Permit me the following comment on water pollution indices drawn from the literature. It does not answer your question directly, but it can generate an interesting discussion.
From the literature review, it is clear that a great variety of water quality indices have been published. These indices differ from each other in terms of their fundamental structures and in terms of the number and types of variables that have been selected for inclusion. Why have so many different indices been developed ? Is there evidence of an evolutionary process that is moving toward a single preferred index structure for the analysis of water quality data ? Scientific inquiry and development and scientific knowledge normally follow a systematic pattern in which each study builds upon the knowledge gained in the previous investigation. Usually each investigator begins by reviewing all of the work of previous investigators to determine how to structure his own study so that it will make a maximum contribution to knowledge. This process helps assure that each study will tend to advance scientific knowledge in a particular topic area. However, the many water quality indices that have been developed in teh decade 1965-1975 give little evidence of the normal evolution that one would expect to find in scientific inquiry. Rather, each index seems to emerge "full blown" from the literature. Indeed, some of the authors do not cite the work of the previous authors, nor do they seem acquainted with other efforts in this field. Thus, after reviewing the literature, one is left with the impression that the authors seldom provide a sense of what has done before. What role does their index play in the scientific literature? What problem does it solve that other indices before it have failed to solve. The possible two exceptions to the above rule are the NSFI and the Harkins' index. The NSFI was the first index to employ a systematic opinion research procedure in tis development. Follow-up sutidies by O'Connor and Landwehr have sought to answer additional questions of importance regarding characteristics of NSFI, and a number of case studies have been carried out using this index. Thus, an evolutionary process has occurred in this case. Harkins' index also has evolved further in work carried out by Schaeffer and Janardan. Except for these two cases, a proliferation of water quality indices has occurred, each differing from the next, and each showing little relationship to the one before it.