Erle C. Ellis, Rong Gang Li, Lin Zhang Yang and Xu Cheng. 2000. Longterm Change in VillageScale Ecosystems in China Using Landscape and Statistical Methods. Ecological Applications 10: 10571073.
Ecological Archives A010006
Data
Quality Pedigree Calculator.
Notes
on the Pedigree Calculation Algorithm
This document describes the algorithm for calculating data quality pedigrees using the Microsoft Excel^{®} Visual Basic program referenced in Ellis et al. (2000) and supplied in the Microsoft Excel^{®} 97 workbook file: pedigree.xls. Application of pedigree.xls is described in the file: pedigree.doc. Parameters used in pedigree calculations are described in Table 1, and the algorithm is outlined in Table 2 and FIG 1, and in the text, below.
When variables are added, the pedigree for their sum is the mean weighted average of their individual pedigrees (MWA, Table 1). When variables are multiplied or divided, a “weaklink” principle is applied, and the minimum pedigree of all variables in the calculation is used as the pedigree of the result. Pedigrees for subtraction and weighted averaging depend on whether the spread (S, Table 1) of the variables is similar to the difference between them (D, Table 1).
When the spread of variables is similar in magnitude to their difference, as tested by the inequality D/S < 5, then subtraction of the variables yields a result that is more uncertain than the original variables themselves. In this case, the pedigree for the results of subtraction should be decreased below the MWA as described in Table 2 and FIG 1. On the other hand, when multiple estimates for a variable are combined using weighted averaging, and D/S < 5, this indicates that the estimates agree, so that the pedigree for their weighted average should be increased above the MWA of the estimates. When calculating pedigree upgrades for weighted averages, we use the difference between the MWA and the maximum possible pedigree (MAP, Table 1), so that lower pedigrees are increased more than higher ones. A slight, 5% per variable, pedigree increase is granted to all weighted averages, regardless of whether D/S < 5, so that data quality always increases when multiple independent estimates are used. Absolute limits are set on pedigree increases for weighted averages, with a maximum increase of 1 for inverse variance weighting and 0.5 for subjective weighting (equal weights or not), because the former represents higher quality estimates. In all calculations, each of the three scores within each pedigree is calculated independently.
TABLE 1: Variables used by the Pedigree Calculation
Algorithm.




The difference between variables. m is the number of variables, and_{ } is the mean of the ith variable in the calculation. 


The number of variables in a calculation. Used in FIG 1. 


The average spread of variables. 


The mean weighted average pedigree. P_{i}_{ }= pedigree of the ith variable, = mean of the ith variable, and n = the total number variables in the calculation. 


Weighted average of pedigrees. P_{i}_{ }= pedigree of the ith variable, W_{i} = weight of the ith variable, and n = the total number variables in the calculation. 


The maximum possible pedigree. 

TABLE 2: Rules for calculating pedigrees I. Multiplication
& Division II.
Addition (simple,
no comparisons, averaging, etc.) III.
Subtraction
(simple). Decrease
the pedigrees when the difference between variables is similar
to their spread, as judged from D/S: IV.
Weighted Averages 
FIG 1: Flowchart of the Pedigree Calculation Algorithm.
