On the special application of Thompson–Howarth error analysis to geochemical variables exhibiting a nugget effect

Abstract

Thompson–Howarth error analysis is based on the assumption that measurement error is normally distributed. As a result, geochemical variables that are not normally distributed, such as those containing rare nuggets, cannot be statistically evaluated using Thompson–Howarth error analysis unless a modification to the procedure, involving use of the group root mean square (RMS) standard deviations, is implemented that makes it independent of the normality assumption. This modification prevents samples exhibiting a positively skewed error distribution, such as that produced by a ‘nugget effect’, from having their measurement errors underestimated (biased) using conventional Thompson–Howarth error analysis. A consequence of the duplicate error analysis of ‘nuggety’ samples is that the maximum feasible relative error (of 141.2%; one standard deviation divided by the mean) may be observed in some samples. Maximum feasible relative errors for n replicates are equal to √ n . Maximum relative errors may be observed because Poisson probabilities of obtaining zero nuggets in one duplicate and one or several nuggets in another are not negligible, and thus very large grade disparities can be obtained in duplicate samples simply due to natural sampling variability. As a result, an abundance of samples exhibiting this maximum relative error is not necessarily an analytical or sample numbering error, but rather an expected consequence of sampling geological materials exhibiting large nugget effects, and may reflect relative measurement error that is larger than the maximum exhibited by duplicate samples. Consequently, if a large number of duplicate samples exhibit relative errors close to the maximum, it is likely that Thompson–Howarth error analysis of duplicate samples will underestimate the actual relative error in the data. As a result, replicate samples (where n >2) that have higher maximum relative error limits should be used to ensure that relative error estimates derived from such a Thompson–Howarth error analysis are not biased low (underestimated).