  To test the effectiveness of a drug one can advice two randomly selected
groups of patients to take or not to take it, respectively. It is well-known
that the causal effect cannot be identified if not all patients comply. This
holds even when the non-compliers can be identified afterwards since latent
factors like patient's personality can influence both his decision and his
physical response. However, one can still give bounds on the effectiveness of
the drug depending on the rate of compliance. Remarkably, the proofs of these
bounds given in the literature rely on models that represent all relevant
latent factors (including noise) by hidden classical variables. In strong
analogy to the violation of Bell's inequality, some of these bounds fail if
patient's behavior is influenced by latent quantum processes (e.g. in his
nervous system). Quantum effects could fake an increase of the recovery rate by
about 13% although the drug would hurt as many patients as it would help if
everyone took it. The other bounds are true even in the quantum case.
  We do not present any realistic model showing this effect, we only point out
that the physics of decision making could be relevant for the causal
interpretation of every-day life statistical data.
