The nugget effect

The nugget effect causes sub-sampling errors in PGE determinations. Previously, large sub-samples (30 g) of all samples were analyzed to decrease sub-sampling errors. This is not cost-effective. Our new approach is firstly, a 10 g sub-sample is used for the routine analysis of all samples secondly, samples with anomalous values are selected for duplicate or triplicate determinations, and the average value of these determinations is considered trustworthy. The selection of these samples is mainly based on the Pt/Pd ratio, statistics of RD% of coded duplicate analyses and total batch data distributions. 

Estimation of the nugget effect can provide valuable information about the process. For example, if it is substantially larger than an estimate of the material variation obtained independently, then we know that extraneous variation and/or bias is being introduced through incorrect sample collection, handling, or imacceptably large analytical variation. Extrapolation of the variogram to... 

Figure 4.15 Extrapolation of the variogram to estimate the nugget effect.

Suppose we can reduce the analytical variation by more than half by using a more precise method. This reduces the nugget effect substantially, and we perform another variographic experiment. By overlaying all the information, the variogram looks like that in Figure 4.20. 

Suppose a plant operates on 12 h work shifts and that samples are normally taken at the beginning of each shift. For our variographic experiment, we collect a sample every hour for several days and estimate the nugget effect with a sample every minute. Combining this information results in the variogram given in Figure 4.21. 

Fractions are used to allow comparison of the nugget-effect value to the estimated material variation. 

The rate of discovery of pristine nonmare rocks has been limited by the scarcity of large lunar rock samples. Identification of a coarse cumulate or otherwise plutonic texture is difficult without a thin section at least several mm across, and determination of trace siderophile elements becomes increasingly difficult (and prone to the nugget effect) if available sample mass falls below —0.1 g. Lunar geochemists must resist... 

Fig. 12.13 Schematic representation of a variogram. The mean distances of point-pairs (h) and the corresponding variances of their measured values (7(h)) are plotted. The relation between individual values diminishes with increasing distance, i.e. the 7(h)-values increase. However, the structural dependence between the point-pairs is only valid up to a specific distance (range). From this point the variances tend to scatter around a certain value (sill), which represents the total variance of all values. The nugget effect, or the apparent mismatch of the variogram to go through the origin, indicates for a regionalized variable that it is highly variable over distances less than the sampling/cluster interval. A spherical model was adapted to the idealized data.

Figure 7.8 Uncertainty in Os concentration, determined via ICP-IDMS. The contribution of the spike calibration dominates the uncertainties at a higher concentration level. Blank contributions dominate the uncertainties at concentration levels approaching the determination limit. The standard deviations of the concentrations of replicate digestions were in most cases higher than the standard uncertainty estimated for the analysis of a single sample. It can therefore be assumed that in cases where the standard deviations of replicate measurements are very large, the nugget effect is dominant.

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