# Table 2 Typology of sex S, social environment E and gender G effects on a health outcome Y

Name

Definitions

Counterfactual formulation

Without-gender total effect of sex (WOGTES)

The effect of sex that would be found in a social environment with the minimal gender phenomena (E = 0)

In practice, this effect more reasonably corresponds to a combined effect of sex and a minimal gender pressure, close to what RES could also mean

$$E\left({Y}_{S=1;E=0}\right)-E\left({Y}_{S=0;E=0}\right)$$

Without-gender total effect of environment (WOGTEE)

The proper effect of the environment not due to the gender phenomena (ideally), i.e., which not vary with sex

$$E\left({Y}_{S=0;E=1}\right)-E\left({Y}_{S=0;E=0}\right)$$

Total effect of gender (TEG)

The difference of the total effect of sex between two social group = the difference of the total effect of the social environment between two sex group (a kind of avoidable effect of the social environment)

These two formulations are conceptually and counterfactually equivalent and corresponds to the writing of an additive interaction between sex and environment

$$\begin{array}{c}\left[E\left({Y}_{S=1;E=1}\right)-E\left({Y}_{S=0;E=1}\right)\right]\\ -\\ \left[E\left({Y}_{S=1;E=0}\right)-E\left({Y}_{S=0;E=0}\right)\right]\end{array}$$

1. With: s for sex, e for social environment, g for gender defined as an e*s interaction, y for outcome