Stability in the absence of treatment

When subjects are measured twice, once at each of two symmetrical locations or times, stability of responses in the absence of treatment within subjec ts, together with comparability of untreated responses between subjects, is often viewed as supporting a conclusion that differences between treated a nd control responses reflect effects actually caused by the treatment. The degree to which this intuitive argument is formally correct is explored in several related models: a multivariate Normal model, a nonparametric model defined by symmetries, an analogous randomized experiment, and a sensitivit y analysis model for observational studies in which treatments are not rand omly assigned to subjects, nor to locations within subjects. Card and Kreug er's study of the employment effects of the minimum wage is used to illustr ate the methods.