funds in an efficient manner likely to produce the desired adequate outcomes. Here, again, is the tension between the design of a "system" and the possible different characteristics of individual students.

Inference from Outcomes by Statistical Analysis

Statistical analysis is one way to relate observed student outcomes to resources, in hopes that adequate resource costs can then be inferred. This method, in effect, conflates into a single step the challenges of inferring adequate resource levels and pricing those levels. Rather than identifying specific instructional components deemed necessary to achieve adequate outcomes, and then pricing these components, this statistical method infers total value of the components by associating total school district spending with adequate outcomes.

In this "black box," or raw correlational approach, the policy system, after determining an acceptable level of pupil performance or proficiency, then determines a delivery system dollar amount associated with it. This strategy bypasses any effort to construct or deduce a desired instructional delivery system. Such a bypass also obviates the need to determine costs of instructional components. Under this correlational approach, the "cost" of attaining "adequacy'' is whatever agencies that achieve adequate outcomes happen to spend, after accounting for any identifiable inefficiencies in these agencies' operations.

While the statistical methods are complex, the principle behind them is relatively simple. With a sufficiently large database, each factor contributing to school costs can be examined and its unique relationship to another factor determined, distinct from the influence of other factors. For example, we may want to know how much more it "costs" to hire a teacher in an urban community than in a nonurban one. If we have sufficient data on teacher salaries and community characteristics, we can separate the common relationship between salary and urbanicity in all communities from the factors that may vary from community to community—like teachers' experience or training, community climate, community housing costs, etc. The result is the statistical generation of an abstract urban community where teacher salaries are uninfluenced by variations in these other costs, or by the choices districts may make in the type of teacher they hire.

If adopted as a basis for policy, this correlational strategy would derive a unit cost (per classroom or per pupil) amount found to be associated with adequate levels of pupil academic achievement and recommend allocation of such resource levels to school districts or other operational agencies. This approach could include statistical controls for social and economic characteristics of students. How available revenues were translated into an instructional delivery system would be of no policy consequence in such a "black box" approach. Presumably, districts or schools would be free to undertake whatever operational translation they desired, knowing that assigned per-pupil revenue amounts had been found sufficient to elevate their mix of pupils to the specified level of performance.

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