While the statistical models being described in this chapter are cost functions, not production functions, they can be derived directly from production functions and embody the same information. Continuing uncertainty about the underlying common relationships therefore raises significant doubts about the extent to which statistical models yield reliable information about the costs of an adequate education for the typical student.

Statistical methods for determining adequate educational costs appear to have a greater level of precision than the other methods discussed in this section, so it is important to keep in mind the assumptions and judgments behind them. Given restrictions on current ability to quantify desirable outcomes and the weaknesses in the production theory on which cost models are constructed, the apparent precision of statistical models may be misleading. While these methods may, especially as they are improved, provide important comparisons with methods of determining costs that are less elegant, they are not yet ripe for use as the primary means for policy makers and the public to discern or understand these costs. (They may at present be more useful in determining cost adjustments, once average costs have been identified—discussed in the next section.)

Inference from Outcomes by Empirical Observation

Another black-box approach involves establishing a level of acceptable pupil performance on an agreed-upon set of outcome measures, identifying school districts or schools that achieve the desired goals, and determining what these "successful" districts or schools spend. This level of resources is then deemed to be adequate. "The underlying assumption is that any district should be able to accomplish what some districts do accomplish, provided they have a similar amount of revenue and that amount is modified for individual districts to take into consideration cost pressures they face that are beyond their control" (Augenblick, 1997:4).

The empirical approach is described in detail in a 1995 investigation undertaken by Augenblick, Alexander, and Guthrie for the State of Ohio, and then revised in a report by Augenblick in 1997 (Augenblick et al., 1995; Augenblick, 1997). It initially involved constructing a representative pool of Ohio school districts, comprised of all Ohio districts save those that were characterized by high and low extremes of property wealth and per-pupil spending. Once such outliers had been removed, remaining districts were ranked by a composite of student performance measures in reading, mathematics, writing, and science. Districts whose average student performance was at the 70th percentile or higher on most measures were defined as providing a minimally adequate education.

Augenblick et al. next examined instructional arrangements of the districts that met the performance criteria. These districts' mixes of instructionally related components such as ratio of professionals to pupils, class sizes, school sizes, and course offerings were distilled and taken to be instrumentally exemplary for

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