Campbell’s and Rubin’s perspectives (detailed in Chapter 8) are brought into the discussion as the basis for suggestions for enhancements that may lead to stronger causal inferences.

Regression Discontinuity (RD) Design

Often society prescribes that treatments be given to those with the greatest need, risk, or merit. A quantitative measure is assessed at baseline (or a composite measure is created from a set of baseline measures), and participants scoring above (or below) a threshold score are given the treatment. To cite three examples from the educational arena, access to free lunches is often given to children whose parents have an income below a specified threshold (e.g., the poverty line), whereas children above the poverty line do not receive free lunches. The recognition of dean’s list is awarded only to students who achieve a specified grade point average (e.g., 3.5 or greater). And children who reach their sixth birthday by December 31 are enrolled in first grade the following August, whereas younger children are not. Given assessment of the outcome following the intervention, comparison of the outcomes at the threshold for the intervention and in control groups permits strong causal inferences to be drawn.

To understand the RD design, consider the example of evaluating the effectiveness of school lunch programs on health, which is illustrated in Figure E-1. In the figure, all children with a family income of less than $20,000 qualify for the program, whereas children whose families exceed this threshold do not. The outcome measure (here a measure of health problems, such as number of school absences or school nurse visits) is collected for each child. In modeling the relationship between the known quantitative assignment variable (family income) and the outcome, the treatment effect will be represented by the difference in the levels of the regression lines at the cutpoint. In the basic RD design, treatment assignment is determined entirely by the assignment variable. Proper modeling of the relationship between the assignment variable and the outcome permits a strong inference of a treatment effect if there is a discontinuity at the cutpoint.

Ludwig and Miller (2007) used this design to study some of the educational and health effects of the implementation of the original Head Start program in 1965. When the program was launched, counties were invited to submit applications for Head Start funding. In a special program, the 300 poorest counties in the United States (poverty rates exceeding a threshold of 59.2 percent) received technical assistance in writing the Head Start grant proposal. Because of the technical assistance intervention, a very high proportion (80 percent) of the poorest counties received funding, approximately twice the rate of slightly better-off counties (49.2 percent to 59.2 percent poverty rates) that did not receive this assistance. The original Head Start program included not only its well-known educational program, but also basic health services to children (e.g., nutrition supplements and education, immunization, screening). In addition to positive effects on educational achievement, Ludwig and Miller

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