Introduction

Typical objectives for environmental resource monitoring programs include estimating the current status of the resource, estimating change in status between two time periods, and estimating trends in status over time. For most monitoring programs, status is estimated using multiple indicators (monitoring variables) determined for each sample site that are derived from measurements of biological, chemical, and physical attributes obtained at the site. What is meant by estimating current status? First, the estimate applies to a specified portion of the region included in the monitoring program, typically the entire region. Second, a specific summary measure must be chosen. Common summary measures are estimates of the population mean, the percentage of the population that is less than a particular value (e.g. percentage of water bodies meeting a water quality standard or percentage of a dry forest region that has tree densities < x trees/ha), the population median, the percentage of the population occurring in categories, or the population standard deviation for an indicator.

An additional summary measure is an estimate of the population cumulative distribution for the indicator. The population cumulative distribution is simply the percentage of the population that is less than or equal to each possible value of an indicator. The population cumulative distribution provides complete information about the indicator distribution (Box 14.1). It has the advantage that it can be used for both categorical and continuous data. It is common in statistics to call the cumulative distribution the cumulative distribution function (CDF) and we will adopt that convention in this chapter. Measurements for indicators obtained from a probability survey can be used to estimate these summary measures of status. For complex survey designs that employ stratification or unequal probability of selection, estimation of current status for any of these summary measures must use weights that are derived from the stratification or unequal probability of selection used in the design.