Abstract ABSTRACT: This paper reports on the technique of Probabilistically Answered Examinations (PAE) as applied to objective tests. The purpose is to establish the relevance of PAE in measuring student performance. A substantive, rather than normative, viewpoint is superimposed, that is, probability assessments are evaluated exclusively within the subject-matter domain in which they are made. After reviewing concepts underlying PAE, it is demonstrated that the methodology is likely to provide more complete information about test scores and the traits measured by the test than that provided by conventional procedures. Examples of performance measures and how they may be applied to PAE are provided.

The recent article in this Review by Anthony Fisher, John Krutilla, and Charles Cicchetti (F-K-C) is an important step towards the development of a general method of analysis of the economics of environmental preservation. They are also commended for their attempt to adapt their model to the investigation of an important environmental policy question concerning the advisability of hydroelectric development in the Hells Canyon region of the Snake River. We feel, however, there is room for improvement in their theoretical models and perhaps in the presentation of empirical results. Sections I and II of their article consist of the development of an allocation model of some degree of sophistication from which some general conclusions are drawn which are not necessarily true. For instance, in Section I, it is stated that .... the marginal opportunity costs of development, the benefits from preservation, are increasing as development increases (p. 607). This certainly follows from the assumptions upon which their model is based; i.e., from their assumptions it follows BPD>0. It is not completely relevant, however, for as their later analysis indicates, the important question is what happens to total benefits rather than marginal. With respect to the portion of Hells Canyon in question, the present level of developed area is very small. Since almost all of the area is in a preserved state, i.e., P_L their assumptions BD> 0 and BDD <0 imply the marginal benefits of development are relatively large. Thus in seeking an optimal allocation of the land between preservation and development, we would seek to increase marginal benefits from preservation and decrease marginal benefits from development. Thus we would seek to increase the developed area D. We might also point out an undeveloped Hells Canyon may be so unique a natural resource that, as F-K-C suggest, there are no adequate substitutes of like quality and as such their procedures are justified. In general, however, we should note theirs is basically a suboptimization procedure in it isolates its analysis upon a single area without regard to other areas. Thus, if such a method were to be used in a piecemeal area by area decision process, the end result may be far from optimnal for the total environment. In Section II, F-K-C use the concept of total benefits and conclude . . as benefits from preservation increase relative to benefits from development, the optimal short-run level of development D*(t) decreases (p. 611). The justification for this statement is provided in their footnote 17. There they correctly derive the relation