Upper Mississippi River Restoration Program Long Term Resource Monitoring

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

Estimating population means - Estimating a multi-stratum mean for a single year

Statistics estimated from multiple LTRM strata need to be adjusted for variation in sampling probabilities and possibly for stratification effects. Failure to adjust for the LTMR’s varying sampling probabilities will lead to biased mean estimates while failure to adjust for stratification may lead to precision errors. We expect that the effect of not adjusting for stratification will often be slight.  Hence, software that allows adjustment for variable sampling probabilities but not for stratification may still be helpful.

SAS code for estimating a multi-stratum mean follows that supplied under Estimating stratum-specific means. Changes include the addition of strata and weight statements and that the "var" statement contains only a single variable. For example, the following code estimates annual pool-wide mean chlorophyll a concentrations in all pools sampled by the LTRM. The code differs from that provided in the previous section in that the input data contains sampling weights (WQallwt; see Calculating sampling weights for water data), while the code adds stratum and weight statements and eliminates stratum from the "by" statement. (Analogous changes may be used with all code supplied under Estimating stratum-specific means.)

ods listing close;
proc surveymeans data = WQallwt;
stratum stratumcode / list;
var chlf; * use any variable here;
weight sweight;
by fs year episode;
ods output statistics = stats;
run;
ods listing;
proc print data=stats; run;

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