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> is
$$
H_0:Y_i(1)=Y_i(0)\quad\text{for every }i,
$$
against 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.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 1 / a / Solution

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.

= Sharp causal null hypothesis
{synonym}


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 Incoming links: Causal null hypothesis