Leibowitz, Scott G., and J.B. Hyman. 1999. Use of scale invariance in evaluating judgement indicators. Environmental Monitoring and Assessment 58:283-303. NHEERL-COR-2178
Indicators are used to draw conclusions about ecological endpoints when these endpoints cannot be measured directly. In many cases, inferences about an endpoint are only possible because assumptions have been made about the relationship between indicator and endpoint; we refer to such indicators as judgement indicators. The validity of inferences made using a judgement indicator can be gauged by examining the known or assumed form of the general relationship between indicator and endpoint. The rules for this kind of inference are a consequence of scale invariance, which originates from measurement theory. For simple indicators comprised of a single indicator measurement, the inferences allowed - equivalence, rank, equality of intervals, and equality of ratios - depend on whether the data are nominal, ordinal, interval, or ratio scaled. For composite indicators containing two or more simple indicators, inferences are also affected by the mathematical form of combination; e.g., whether the terms are summed or multiplied. Standardizing simple or composite indicators can allow inferences about the relative importance of observations, based on the natural range of occurrence. Scale invariance is a particularly important consideration in landscape assessments, since these often make use of judgement indicators.