Statisticians typically distinguish among design- and model-based inferences. The former derive from the design itself and are addressed under both Estimating Means and Standard Errors from LTRMP Survey Data and Estimating Trends in LTRMP Survey Data. By contrast, “models” are typically viewed as presuming an infinite or essentially infinite set of outcomes. An example is any statistical model that presumes observations are normally distributed.

The use of models to represent LTRMP data typically represents a scientific effort and, hence, falls under the LTRMP’s second mandate (i.e., that of understanding patterns in the monitoring data). Analytical efforts associated with such scientific efforts are the responsibility of the given effort and are beyond the scope of this web site. We do, however, address the use of means from LTRMP data sets.

Modeling Using Means

Modeling using means of LTRMP data should be approached with care. This is primarily because such means possess not only sampling but also parameter variance. The latter variance component arises because the mean of a sampled variable will actually vary by sampling event (i.e., not just as a result of sampling variance). Further considerations include: (1) the sampling variance of a given mean is a function of the sample size and sample sizes in the LTRMP have not been constant over sampling events; (2) for means from stratified random samples, the sampling variance is a function of sampling probabilities and strata-specific variances: the former may often be treated as having been essentially constant over the Program’s duration while the latter should not; (3) means from LTRMP stratified random samples should not a priori be presumed normally distributed (Thompson 2002); (4) the sampling variances of means of categorical and count data are themselves functions of the means (i.e., the sampling variance varies not only as a function of sample size but also of the mean); (5) for nonnormal data, parameter variance is typically presumed to vary linearly on a distributional scale other than that on which the data were sampled; and (6) means from the biotic components should, in the absence of evidence to the contrary, be presumed temporally correlated. Further discussion of modeling using means is provided by Snijders and Bosker (1999).

References

Snijders, T. A. B., and R. J. Bosker. 1999. Multilevel analysis. Sage, London.

Thompson, S. K. 2002. Sampling. Second edition. Wiley & Sons, New York.

Contact: Questions or comments may be directed to Brian Gray, LTRMP statistician, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin, at brgray@usgs.gov.