It is common for data sets to have been selected in some sense. Outcome tests are a method for detecting bias in these selection procedures using data on selected units, but such tests do not establish the magnitude of the bias. We use principal stratification combined with a trimmed means and least trimmed squares type approach to establish lower and upper bounds on this bias for general outcomes. We also establish minimal assumptions for these bounds. We show that without covariates and with binary outcomes, this approach produces the same estimator as Knox et al. (2020). We illustrate these methods with a re-analysis of the data in Anzia and Berry (2011) on the delivery of federal spending by male and female members of Congress.