TECH Brief 16 – Application of ANOVA and Bonferroni Post hoc T-tests in Data Comparison

In establishing the final purchase price, mining companies supplying chromite concentrate to buyers will typically have a sample of the concentrate analysed by a referee laboratory to confirm the Cr2O3 content. The sample taken is also analysed by the mine laboratory for comparison with the analysis result obtained by the referee laboratory, and often two or three additional laboratories may also participate. As there is uncertainty in all analytical measurements, it would be expected that there would be differences in the means on a sample analysed by the different laboratories. Typically, the result of the referee laboratory is taken as the value of the consignment, and the mining company pays penalties on any differences. This approach is very subjective and could result in the mine paying unnecessary penalties and losing valuable revenue. This is because a valid decision cannot be made based on a single result alone and all analysis is conducted to make an informed decision. Therefore, an objective statistical test is needed to determine if all the means are statistically different, or some are different, or none are different.