Upper Mississippi River Restoration Program Long Term Resource Monitoring

Estimating means and temporal trends using LTRM data: details with examples

This and subsequent pages address estimation of means and temporal trends from LTRM data.  Estimating these statistics from LTRM data will often require adjustments for design factors, including for nonproportional sampling and possibly for stratification. For estimating temporal trends and means of data collected from multiple years, users will also typically need to adjust for clustering of data within years. Estimating means, trends or other statistics without making these adjustments may lead to erroneous conclusions.

While the focus of the subsequent pages is methodological, we include software code to illustrate methods. We supply code in SAS because SAS is commonly used by US federal government and LTRM partner field station personnel. Code in SAS-callable SUDAAN is supplied where estimation cannot be performed by SAS. Further information about SAS and SUDAAN may be obtained at http://support.sas.com/documentation/onlinedoc/91pdf/index.html and www.sudaan.rti.com. The methods recommended may be employed using a number of software packages; use of proprietary software does not imply endorsement by the U.S. government.

Design corrections address the following issues:

• for multi-strata estimates, not addressing variation in sampling probabilities will bias results towards strata that were sampled more intensively;
• for multi-strata estimates, not adjusting for stratification may yield overestimates of sampling variances;
• estimating means from only a portion of a stratum may overstate the precision of mean estimates (because the number of samples in the ‘portion’ of the stratum is a random variable—unknown prior to the sample being taken);
• using data from multiple years without acknowledging that such data are clustered within years will typically overstate the precision of estimated means and trends

More information about these issues may be found in standard sampling texts, including in Lohr (1999) and Thompson (2002).  Discussion of additional design considerations may be found in the background webpages.

Subsequent pages are organized as follows. First, we provide sample datasets, and suggestions regarding the calculation of sampling weights.  We then address the estimation of population means and temporal trends. The former includes, for example, estimating mean (“average”) chlorophyll a concentration in Navigation Pool 13 in summer 2000, or in summers of all sampled years. Similar estimates might be derived for a specific stratum, or for that portion of a stratum with depth less than, say, 2 m. Multi-year, temporal trends may be calculated for Navigation Pools, individual strata or portions of strata.

We address estimating population means and temporal trends in means separately. The former includes, for example, estimating mean (“average”) chlorophyll a concentration in Navigation Pool 13 in summer 2000, or in summers of all sampled years. Similar estimates might be derived for a specific stratum, or for that portion of a stratum with depth less than, say, 2 m. Multi-year, temporal trends may be calculated for Navigation Pools, individual strata or portions of strata.

Datasets

Calculating sampling weights

Estimating population means

Estimating temporal trends
 
References

Lohr SL. 1999. Sampling: design and analysis. Brooks/Cole, Pacific Grove, California.

Thompson SK. 2002. Sampling, 2nd ed.Wiley, NewYork, New York.

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