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Minimum-variance sampling schemes for the scaling of logs by weight Nokoe, Sagary

Abstract

Traditionally, logs have been measured individually (scaled) to estimate their total cubic foot content of wood, inside bark. Recently, procedures have been developed for estimating firm wood volumes from ratio of volume of logs to their weight. The objectives of the study were to examine minimum-variance sampling schemes for ratio estimation, and the selection of the most appropriate sampling procedure for weight scaling. Minor objectives included the use of double-sampling and post-stratification procedures for greater efficiency. After considering expected variation, appropriate sampling procedures were devised, and then used to draw samples from generated populations and weight scale data respectively, without replacement. The sampling schemes included the "completely random", "representative (or restricted) random", "modified (or uniform) random", frequency^-dependent, and size-dependent sampling schemes. The different populations were generated according to hypothetical ratio estimates, and the exponent (p) by which the auxiliary variates were related to the variance of the corresponding variates of the population of interest. Initial results indicated that for a particular sample size, a scheme resulting in the highest sample correlation coefficient did not necessarily give the smallest variance. Among all modifications of a particular sampling scheme, that modification resulting in the highest sample correlation coefficient also gave the smallest variance of the population of interest. For populations with positive "p" values, including the weight scaling data, it was found that sampling for ratio estimation with probability proportional (or inversely proportional) to the magnitude of the auxiliary variable, and for only five frequency classes, led to the "best" minimum-variance estimate of the mean of population of interest. These schemes gave consistently large mean deviations from the mean of the population of interest. With increasing number of classes, the magnitude of the mean deviations was reduced but the property of minimum-variance was not necessarily retained. For populations with negative values of "p", the other schemes performed better than these but still had major deficiencies. On the basis of reasonably small variances and deviations, the "modified random sampling" scheme was selected as the best. Examination of the scaling data showed almost constant variances for sub-divisions based on arrival times or periods. For the modified random scheme, equal numbers of observations were taken within each group of arrival of truck loads. Its ultimate selection as the best of all the minimum-variance schemes for weight scaling, in particular, could therefore be linked with the homogeneity of the group variances. Post-stratification resulted in greater efficiency, especially for large numbers of groups. Double-sampling procedures did not lead to any improvement in the results. It was suggested that "modified (or uniform) random" sampling procedures, used jointly with post-stratification by arrival of truck loads, would be ideal for the scaling of logs by weight.

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