= Standardization with common weights
{title2=$p_g^{(w)}=\sum_s w_s p_{gs}$}
Let $p_{gs}$ be a group-specific <conditional probability> in stratum $s$, and let $w_s\ge0$ with $\sum_s w_s=1$. Average each group's <conditional probabilities> using the same weights. Then
$$
p_1^{(w)}-p_0^{(w)}=\sum_s w_s(p_{1s}-p_{0s}).
$$
This is a descriptive comparison under a common covariate composition. Its difference from a crude contrast need not be a <causal effect>. Causal <outcome standardization> additionally requires its identification assumptions.
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