Covariate balance
= Covariate balance
<Covariate balance> means that the compared <treatment> groups have similar distributions of specified pretreatment <covariates>. Exact distributional balance in a weighted population is
$$
\mathcal L_w(X\mid A=1)=\mathcal L_w(X\mid A=0).
$$
This is a property of the represented <covariates> and chosen weights. <Matching (statistics)> and <inverse probability weighting> can aim to approximate it.
Equal <means> are weaker than equal <probability distributions>. For example, a <covariate> taking values $-1,1$ equally often in one group and $-2,2$ equally often in the other has mean zero in both, but <variances> one and four. A zero <standardized mean difference> would miss that discrepancy. Inspect relevant spreads, tails, categories and combinations as well as <means>.
A nonsignificant difference test does not demonstrate <covariate balance>: small samples may have low <statistical power>, while large samples can detect negligible discrepancies. <Covariate balance> on measured pretreatment variables also cannot establish <conditional exchangeability> for unmeasured <potential outcomes>.