A Note on the Analysis and Interpretation of Designed Experiments with Factorial Treatment Structure

Agricultural researchers often use factorial treatment structures, where treatments consist of combinations of two or more levels of two or more factors. Factorial experiments are more efficient than performing experiments involving one factor at a time. They also allow researchers to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable. When interactions are significant, proper interpretation of results is often complicated. Over the years, several post-analysis of variance (ANOVA) techniques have been used to interpret results. A partial data set for a 2 x 2 x 4 factorial arrangement of treatments in a randomized complete block design was used to demonstrate and compare three commonly used post-ANOVA methods when the three-way interaction is significant. In the presence of interaction, there may be situations where marginal means (main effects means) can be compared but slicing the data set without separating the data usually provides the most information and allows correct interpretation of the results. The advantage of slicing is that all the data are used for the analysis and the effect of one factor can be evaluated while holding the other factors fixed.