A study explored which nonexperimental comparison group methods provide the most accurate estimates of the impacts of mandatory welfare-to-work programs and whether the best methods work well enough to substitute for random assignment experiments. Findings were compared for nonexperimental comparison groups and statistical adjustment procedures with those for experimental control groups from a large-sample, six-state random assignment experiment--the National Evaluation of Welfare-to-Work Strategies. The methods were assessed in terms of their ability to estimate program impacts on annual earnings during short-run and medium-run follow-up periods. Findings with respect to the first issue suggested in-state comparison groups perform somewhat better than out-of-state or multi-state, especially for medium- run impact estimates; a simple difference of means or ordinary least squares regression can perform as well or better than more complex methods when used with a local comparison group; impact estimates for out-of-state or multi-state comparison groups are not improved substantially by more complex estimation procedures but are improved somewhat when propensity score methods are used to eliminate comparison groups that are not balanced on their baseline characteristics. Findings with respect to the second issue indicated the best methods did not work well enough to replace random assignment. Statistical analyses are appended. (Contains 51 references.) (YLB)