  The internal validity of observational study is often subject to debate. In
this study, we define the unobserved sample based on the counterfactuals and
formalize its relationship with the null hypothesis statistical testing (NHST)
for regression models. The probability of a robust inference for internal
validity, i.e., the PIV, is the probability of rejecting the null hypothesis
again based on the ideal sample which is defined as the combination of the
observed and unobserved samples, provided the same null hypothesis has already
been rejected for the observed sample. When the unconfoundedness assumption is
dubious, one can bound the PIV of an inference based on bounded belief about
the mean counterfactual outcomes, which is often needed in this case.
Essentially, the PIV is statistical power of the NHST that is thought to be
built on the ideal sample. We summarize the process of evaluating internal
validity with the PIV into a six-step procedure and illustrate it with an
empirical example (i.e., Hong and Raudenbush (2005)).
