Plot-GEM

Your personal assistant for exploration of sampling alternatives

The question "How much is enough?" is ever-present when trying to determine how many plots need to be collected 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, a web-based software application named Plot-GEM (Plot Graphics of Estimation of the Mean) to help address sampling issues was developed. Plot-GEM can be used to answer many sampling questions, such as:

• 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 for 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 thevconfidence interval for the estimate of the means of forest attributes. These calculations can be performed over a range of samplevsizes (also referred to as sampling intensities). Plot-GEM creates graphs so that the change in estimation accuracy, as sample sizevchanges, can be visualized. Plot-GEM also enables the user to explore their options and alternative accuracy objectives byvproviding 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.

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 (PDF). Journal of Nutrition, Vol. 129, No. 10, p. 1915-1919.
• Yafune, A., Ishiguro, M., (1999). Bootstrap approach for constructing confidence intervals for population pharmacokinetic aparameters. I: A use of bootstrap standard error. Statistics in Medicine, Vol. 18, No. 5, p. 581-599.

Staff Contact

Rick Ullrich
Assistant Director
U.S. Forest Service Resource Information Group (RIG)
202-205-1120 or rullrich@fs.fed.us