If both potential outcomes were observable, the causal effect could be directly calculated for each participant. But one of the potential outcomes is inevitably missing. Suppose, by contrast, that E or C could be selected by each child's parents. Then the potential outcomes would be nonrandomly missing. The outcome under E would come to be observed more often for advantaged than for disadvantaged children.
Selection bias is thus a problem of nonrandomly missing data.
Even more insidiously, suppose that some parents had previous knowI- edge about how well their child is likely to fare under the new day care program. For example, one parent might know that, without the new pro- gram, her child will be cared for by the paternal grandmother, who is known to be a master teacher of young children. Thus, this parent decides not to participate in the new day care program, knowing that the child will probably do better without it. Other parents who know their families do not include talented teachers with time to care for their child choose the new program. Such information is rarely available to researchers, yet it produces nonrandomly missing data.