MMP.15:5.1 - Separate a production action from the batches receiving it

A production team asks whether enabling a stabilization mode (A=1), rather than (A=0), increases the probability of a conforming item (Y=1). Incoming batch condition (L) is recorded before mode selection. Half the target batches have (L=0), half (L=1). Mode 1 is used on 80% of (L=0) batches and 20% of (L=1) batches.

The subject account asserts consistency and mean exchangeability given (L); both modes occur in both strata. Adjustment therefore gives (\mu_0=0.5(0.10)+0.5(0.70)=0.40), (\mu_1=0.5(0.20)+0.5(0.80)=0.50), and (\Delta=0.10).

The selected groups instead give (E[Y\mid A=1]=0.8(0.20)+0.2(0.80)=0.32) and (E[Y\mid A=0]=0.2(0.10)+0.8(0.70)=0.58): an association of (-0.26). Its sign differs because the two modes receive different batch mixtures.

This positive average effect is conditional on the causal account; the table does not prove exchangeability. An already supported account and sufficient estimate need no new experiment.