Research Summary

Comparison of Ranked Set Sampling to Alternative Sample Designs and Investigation of its Usefulness in Environmental Monitoring
Loveday L. Conquest
Ranked set sampling (RSS) is a two-phase sampling procedure involving initial ranking of each of m samples of size m (often via a relatively cheap or fast method of measurement), followed by observing (often using a more accurate and more expensive method of measurement) the first order statistic from the first sample, the second order statistic from the second sample, and so on, until the mth order statistic from the mth sample yields a secondary sample of size m from the initial m^2 data points. Two examples are as follows:

1. Assessing sediment contamination can involve measuring the amount of a toxic substance in samples of sediment. Suppose there is a cheap way to get a rough estimate of the amount of contaminant present in a batch of sediment, along with a more expensive way which yields a more accurate estimate. We cannot afford to do too many of these expensive measurements, so it is important to obtain as representative a sample of the population as possible.

2. Much of stream and wetland monitoring involves measuring the amount of area present that can be attributed to different habitat types, such as pools and riffles in a stream, or types of different vegetative cover in a wetland. Currently, measurement of habitat unit or vegetative cover area is done largely by visual examination (which is quick and has many problems) and occasionally by more precise measurement (more labor intensive and thus more costly).

In both of the above examples, RSS could potentially yield more representative samples. By making use of the cheaper measurement method, the initial ranking (of m samples of size m) could be accomplished at a lower cost per unit, thus saving the more expensive and more accurate measurement method for the second stage of sampling, when only m units are measured. It is also possible to run additional cycles of m ranked sets to yield m more measured units per cycle.

Previous research on RSS has evaluated its utility compared to simple random sampling (SRS) designs and has demonstrated its superiority over SRS. We will examine alternative sample designs that are used in other fields to see under what conditions RSS is an appropriate procedure. The dual phase nature of ranked set sampling raises many interesting statistical questions. For example, more extensive stratification in phase 1 might help, particularly if first-phase sample points were ranked relative to the assumed distribution of the entire data set (using chosen "cup points" based on prior knowledge). Another issue concerns the effect of ranking errors. Assessing effects of errors in ranking could increase the usefulness of RSS for environmental managers. We also plan to apply RSS to actual sets of data concerning habitat measurements for streams and estuarine areas in Washington and Oregon. For more information go to A Comparison of Methods for Estimating Stream Habitat Area.