The Contribution of Earlywood and Latewood Specific Gravities to Overall Wood Specific Gravity
Keywords:Variance components, density, regression analyses, multiplicative models, coniferous species, Pseudotsuga menziesii
A detailed analysis of the mathematical identity relating overall wood specific gravity to earlywood and latewood specific gravities and proportions is presented. The exact formula for expressing the variance of the overall specific gravity in terms of the means, variances, and covariances of these variables is developed. A small but typical data set is used to illustrate the formula. In this example the major contributor (34%) to the overall variance is the variance of the proportion of latewood weighted by the square of the difference between the mean latewood and earlywood specific gravities. The covariance between the earlywood specific gravity and the proportion of latewood, again appropriately weighted, also makes an important contribution (18%) to the overall variance. These results are supported by analysis of an independent data set.
As a byproduct of the theory, it is possible to predict the behavior of linear regressions of overall specific gravity on any combination of the above components.
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