Accounting for Bias and Uncertainty in Nonlinear Stand Density Indices

Abstract

Abstract Several commonly used stand density indices, such as Reineke's stand density index, Drew and Flewelling's relative density index, and Curtis's relative density index, depend in a nonlinear fashion on stand-level means of measured variables. Thus, the stand-level index value is not necessarily the mean of the plot-level index values. We show formally that this dependency introduces a bias that depends on the sample size or number of plots and on the variance-covariance structure of the measured variables. We then present formulas for estimating the bias and variance or standard error of estimated densities based on a priori knowledge of the variances and covariances or on observed sample data. We also present and compare bootstrap and jackknife methods of estimating the bias and variance associated with sample estimates. The results suggest that for some indices, the bias and variance arising from quick "grab samples" may be large enough to be of practical significance. These results have strong implications for the development and interpretation of stocking guides derived from single plots or from measurement schemes other than those employed in practical applications. For. Sci. 45(3):452-457.