Fig. 1: Understanding factorial analysis.

In factorial analysis, a single statistical model is fitted to the data to understand how the different factors influence an outcome metric of interest. The most well-known example, suitable for a continuous normally distributed variable, is a 2-way ANOVA. In such an analysis, the data will be queried with three hypothesis questions testing two main effects (the effect of sex and treatment) and an interaction between sex and treatment. This strategy enhances sensitivity (as the data is shared between the sexes), allows the sex-related variation to be accounted for, and allows a statistical test of whether sex explains variation in the treatment effect. A and B illustrate how the same data are assessed for main (A) and interaction (B) effects. A The treatment effect is assessed by pooling data across males and females to estimate the average effect of treatment. This is demonstrated by the bluish green arrow which indicates the difference between the control group average (including females and males) and the treatment group average (including males and females). While the effect of sex is mathematically assessed by pooling data across the treatment conditions to estimate the average difference between female and male samples. This is demonstrated by the sky blue arrow, which indicated the difference between the male average (including both control and treated) and the female average (including both control and treated). B In the assessment of the interaction, the size of the treatment effect is compared between the females and males. Here, the vermillion arrow indicates the effect of treatment in males, and the blue arrow indicates the effect size of treatment in females. C-E Illustrate some of the possible different outcomes from a factorial analysis. C An example of a generalizable treatment effect between the females and males where there is no baseline difference between the sexes. D An example of a generalizable treatment effect between the males and females in the context of a baseline difference. E An example where sex-explains variation in the treatment effect. For both (C) and (D), the interaction is not significant, and the treatment effect can be assessed solely by looking at the significance of the treatment term in the model and then assessing the estimated treatment effect. For (E), the interaction is significant; in these situations, you would run additional analysis to estimate the treatment effect within each sex to understand where the significant differences lie.