.g. three-way interactions before two-interaction, etc.).
* interpretation of the main effect should never be done before interpreting the interaction terms.