FIGURE 10.1 Plot of hypothetical test score data.

points and providing schools with a ready diagnosis of why their measured performance is high or low. To implement such a system would require a reasonably comprehensive set of school process and input indicators.16

Perhaps the best way to illustrate the logic and mechanics of the value-added approach is with an example. Let us consider a hypothetical dataset containing information on student achievement for students from four different schools. The data are based on a highly simplified model of growth in student achievement that contains only a single control variable—prior achievement.17 As a result, the data can conveniently be displayed on a two-dimensional graph. For simplicity, the discussion here is limited to the total performance indicator; analysis for the intrinsic performance indicator would be similar.

To interpret properly the indicators discussed below, it is important to know something about the distribution of the pre- and posttests that underlie them. Both tests were scored in a manner similar to the Scholastic Assessment Test; scores were centered around a national mean of 500, with a range of approximately 200 to 800. Figure 10.1 plots pre- and posttest scores for 25 students from

16  

See Porter (1990) for a discussion of a system of process indicators.

17  

The data were generated by using a model of achievement growth in which the coefficient on prior achievement was equal to θ = 0.8.



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