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A causal null hypothesis states that an intervention has no effect on a specified potential-outcome contrast. A sharp causal null sets every unit's treated and untreated potential outcomes equal; an average causal null sets their population mean difference to zero.

Let $Z=1$ denote gestation under unrestricted sugar and $Z=0$ gestation under rationing, and let $Y_i(z)$ be person $i$'s potential outcome for later Type 2 diabetes under exposure $z$. A sharp causal null hypothesis isagainst the alternative that the two potential outcomes differ for at least one person. An average-effect formulation instead tests $H_0:\mathbb{E}[Y(1)-Y(0)]=0$ against a nonzero, or scientifically directed positive, average effect.