based on the combination of two dimensions: assignment rule and primary dimension for assignment of units.
With respect to assignment rule, units can be assigned (1) according to a randomized allocation scheme, (2) on the basis of a quantitative assignment rule, or (3) according to an unknown assignment rule. Randomization schemes in which each unit has an equal probability of being in a given treatment condition are familiar. A quantitative assignment rule means that there is a fixed rule for assigning units to the intervention on the basis of a quantitative measure, typically of need, merit, or risk. For example, organ transplants are allocated on the basis of a weighted combination of patient waiting time and the quality of the match of the available organ to the patient. Finally, unknown assignment rules commonly apply when units self-select into treatments or researchers give different treatments to preexisting groups (e.g., two communities, two school systems). Unknown assignment rules are presumed to be nonrandom.
With respect to units, participants (people or small clusters of people), times, settings, or outcome measures may serve as the units of analysis. Research in public health and medicine commonly assigns treatments to individual (or small groups of) participants. But other units of assignment are possible and should be entertained in some research contexts. Time can be the unit of assignment, as, for example, in some drug research in which short-acting drugs are introduced and withdrawn, or behavior modification interventions are introduced and withdrawn to study their effects on the behavior of single patients. Settings can be the unit of assignment, as when different community health settings are given different treatments, or different intersections are given different treatments (e.g., photo radar monitoring of speeding in a traffic safety study). Finally, even outcome measures can be assigned to different conditions. In a study of the effectiveness of the Sesame Street program, for example, different sets of commonly used letters (e.g., [a, o, p, s] versus [e, i, r, t]) could be selected for inclusion in the program. The knowledge of the specific letters chosen for inclusion in the program could be compared with the knowledge of the control letters to assess the program’s effectiveness. Once again, each of these types of units could potentially be assigned to treatment conditions using any of the three assignment rules.
Reichardt provides a useful heuristic framework for expanding thinking about strong alternative research designs. When individuals are not the unit of analysis, however, complications may arise in the statistical analysis. These complications are addressable.
In this section, some commonly utilized quasi-experimental designs from Reichardt’s framework are described. First, two designs involving nonrandom, quantitative assignment rules—the regression discontinuity design and the interrupted time series design—are discussed. Next, the observational study (also known as the nonequivalent control group design or nonequivalent recipients design), in which the basis for assignment is unknown, is considered. Finally, the pre-experimental pre–post design, commonly utilized by decision makers, is discussed. For each design,