The U.S. Department of Agriculture Forest Service has conducted many studies to determine what proportion of the timber harvested in the South is actually utilized. This paper describes the statistical methods used to determine required sample sizes for estimating utilization ratios for a required level of precision. The data used are those for 515 hardwood and 1,557 softwood trees harvested in east Texas and classified into 5 product types. Two-stage sampling was used to collect the utilization data. The primary units were the logging operation locations and the secondary units were the trees within locations. The ratio of means estimator was used to calculate each of three utilization ratios. How ever, for simplicity, the mean of ratios approach was used to develop the statistical methodology for estimating sample sizes for a specified level of precision, defined as half the width of the 95-percent confidence interval. The infinite population model was used and variance components for the two-stage nested analysis of variance were obtained using PROC MIXED. The three utilization ratios were computed for all product classes for hardwoods and softwoods, as were the standard errors and 95-percent confidence intervals. The variance components were then obtained and used to develop tables that yield sample size scenarios based on specified levels of precision.
Mean of ratios
ratio of means
Zarnoch, Stanley J.; Bentley, James W.; Johnson, Tony G. 2004. Determining sample size for tree utilization surveys. Res. Pap. SRS-0 34. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. 11 p.