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 mean from a portion of one or more strata

Estimating a mean from an area that includes a portion of a stratum adds an additional level of variability. For example, a user might want to estimate mean dissolved oxygen (DO) levels when water temperature exceeded some threshold, say 20° C. Since LTRM sampling designs do not incorporate temperature at the time of sampling, the sample size for this analysis is a random variable. This extra source of variability is addressed using subpopulation (domain) analysis.

Subpopulation analysis in SAS requires defining a variable that indicates the subpopulation of interest. For the example below, the new variable is called ‘tempgt20C,’ and has value 1 if the sample was associated with temperatures above 20° C and 0 otherwise. 

The new variable is then used in a subpopulation statement (SAS uses the term ‘domain’ statement). Any of the sets of code listed under Estimating stratum-specific means and Estimating multi-strata means may be modified for subpopulation analysis by adding a subpopulation statement.  For example, the stratum-specific chlorophyll a code used earlier may be modified as below to supply the DO estimates for temperature categories greater than 20° C and less than or equal to 20° C.

data WQalltempind;
set WQall;
if temp gt 20 then tempgt20 = 1; else tempgt20 = 0;
if temp = . then tempgt20 = .;

ods listing close;
proc surveymeans data=WQalltempind total=capN_h_water;
var DO;
domain tempgt20C;
by fs year episode strat;
ods output statistics = stats domain=domain;
run;
ods listing;
proc print data=domain; run;

In the above code, capN_h_water contains population totals that are generated when generating sample weights (see Calculating sampling weights for water data) while the domain or subpopulation statement yields separate estimates for each temperature category.

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