By William K. Fletcher

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2) Each bulk sample was then ground for 12 hours in an aluminium oxide ceramic-lined mill with ceramic balls untill 97% of every sample would pass a 325-mesh (44 μπι) screen. During grinding frictional heating to 80—90°C may have caused partial loss of volatile elements and contamination by alumina resulted from wear of the ball mill. (3) Bulk samples were then divided between 45-kg drums and 80-g bottles filled from each drum, each bottle being assigned a random number. To test sample homogeneity an analysis of variance model, described in detail by Allcott and Lakin (1975), was used to establish variance between drums, within layers within drums, between bottles within layers and between determinations within drums.

Two types of errors contribute to unreliability of an analytical result: >u C. p _ x ' JA D. CONCENTRATION p _ x " ► Fig. 2-1. Random and systematic errors. The variation in concentration caused by random errors is represented by the normal curve with an average value X: μ is the true concentration of the analyte. A. e. X = μ and results are both accurate and precise. B. The dispersion is greater but still symmetrical about μ — precision is therefore relatively poor and although the average value (X) is accurate, this is not necessarily true of individual analyses.

By including duplicates or replicates at appropriate stages in the analysis the necessary estimates can be made from an analysis of variance. As a simple example Table 2-II tabulates results of duplicate (; = 2) analyses of a sample in each of six (i = 6) batches. We wish to evaluate the possibility that errors between the batches are significantly greater than those within batches. 81. then: SSB «-s and Sw = SSW N-k where k is the number of batches (/), n the number of replications (;) and N the total number of analyses: C is the overall average concentration and C, the average of the n replications on the ith batch.

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