A Comparison of Variance of Stream Network Resources 
Sarah J. Williams, Master's Candidate
Department of Statistics, Colorado State University
Wednesday, October 25, 2006
3:10 p.m.4:00 p.m.
203 Engineering
ABSTRACT
Many studies of environmental resources are designed to make statements about the status of the resource. A second objective often relates to detecting change in the resource. Changes may be practically undetectable at rates as low as 1 to 2percent over a 1015 year period. One way of collecting data to ensure detection of change is through a probability sampling design. In any sampling there will be variance and there already exists a variety of methods to choose from to compute the estimated variance of the status of a resource. When there exists directional trend of a response variable there will also be an underlying linear trend, so we consider the use of a linear model. For an environmental indicator the linear model could be as simple as an overall mean plus slope by time with random factors of site and visit year. Such a linear model can be interpreted in terms of components of variance of a mixed linear model. By Contrast, Stevens and Olsen (2003) proposed a local area neighborhood method for estimating variance. This designbased estimate of variance lacks consideration of time. Instead, with a linear model we can examine what aspects of the study design contribute to the variance of an environmental indicator. We relate these two methods of estimating variance using an extensive set of data. The Oregon Coastal Range coho salmon habitat data, consisting of 1535 field visits to 1055 distinct sites over a period of eight years, has 35 response variables over which to compare the two methods of estimating variance. Its analysis shows that the local estimate decreases as the site variance increases. Conversely the local estimate increases as the residual variance increases. The local neighborhood estimate also can be described as a linear combination of these components of variance; the local neighborhood estimate increases as either of the components of variance increases. We conclude that, although related, these two methods of estimating variance should be used for different purposes: the local estimate for status and the components of variance for evaluating trend detection.
