Fig. 2

Pictorially representation of two approaches to incorporate multiplicity into non-trivial explanatory structures. a Option 1. Rank, filter, model (RFM). This approach first applies a multiplicity correction to the one-way ANOVA obtained from the saturated model to filter out non-significant responses and then applies a model selection step to obtain a response specific predictive model. b Option 2, Model, rank, filter (MRF). This approach first performs a model selection step to obtain a response specific predictive model, from which a one-way ANOVA is applied and corrected for multiplicity to filter out non-significant responses. c For the two-factor model in Eq. 5 with a 3x4 factorial treatment structure and a replication of 3, this shows the relationship between the one-way ANOVA obtained from a saturated model (fixed variance ratio of 2 and associated significance value of 0.075 – shown by the solid black line) and the one-way ANOVA obtained from the predictive model (for an increasing interaction effect). Thus, as the variance ratio of the interaction term (shown by the solid red line) decreases, the associated p-value of the one-way ANOVA of the predictive model also decreases