2.1.6 Survey-based Design
2.6.1.2.11 GRTS stratified or variable probability design pros & cons
Generalized Random-Tessellation Stratified (GRTS) design produces a probability sample with design-based variance estimators. It provides a spatially balanced, random sample, allows for unequal probability sampling, and can provide an over-sample of sample sites to accommodate field implementation issues. There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling.
A GRTS stratified sample is obtained by taking a GRTS sample in each stratum or sub-group of a population. When we sample a population with several strata, having the sample size in each stratum proportional to the population size in each stratum generally results in better precision for estimates for the entire population than other sample size allocation options. When results are wanted for each stratum, then sample allocation proportional to stratum size may not be possible.
Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata).
Variable probability sampling is an alternative to stratified sampling when explicit strata are not of interest and it is possible to have the probability of selecting a site be proportional to the measurement of interest. Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are:
- the cost per observation in the survey may be reduced;
- estimates of the population parameters may be wanted for each sub-population;
- increased accuracy at given cost.
Tools:
Software to implement such a design is available on the Aquatic Resource Monitoring web site or directly from R project package spsurvey.
Pros and Cons:
The following pros and cons of GRTS stratified or variable probability designs should assist you in determining if it is appropriate for your monitoring needs.
GRTS Stratified Samples
Site selection
Pros:
- Provide spatially balanced sample
- Can ensure monitoring design includes important sub-populations
-
Provide representative sample of the target population within each stratum
- Do incorporate some characteristics of, or information about, target population by using strata
-
Can reduce cost to obtain same sampling error compared to non-stratified sample
-
Allow replacement of sites if sites are dropped (for valid
reasons)
Cons:
- Requires additional information about the target population to define the strata
- May not know if homogeneous subgroups exist to define strata or if the homogeneous subgroups are the same for all measurements
- Can increase field operation costs due to inaccessibility of sites
- Sample selection procedures are not as readily available as for simple random sample
- Are relatively unknown nor yet widely used and it can be difficult to understand the GRTS site selection procedure
- Errors in the sampling frame may result in the sampling frame excluding some sites that are in the target population or including some sites that are not in the target population
- Sampling frame based on different GIS scales (e.g., 1:100000 and 1:24000) may result in different estimates for the target population
Statistical Inference
Pros:
- Procedures for estimating characteristics of target population are available and result in unbiased estimates and associated unbiased estimates of variance
- Variance estimates are unbiased and may result in smaller variance estimates (compared to simple random sample) when a local neighborhood variance estimator is used
- Precision and power depend on sample size and variability of the metric
- May reduce sampling variance when strata are constructed for that purpose
Cons:
- May increase sampling error compared to non-stratified sample if stratification does not result in homogeneous subgroups
- Can be expensive to achieve desired sampling error
- When simple random sample variance estimators (i.e., Horwitz-Thompson) are used instead of local neighborhood variance and the sampled variable exhibits a spatial pattern, variance estimates are biased high
GRTS Variable Probability Sampling
Site selection
Pros:
- Do incorporate some characteristics of, or information known about, population by using variable probability of selection based on those characteristics
- Provide spatially-balanced representative sample of the target population subject to constraint of variable probability of selection
- Can ensure monitoring design includes important sub-populations
- Can reduce cost to obtain same sampling error compared to non-stratified sample
- Allow replacement of sites if sites are dropped (for valid reasons)
Cons:
- Requires additional information about population to define auxiliary variable on all elements of the population
- Can be difficult to select auxiliary variable that is positively correlated to all response variables
- Errors in the sampling frame may result in the sampling frame excluding some sites that are in the target population or including some sites that are not in the target population
- Sampling frame based on different GIS scales (e.g., 1:100000 and 1:24000) may result in different estimates for the target population
Statistical Inference
Pros:
- Procedures for estimating characteristics of target population are available and result in unbiased estimates and associated unbiased estimates of variance
- Variance estimates are unbiased and may result in smaller variance estimates (compared to simple random sample) when a local neighborhood variance estimator is used
- Precision/power depends on sample size and metric variability
- May reduce variance estimates when auxiliary variable is positively correlated with response variable
Cons:
- May increase sampling error compared to equal probability sample if auxiliary variable is not positively correlated to response variables
- Local neighborhood variance estimator is difficult to understand and compute without using spsurvey software
- When simple random sample variance estimators (i.e., Horwitz-Thompson) are used instead of local neighborhood variance and the sampled variable exhibits a spatial pattern, variance estimates are biased high
- Can be expensive to achieve desired sampling error
