Results from large-scale evaluation studies form the foundation of evidence-based policy. The randomized experiment is often considered the gold standard among study designs because the causal impact of a treatment or intervention can be assessed without threats of confounding from external variables. Policy-makers have become increasingly interested in the external validity of results, or the extent to which the results from a study generalize to a population of interest. In this paper, the author derives partial identification bounds on the expected treatment effect for the population under three different frameworks: (1) Worst-case framework with no assumptions on the data; (2) Treatment optimization where subjects select the treatment that optimizes the expected outcome and; (3) Monotone treatment response where the response function is assumed to be weakly increasing in the treatment. Under each framework, the author analyzes the impact that additional, but weak, assumptions have on the width of the estimation bounds and discuss important differences between the bounds for the expected treatment effect for the sample and those for the treatment effect for the population. Tables and figures are appended.