## Quantifying Uncertainty in Causal Analysis

The uncertainty associated with the data may be partially estimated by conventional statistical analysis (see the Data Quality and Interpreting Statistics sections). However, overall uncertainty also includes uncertainty about the applicability of the data. If data must be extrapolated between species or from one life stage to another, if old data are used to estimate current conditions, or if, for some other reason, data are not directly applicable, the associated uncertainty should be estimated. The uncertainty in statistical models, such as regressions of biological properties against levels of potential causes, may be estimated using goodness-of-fit statistics or confidence limits. The uncertainty due to the parameters in mathematical models, such as models of dissolved oxygen depression due to nutrient inputs, may be estimated either analytically or by Monte Carlo simulation (U.S. EPA 1996, 1999). If a causal inference is logically clear and is based predominantly on the results of a statistical or mathematical model, the uncertainties concerning the results of the model may serve to estimate the uncertainties concerning the inference.

In many cases, unquantified uncertainties will dominate. These sources of uncertainty may include lack of data on the presence or levels of particular stressors, incomplete biological data, uncertainty about when the impairment began, and many more. In addition, most causal inferences are based on the strength of evidence, so that no single source of uncertainty characterizes the uncertainty concerning the conclusion. Therefore, the uncertainty concerning most causal analyses must be characterized qualitatively. This qualitative judgment of overall uncertainty should be accompanied by a list of major sources of uncertainty and their possible influence on the results.