  Spurious association arises from covariance between propensity for the
treatment and individual risk for the outcome. For sensitivity analysis with
stochastic counterfactuals we introduce a methodology to characterize
uncertainty in causal inference from natural experiments and quasi-experiments.
Our sensitivity parameters are standardized measures of variation in propensity
and individual risk, and one minus their geometric mean is an intuitive measure
of randomness in the data generating process. Within our latent propensity-risk
model, we show how to compute from contingency table data a threshold, $T$, of
sufficient randomness for causal inference. If the actual randomness of the
data generating process exceeds this threshold then causal inference is
warranted.
