MMP.15:5.3 - Transfer an experiment to another mixture of sites

An ecological model asks for the effect of a specified irrigation change (A) on establishment of a seedling (Y), averaged across a target collection of sites. Soil stratum (L) is known from an existing inventory. A selected experiment randomized both irrigation levels within each stratum, recorded every outcome, and used the same irrigation implementations as the target question.

Suppose the subject account supports equality of conditional potential-outcome means between experimental and target sites. Experimental sites are 80% (L=0) and 20% (L=1); the target inventory is 25% (L=0) and 75% (L=1).

The experimental average effect is (0.8(0.30)+0.2(0.10)=0.26). The target means are (\mu_0=0.25(0.20)+0.75(0.60)=0.50) and (\mu_1=0.25(0.50)+0.75(0.70)=0.65). The requested effect is 0.15. Randomization identifies the comparisons inside the experiment; the transport assumption and target inventory justify the different outer average.

Now suppose the source is found to contain experimental outcomes only for (L=0); the supplied (L=1) values were extrapolations, with no justified response relation supporting them. Retain the target inventory and transport within the covered stratum. With no outcome restriction for (L=1) beyond binary outcomes, its mean effect (\delta_1) lies in ([-1,1]). Therefore

[ \Delta=0.25(0.30)+0.75\delta_1\in[-0.675,0.825]. ]

The endpoints are attainable by making every uncovered site respectively harmed or helped: ((Y(0),Y(1))=(1,0)) or ((0,1)). Those choices do not alter any available experimental outcome. The bound is sharp under these assumptions, and the sign of the target effect is not identified. The effect 0.30 remains available for the covered stratum if that is the agreed receiving question; it must not silently replace the original population target.