The question "How much is enough?" is ever-present when trying to determine how many plots need to be collect in order to answer managerial questions.
In a continuing effort to provide technical assistance to Forest Service personnel designing inventory and monitoring projects or
attempting to analyze existing data sets, the Inventory & Monitoring Institute has developed a web-based software application named
Plot-GEM to help address sampling issues. Plot-GEM (Plot Graphics of Estimation of the Mean) is located on the
Inventory & Monitoring Institute Internet website at www.fs.fed.us/institute/Plot-GEM.
Plot-GEM can be used to answer many sampling questions, a few examples are:
- Do we have enough plots to adequately address our issues?
- What sample size is necessary to achieve our accuracy goals?
- How many more plots do we need?
- How accurate are our estimates based on the plots we have?
- How accurate is the current estimate of the mean?
- What estimation accuracy is possible?
- What estimation accuracy is feasible?
- We're collecting a lot of data on many different attributes/variables,
which attributes meet our accuracy objectives?
- For which attributes can the mean be accurately estimated?
- We're thinking about stratifying our inventory, but which strata should we use?
- For which strata can the mean of an attribute be accurately estimated?
- Which strata classification algorithm "fits best?"
Plot-GEM can help answer these questions by providing visual displays (graphs) based on calculation of the percent error and the
confidence interval for the estimate of the means of forest attributes. These calculations can be performed over a range of sample
sizes (also referred to as sampling intensities). Plot-GEM creates graphs so that the change in estimation accuracy, as sample size
changes, can be visualized. Plot-GEM also enables the user to explore their options and alternative accuracy objectives by
providing graphs that depict the confidence intervals associated with different sample sizes. The user can quickly explore "what if"
scenarios for different numbers of plot, different suites of variables, and different ways of stratifying their sample.
Plot-GEM uses a bootstrap algorithm to calculate the percent error and confidence interval for the estimates of the means.
The bootstrap algorithm is well suited to the plot data situation because it makes no assumptions about the complicated correlation
structure that exists among primary sampling units and subplots.
For additional Plot-GEM information and support contact Andy Leach
(aleach@fs.fed.us) of the
Inventory & Monitoring Institute in Fort Collins, Colorado.
Refer to the following sources for further reading on the advantages of the bootstrap:
- Efron, B., (1981). Nonparametric Estimates of Standard Error: The Jackknife, the Bootstrap and Other Methods.
Biometrika, Vol. 68, No. 3., p. 589-599.
- Efron, B., Tibshirani, R. J., (1993). An Introduction to the Bootstrap (Monographs on Statistics and Applied Probability, No
57). (Chapman & Hall/CRC, Florida).
- Hansen, C. M., Evans, M. A., Shultz, T. D., (1999). Application
of the bootstrap procedure provides an alternative to standard statistical procedures in the estimation of the vitamin B-6
requirement. Journal of Nutrition, Vol. 129, No. 10, p. 1915-1919.
- Yafune, A., Ishiguro, M., (1999). Bootstrap
approach for constructing confidence intervals for population pharmacokinetic
parameters. I: A use of bootstrap standard error. Statistics in Medicine, Vol. 18, No. 5, p. 581-599.
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