Statisticians have developed propensity score methods to improve generalizations from studies that do not employ random sampling. However, these methods rely on assumptions whose plausibility may be questionable. We introduce and discuss bounding, an approach that is based on alternative assumptions that may be more plausible. The bounding framework nonparametrically estimates population parameters using a range of plausible values. We illustrate how to tighten bounds using three approaches: imposing a monotonicity assumption, redefining the population of inference, and using propensity score stratification. Using two simulation studies, we examine the conditions under which bounds are tightened. We conclude with an application of bounding to SimCalc, a cluster randomized trial that evaluated the effectiveness of a technology aid on mathematics achievement.