This reduces the external validity problem to an exercise in graph theory, and has led some philosophers to conclude that the problem is now solved. An important variant of the external validity problem deals with selection bias, also known as sampling bias—that is, bias created when studies are conducted on non-representative samples of the intended population. For example, if a clinical trial is conducted on college students, an investigator may wish to know whether the results generalize to the entire population, where attributes such as age, education, and income differ substantially from those of a typical student. The graph-based method of Bareinboim and Pearl identifies conditions under which sample selection bias can be circumvented and, when these conditions are met, the method constructs an unbiased estimator of the average causal effect in the entire population. The main difference between generalization from improperly sampled studies and generalization across disparate populations lies in the fact that disparities among populations are usually caused by preexisting factors, such as age or ethnicity, whereas selection bias is often caused by post-treatment conditions, for example, patients dropping out of the study, or patients selected by severity of injury. When selection is governed by post-treatment factors, unconventional re-calibration methods are required to ensure bias-free estimation, and these methods are readily obtained from the problem's  graph. If age is judged to be a major factor causing treatment effect to vary from individual to individual, then age differences between the sampled students and the general population would lead to a biased estimate of the average treatment effect in that population. Such bias can be corrected though by a simple re-weighing procedure: We take the age-specific effect in the student subpopulation and compute its average using the age distribution in the general population. This would give us an unbiased estimate of the average treatment effect in the population. If, on the other hand, the relevant factor that distinguishes the study sample from the general population is in itself affected by the treatment, then a different re-weighing scheme need be invoked. Calling this factor "Z", we again average the "z"-specific effect of "X" on "Y" in the experimental sample, but now we weigh it by the "causal effect" of "X" on "Z". In other words, the new weight is the proportion of units attaining level "Z=z" had treatment "X=x" been administered to the entire population. This interventional probability, often written formula_1, can sometimes be estimated from  observational studies in the general population.