Sub-sampling bias

The dimensions and shape of the implement used for sub-sampling coarse samples (e.g. dried soils) have been found to introduce sub-sampling bias. Scoops with sides are preferable to flat spatulas or pallette knives because larger particles tend to roll off the heap which is formed when the sample is taken (Smith James 1981). 

By simplifying the theory developed by Gy we can derive a safety rule  

W= minimum sub-sample size (g), d= maximum particle size (cm). 

This safety rule can be used to construct a simple table broadly indicating the maximum particle size and minimum sub-sample weight limits for safe subsampling. 

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The Gy equation assumes that random samples are taken from a mixture in which all particles have an equal opportunity of being selected (i.e. the sample must be completely homogenous). In addition, it assumes that the statistical errors associated with random sampling follow a Normal distribution (i.e. it is important to eliminate sub-sampling bias caused by poor equipment or an unsuitable sub-sampling method). 

Table 11.3 Comparison of errors generated during the analysis of XRD data (Cu Kot) from three sub-samples of Sample 4 from the lUCr CPD round robin on quantitative phase analysis. The bias values are (measured - weighed) while the values denoted XRF are the phase abundances generated from elemental concentrations measured by X-ray fluorescence methods.

A final bias has to be avoided when the samples are subjected to composition analysis. A sample withdrawn from a mixture is a point sample at a carefully chosen scale of scrutiny. When this sample is analysed for quality it is unlikely that the quantity required for analysis is the same as the scale of scrutiny for the process and it is vital that any sub-sampling of the point sample is carried out in an efficient spinning riffler. That is, for analytical purposes a bulk sample has to be taken from a point sample. Alternative methods ofobtaining a bulk analysis of the point sample would be to dissolve the entire point sample in a liquid or to grind the sample down to a fine cohesive state and elimate segregation. 

If the stress is applied normal to the layers, the stress is constant and the strain on the individual sub-phase is different. Applied stress will bias segmental motion of paraffinic chains in the direction parallel to the chain axis. Alternatively, if the stress is applied parallel to the layers, a constant strain is induced in each sub-phase. Applied strain will deform paraffinic segments in the direction normal to the chain axis. The splitting of the yj-peak in the quenched samples of HTH-Cjo polyester into two separate loss peaks could then reflect the different response to the series (yu) and parallel (ym) models to an applied external stress. 

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