Selecting expansion factor and number of sampling positions for point and plot sampling

Variance approximations were developed to estimate the variances of total basal area per acre and total volume per acre for both point and plot samples. These variance approximations reflect the role that stand characteristics and expansion factor play in either sampling procedure. Validation of the estimated variances was done through a sampling simulation.

Most of the variance approximations were considered unbiased and good in the estimation of their respective variances; only in plot samples with expansion factors of 5 was this not true. The variance approximation was considered best at expansion factor 40; with each decreasing expansion factor value, the approximations were less accurate in estimating the variance. Across the range of expansion factor values, point sampling approximations were generally more accurate than plot sampling approximations in estimating the variance; overall, the point sample variance approximation for total basal area per acre performed the best.

Variance approximations were used with a cost analysis in order to select the optimal expansion factor and number of sampling positions. Plot samples require a higher expansion factor than point samples when the number of trees per acre is greater than the total basal area per acre for variances of either characteristic. For the same expansion factor, little difference existed between the optimal number of sampling positions required in either sampling method when variances were minimized. When cost was minimized, generally fewer plots than points are needed in stands where the average dbh is less than 13.5 inches.